Color prediction and color matching method and apparatus with improved accuracy

Abstract

The present invention relates to a method and apparatus for determining correction terms of a color prediction model to allow reliable color prediction and color matching operations using input data determined under different physical conditions than color data associated with a reference coating used as a standard. The present invention further relates to a color prediction and color matching method and apparatus exhibiting improved accuracy due to the use of correction terms determined according to the present disclosure.

Description

Technical Field

[0001] The present invention relates to a computer-implemented method for providing a correction term for a color prediction model, a computer-implemented method and apparatus for determining the color of an adjusted sample coating present under a second physical condition based on color data of an adjusted sample coating present under a first physical condition, a computer-implemented method and apparatus for determining a second adjusted sample coating formulation to match the color of a reference coating present under a second physical condition based on color data of a first adjusted sample coating present under a first physical condition, the use of a correction term determined by the method of the present invention, and a computer program element. Background Art

[0002] This disclosure generally relates to color prediction and color matching methods and apparatus, such as computer-aided color prediction and color matching methods.

[0003] Color adjustment of a sample coating formulation to match the color of a reference coating is an iterative process. Starting from a preliminary sample coating formulation, it is usually necessary to adjust the preliminary sample coating formulation several times until the color of the adjusted sample coating is found to be sufficiently matched to the color of the reference coating, which makes the color adjustment process time-consuming and expensive.

[0004] To reduce the time and cost associated with color adjustment, computer-aided color prediction and color matching methods based on physical models that describe the interaction of light with a scattering or absorbing medium (e.g., colorants or pigments present in a coating) are currently used. The physical model is capable of predicting the light reflection properties (e.g., color data) of a coating based on information about the formulation of the coating material used to prepare the corresponding coating and optical constants that describe the absorption and scattering properties of the formulation components (such as colorants or pigments) in the context of the corresponding physical model. The specific optical properties of the colorant can be determined based on a coating present under defined physical conditions (such as under dry physical conditions (e.g., being dried and / or cured) or wet physical conditions (e.g., not being dried and cured)) according to known coating formulation data and measured coating reflectance data. Thus, color prediction and color matching methods using the physical model and optical constants are always associated with the physical conditions of the coating used to determine the optical constants.

[0005] However, the color tolerance of the reference coating is defined for specific physical conditions of the reference coating (such as a dry state (e.g., dried and / or cured)), while the resulting sample coating material may exist under different physical conditions (such as a wet condition (e.g., not dried and cured)). Using data of a sample coating that exists under physical conditions different from those of the reference coating for color prediction and color matching methods using the physical model and optical constants typically results in high inaccuracies because the optical properties of the coating (such as reflection properties) highly depend on the physical conditions of the coating, e.g., whether the coating exists under wet or dry conditions, or the application process used to apply the coating material to the substrate.

[0006] Due to such high inaccuracies, the color of each adjusted coating associated with each adjusted sample coating formulation obtained during the color matching process still has to be measured under the same physical conditions as those of the reference coating. Thus, for example, if color data of a reference coating that exists in a dry state is to be used for comparison, each adjusted sample coating formulation has to be applied to a substrate using the same application process as that of the reference coating and dried and / or cured to obtain the same physical conditions before determining the color data of the adjusted sample coating.

[0007] Accordingly, there is a need to provide color prediction and color matching methods that produce more accurate results, thereby avoiding the preparation of cured adjusted sample coatings after each adjustment of the sample coating formulation during the color matching operation.

[0008] Accordingly, an object of the present disclosure is to provide color prediction and color matching methods and apparatuses that produce more accurate color prediction and color matching results, for example, when using data of a sample coating or an adjusted sample coating that exists under physical conditions different from those of the reference coating in color prediction and / or color matching methods. SUMMARY OF THE INVENTION

[0009] In one aspect, the present disclosure relates to a computer-implemented method for providing a correction term for a color prediction model, the correction term being associated with adjusted sample coatings that exist under at least two different physical conditions, the method comprising:

[0010] - receiving, by at least one processor via a communication interface, a request providing:

[0011] · a color difference (CD1) between the measured color data of the adjusted sample coating that exists under a first physical condition and the predicted color data of the adjusted sample coating that exists under the first physical condition,

[0012] · The color difference (CD2) between the measured color data of the sample coating existing under the second physical condition and the measured color data of the sample coating existing under the first physical condition, where the sample coating is associated with the adjusted sample coating, and

[0013] · The color difference (CD3) between the predicted color data of the adjusted sample coating existing under the second physical condition and the predicted color data of the adjusted sample coating existing under the first physical condition; and

[0014] - In response to the request, using the at least one processor to determine a correction term for the color prediction model using the provided color differences (CD1) to (CD3); and

[0015] - Providing the determined correction term for the color prediction model via a communication interface.

[0016] In another aspect, the present disclosure relates to a computer-implemented method for determining the color of an adjusted sample coating existing under a second physical condition based on color data of the adjusted sample coating existing under a first physical condition, the method comprising:

[0017] - Receiving, by at least one processor via a communication interface, a request providing:

[0018] · The color difference between the measured color data of the sample coating existing under the second physical condition and the predicted color data of the sample coating existing under the second physical condition, where the sample coating is associated with the adjusted sample coating,

[0019] · Optical data of individual color components associated with the first physical condition,

[0020] · Adjusted sample coating data, where the adjusted sample coating data includes the formulation of the adjusted sample coating,

[0021] · Condition adaptation parameters associated with the difference between the first and second physical conditions of the adjusted sample coating,

[0022] · A correction term for the color prediction model determined according to the computer-implemented method for providing a correction term for the color prediction model disclosed herein,

[0023] · A color prediction model configured to predict the color of the adjusted sample coating existing under the second physical condition by using the color difference, the optical data of the individual color components, these condition adaptation parameters, the adjusted sample coating data, and the correction term as input data; and

[0024] - In response to the received request, using the at least one processor, use the color prediction model and the data provided in step (a) to determine the color data of the adjusted sample coating present under the second physical condition; and

[0025] - Provide, via the communication interface, the determined color data of the adjusted sample coating present under the second physical condition.

[0026] In another aspect, the present disclosure relates to a computer-implemented method for determining a second adjusted sample coating formulation to match the color of a reference coating present under a second physical condition based on the color data of a first adjusted sample coating present under a first physical condition, the method comprising:

[0027] - Receive, by at least one processor via a communication interface, a request providing:

[0028] · The color difference between the measured color data of a sample coating present under the second physical condition and the predicted color data of the sample coating present under the second physical condition, the sample coating being associated with the first adjusted sample coating,

[0029] · Optical data of individual color components associated with the first physical condition,

[0030] · Reference coating data, the reference coating data including the color data of the reference coating present under the second physical condition,

[0031] · First adjusted sample coating data, the first adjusted sample coating data including the formulation of the first adjusted sample coating,

[0032] · Condition adaptation parameters associated with the difference between the first physical condition and the second physical condition of the first adjusted sample coating,

[0033] · A correction term for the color prediction model determined according to the computer-implemented method for providing a correction term for the color prediction model disclosed herein,

[0034] · A color prediction model configured to predict the color of the second adjusted sample coating present under the second physical condition by using the color difference, the optical data of the individual color components, the reference coating data, the first adjusted sample coating data, these condition adaptation parameters, and the correction term as input data; and

[0035] - In response to the request, use the at least one processor to use the color prediction model and the data provided in step (a) to determine the second adjusted sample coating formulation; and

[0036] -Provide the determined second adjusted sample coating formulation via the communication interface.

[0037] In yet another aspect, the present disclosure relates to an apparatus comprising: one or more computing nodes; and one or more computer-readable media having computer-executable instructions that, when executed by the one or more computing nodes, cause the apparatus to perform the computer-implemented methods disclosed herein.

[0038] In yet another aspect, the present disclosure relates to the use of correction terms determined according to the computer-implemented methods disclosed herein to improve the accuracy of color data of an adjusted sample coating present under a second physical condition, the color data being predicted by a color prediction model based on the color data of the adjusted sample coating present under a first physical condition.

[0039] In yet another aspect, the present disclosure relates to a computer program element, such as a computer-readable storage medium, a computer program, or a computer program product, comprising instructions that, when executed by one or more computing nodes or a computing system, cause the (one or more) computing nodes or the computing system to perform the steps of the computer-implemented methods disclosed herein.

[0040] In yet another aspect, the present disclosure relates to a computer program element, such as a computer-readable storage medium, a computer program, or a computer program product, comprising instructions that, when executed by the apparatus disclosed herein, cause the apparatus to perform the steps that the apparatus is configured to perform.

[0041] Any disclosure and embodiment described herein relate to the methods, apparatuses, and computer program elements listed above and below, and vice versa. Advantageously, the benefits provided by any embodiment and example apply equally to all other embodiments and examples, and vice versa.

[0042] The methods, apparatuses, and computer program elements of the present disclosure allow for more accurate prediction of the optical properties (such as color) of an adjusted sample coating formulation (e.g., a sample coating formulation that has been adapted at least once (e.g., by coloring at least one produced batch of the sample coating formulation)) present under a first physical condition (such as a dry state (e.g., dried and / or cured)) based on optical property data (such as color data) of the adjusted sample coating present under a second physical condition (such as a wet state (e.g., not dried and cured)). Thus, for example, the predicted color of the adjusted sample coating present in the dry state more accurately matches the color of a reference coating present in the dry state, even if the prediction is based on data of the adjusted sample coating present in the wet state, and vice versa.

[0043] This also applies to the color matching methods of the present disclosure, which allow for a more accurate calculation of the adjusted formulation of a sample coating to match the optical properties of a reference coating present under a first physical condition (such as a dry state) based on data associated with the sample coating or a previous adjustment of the sample coating present under a second physical condition (such as a wet state), and vice versa.

[0044] The accuracy of the color prediction and color matching methods of the present disclosure is improved by determining correction terms for the physical models used in color prediction and / or color matching operations. The correction terms transform the systematic error of the physical model for a second condition (such as a wet state) to the systematic error of the physical model for a first physical condition (such as a dry state), and vice versa. Transforming the systematic error from the physical condition of the sample coating or the adjusted sample coating to the corresponding physical condition of the reference coating allows for consideration of the strong influence of the physical condition of the respective coating on its optical properties (such as reflection properties), thus significantly improving the prediction and matching results.

[0045] The significantly improved prediction and matching results allow for a reduction in the amount of coated substrates (hereinafter also referred to as ejecta) that must be prepared during color matching operations to ensure that the adjusted sample coating formulation produces optical properties within a given tolerance associated with the reference coating. The reduction in the required amount of ejecta saves costs and allows for an increase in the efficiency of the coating material production process. In addition, the reduction in the amount of ejecta improves the reproducibility of the optical properties of the adjusted sample coating, as the influence of the preparation of the ejecta on the optical properties of the resulting coating is avoided.

[0046] Furthermore, the color prediction and color matching methods according to the present disclosure allow for the automation of the coloring process in coating material production, where the batches produced typically need to be colored to ensure sufficient color matching with the corresponding reference coating. Since the coating material produced is typically in a wet state, the coloring process is also performed in the wet state. Accurately predicting the necessary coloring of the batches of coating material produced using the color prediction and color matching methods according to the present disclosure allows for a significant increase in production efficiency by reducing or avoiding the preparation of ejecta to ensure a sufficient degree of color matching between the batches of coating material produced and the reference coating, thereby reducing the costs and time associated with producing the colored coating material. Examples

[0047] Hereinafter, the terms used herein and / or the technical field of the present disclosure will be outlined by way of examples and / or illustrations. In the case of examples being given, it should be understood that the present disclosure is not limited to the examples. All terms and definitions used herein are to be understood in a broad sense and have their general meaning.

[0048] In an embodiment, a correction term may refer to a term introduced into a physical model (such as a color prediction model), which is necessary for making the result obtained with the physical model consistent with the measurement result.

[0049] In an embodiment, a color prediction model may refer to a deterministic model based on physical laws, which is configured to predict color data of a coating. The color prediction model may be based on, for example, physical laws describing the light absorption and light scattering properties of a coloring system (such as a colored coating).

[0050] In an embodiment, a coating may refer to a complete layer of a coating material to be applied or already applied to a substrate. The coating may be characterized in more detail according to different criteria, such as the type of coating material (paint, varnish, powder coating) or the type of application process (painting, spraying, dip coating, casting coating, filler coating, etc.). The one or more coatings may be prepared by applying the corresponding coating material to the substrate (for example, by using one of the above application processes). After application, the coating material may form a continuous layer (such as a coating film) on the substrate, and the continuous film may be dried and / or cured. If more than one coating material is applied to the substrate, each applied coating material may be dried and cured separately, or curing may be performed jointly, for example, after at least two coating materials have been applied and optionally dried.

[0051] In an embodiment, a reference coating may refer to a coating having defined properties (such as defined chromaticity properties). The reference coating may be prepared by applying at least one defined coating material (such as a reference coating material) to a surface using a defined application process and drying and / or curing the applied coating material. At least one of the defined coating materials may contain at least one colorant.

[0052] In an embodiment, a sample coating may refer to a coating that is evaluated in terms of at least one defined property (such as chromaticity property) compared to a reference coating. The sample coating may be prepared as described for the reference coating, for example, by using a corresponding sample coating material.

[0053] In one embodiment, an adjusted sample coating may refer to a sample coating in which at least one component present within the sample coating formulation (e.g., an unmodified sample coating formulation) has been modified at least once, e.g., by modifying the amount and / or type of the component. The sample coating used as a basis for preparing the adjusted sample coating may be referred to as the "sample coating associated with the adjusted sample coating". To indicate the number of adjustments relative to the sample coating, consecutive numbers may be used in combination with the term "adjusted sample coating". For example, a first adjusted sample coating may refer to the first adjustment of the sample coating formulation, while the term second adjusted sample coating may refer to the second adjustment of the sample coating formulation, and so on. The terms "formulation", "color formulation", and "paint formulation" are used synonymously herein.

[0054] In one embodiment, the physical condition may refer to the state of the respective coating (such as the adjusted sample coatings of a reference coating, a sample coating, a first adjusted sample coating, and a second adjusted sample coating). The state may be a wet state or a dry state. The wet state may represent the state in which the respective coating has not been dried and / or cured (e.g., by using an elevated temperature). Thus, the wet state may represent the produced coating material (e.g., present within the measuring unit), and the dry state may represent the dried and / or cured state of the coating produced from the respective coating material. The dried state may refer to the state of the coating after the evaporation of the organic solvent and / or water present in the coating material or film after the coating material has been applied to the substrate. Drying may be performed, for example, at 15 °C to 35 °C and / or at an elevated temperature of, for example, 40 °C to 90 °C. Although the coating material is at least directly free-flowing after application and can form a uniform and smooth coating film by leveling, drying the formed coating film causes the film to no longer be free-flowing. However, the formed coating is still soft and / or sticky, and its properties (such as hardness or adhesion to the substrate) do undergo further significant changes upon further exposure to curing conditions as described below. The cured state may refer to the state of the coating in which its properties (such as hardness or adhesion to the substrate) do not undergo any further significant changes when further exposed to curing conditions (such as an elevated temperature (e.g., 80 °C to 200 °C)) for a period of 10 to 60 minutes. Compared with the dried coating, the cured coating is no longer soft or sticky but has been conditioned to a solid coating. This state may also be a state associated with a specific application process (such as spraying, roll coating, brush coating, spin coating, etc.).

[0055] In one embodiment, the application process may refer to applying a coating material to a substrate. Applying the coating material to the substrate may further include post-treating the applied coating material, such as by drying and / or curing at an elevated temperature and / or for an extended duration. Applying the coating material to the substrate may be carried out by various methods known in the prior art (such as spraying, dip coating, roll coating, spin coating, electrocoating, etc.).

[0056] In one embodiment, an individual color component may refer to an individual component present in a coating material formulation (such as a sample coating formulation, a reference coating formulation, or an adjusted sample coating formulation). Examples of individual color components include pigments (such as colored pigments and effect pigments), binders, solvents, and additives (such as matting agents).

[0057] In one embodiment, the optical data of an individual color component may refer to the optical properties and / or specific optical constants of the individual color component. The optical constants of an individual color component are parameters in a physical model, and these parameters can be determined by preparing a coating using a defined batch of pigment paste and determining the optical properties (such as by measuring the reflection spectrum of the prepared coating using a spectrophotometer). Based on the reflection spectrum and the corresponding formulation data, specific optical properties, such as the K / S constant, can be determined and assigned as optical data to the corresponding individual color component. The terms "optical data of individual color components" or "optical data of the individual color components" are used synonymously with "optical data of colorants".

[0058] In one embodiment, the systematic error of a color prediction model can refer to the limitations of a physical model and / or the systematic error within the optical data of individual color components included in a corresponding coating formulation. The systematic error within the optical data of individual color components may be caused by differences in the colorant strength characteristics of pigment slurries, as these characteristics vary between batches due to deviations in the raw materials (such as pigments) used to prepare the pigment slurries. In one example, the systematic error of a color prediction model can represent the difference between the color data of a coating predicted by the color prediction model and the measured color data of the coating. In another example, the systematic error can represent the difference between the color data of a coating / coating material predicted by the color prediction model for a first physical condition and the color data of the coating / coating material predicted by the color prediction model for a second physical condition. The systematic error of the color prediction model can be adjusted by considering the systematic error associated with the color prediction of a sample coating or a previous adjustment of the sample coating (e.g., a previous systematic error). The systematic error can be considered, for example, by adding the previous systematic error to the predicted color of the corresponding adjusted sample coating. For example, if the systematic error associated with the color prediction of an adjusted sample coating is to be adjusted, the systematic error associated with the sample coating used to prepare the adjusted sample coating (e.g., the difference between the measured sample coating color data and the predicted sample coating color data) is considered, for example, by adding the systematic error to the predicted color data of the adjusted sample coating.

[0059] In one embodiment, a condition adaptation parameter may refer to a difference between a first physical condition and a second physical condition, such as a specific transfer function (e.g., a difference between the wet state and the dry state of a corresponding coating or a difference between a first application process and a second application process). The condition adaptation parameter may include differences associated with pigments, differences associated with different physical conditions, and / or differences associated with appearance changes when physical conditions are changed. Differences associated with pigments may include effect flake orientation adaptation, effectiveness of color pigments, and / or effectiveness of effect pigments. Effect flake orientation adaptation may allow for consideration of better or worse flake orientation in an effect coating (e.g., a coating including at least one coating containing an effect pigment) and may be used to adjust their brightness transition / color transition behavior. The effectiveness of color pigments may allow for consideration of differences in the coloring intensity of solid colorants adjusted more or less effectively by color pigments, which may be caused, for example, by shear effects or by agglomerates. The effectiveness of effect colorants may allow for consideration of differences in the reflection ability of effect pigments adjusted more or less effectively by effect colorants, which may be caused, for example, by overspray loss or sedimentation or leaving effects. Differences associated with different physical conditions may include light loss adaptation of the coating material present in a cuvette or a measurement unit under wet conditions and / or a conversion term of the refractive index between different physical conditions (such as wet conditions and dry conditions). Differences associated with appearance changes when physical conditions are changed may include compensation for components having a certain degree of opacity (such as a mixed varnish in the coating material present under wet conditions), and these components become transparent when physical conditions are changed (such as when the coating is dried and / or cured). The condition adaptation parameter may relate to a systematic error of a color prediction model associated with a color prediction of a coating formulation under a first physical condition compared to a color prediction of the coating formulation under a second physical condition. The systematic error may be taken into account, for example, by adding the systematic error to the predicted color of the corresponding coating formulation. For example, if a condition adaptation parameter associated with a color prediction of an adjusted sample coating is to be taken into account, the systematic error may be added to the predicted color data of the adjusted sample coating.

[0060] In an embodiment, a computing node may refer to any device or system including at least one physical tangible processor and a physical tangible memory capable of having computer-executable instructions executed thereon by the processor. The (one or more) computing nodes may be, for example, a handheld device, a production facility, a sensor, a monitoring system, a control system, an appliance, a laptop computer, a desktop computer, a mainframe, a data center, or even a device not conventionally considered a computing node, such as a wearable device (e.g., glasses, watches, etc.). The memory may take any form and depends on the nature and form of the computing node.

[0061] In an embodiment, a processor may refer to any circuit (such as any logic circuit or quantum circuit) configured to perform basic operations of a computer or system, and / or generally refers to a device configured to perform computing or logical operations. In particular, a processor or computer processor may be configured to process basic instructions that drive a computer or system. A processor may be a semiconductor-based processor, a quantum processor, or any other type of processor configured to process instructions. As an example, a processor may be or may include a central processing unit (“CPU”). A processor may be a graphics processing unit (“GPU”), a tensor processing unit (“TPU”), a complex instruction set computing microprocessor (“CISC”), a reduced instruction set computing (“RISC”) microprocessor, a very long instruction word (“VLIW”) microprocessor, or one processor implementing other instruction sets or multiple processors implementing a combination of instruction sets. The processing device may also be one or more dedicated processing devices, such as an application specific integrated circuit (“ASIC”), a field programmable gate array (“FPGA”), a complex programmable logic device (“CPLD”), a digital signal processor (“DSP”), a network processor, etc. The methods, systems, and devices described herein may be implemented as software in a DSP, a microcontroller, or any other auxiliary processor, or as hardware circuits within an ASIC, CPLD, or FPGA. It should be understood that the term processor may also refer to one or more processing devices, such as a distributed processing device system located on multiple computer systems (e.g., cloud computing), and is not limited to a single device, unless otherwise specified.

[0062] In an embodiment, the memory or data storage medium may refer to a physical system memory, which may be volatile, non-volatile, or a combination thereof. The memory may include non-volatile mass storage, such as a physical storage medium. The memory may be a computer-readable storage medium (such as RAM, ROM, EEPROM, CD-ROM) or other optical disc storage, magnetic disk storage, or other magnetic storage device, non-disk storage (such as a solid state drive) or any other physical tangible storage medium that can be used to store desired program code means in the form of computer-executable instructions or data structures and can be accessed by a computing system. Additionally, the memory may be a computer-readable medium (also referred to as a transmission medium) that carries computer-executable instructions. Further, after reaching various computing system components, program code means in the form of computer-executable instructions or data structures can be automatically transferred from the transmission medium to the storage medium (and vice versa). For example, computer-executable instructions or data structures received over a network or data link may be buffered in RAM within a network interface module (e.g., “NIC”) and then ultimately transferred to the computing system RAM and / or a less volatile storage medium at the computing system. Thus, it should be understood that the storage medium can include within computing components that also (or even primarily) utilize the transmission medium.

[0063] In an embodiment, the computer-readable program instructions for performing the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state-setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages (such as Java, Smalltalk, C++) and traditional procedural programming languages (such as the "C" programming language or similar programming languages). The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, executed as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer may be connected to the user's computer through any type of network (including a local area network (LAN) or a wide area network (WAN)), or may be connected to an external computer (e.g., using an Internet service provider via the Internet). In some embodiments, an electronic circuit including, for example, a programmable logic circuit, a field-programmable gate array (FPGA), or a programmable logic array (PLA) may execute the computer-readable program instructions by utilizing the state information of the computer-readable program instructions to personalize the electronic circuit, thereby performing aspects of the present invention. In an embodiment, the computer-readable program instructions may be downloaded from a computer-readable storage medium to a corresponding computing / processing device via a network (e.g., the Internet, a local area network, a wide area network, and / or a wireless network), or downloaded to an external computer or an external storage device. The network may include copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device may receive the computer-readable program instructions from the network and may forward the computer-readable program instructions to be stored in a computer-readable storage medium within the corresponding computing / processing device.

[0064] In an embodiment, a communication interface may refer to a software and / or hardware interface for establishing communication (such as transmitting or exchanging or signaling or data). The software interface may be, for example, a function call, an API. The communication interface may include a transceiver and / or a receiver. The communication may be wired or wireless. The communication interface may be based on or support one or more communication protocols. The communication protocol may be a wireless protocol, for example: a short-range communication protocol, such as or WiFi; or a long-range communication protocol, such as a cellular or mobile network, for example, a second-generation cellular network ("2G"), 3G, 4G, Long Term Evolution ("LTE"), or 5G. Alternatively or additionally, the communication interface may even be based on a proprietary short-range or long-range protocol. The communication interface may support any one or more standards and / or proprietary protocols.

[0065] In one embodiment, a database may refer to a collection of relevant information that can be searched and retrieved. The database may be a searchable electronic document (such as a digital, alphanumeric, or text document), a searchable PDF document, or a Microsoft spreadsheet; or a database known in the prior art. The database may be a set of electronic documents, photos, images, charts, data, or drawings residing on a computer-readable storage medium that can be searched and retrieved. The database may be a single database or a set of related databases or a set of unrelated databases. Related databases may include databases that contain at least one common information element in the related databases that can be used to associate these databases.

[0066] The paint production process for a given color typically starts with an initial coating material formulation or a sample coating material formulation (e.g., a formulation loaded from a database). Then, based on this initial coating material formulation, an initial batch of coating material is manufactured by adding at least one pigment paste (also referred to hereinafter as a colorant) to a base varnish containing a binder, a solvent, and optionally additives. The pigment paste is an intermediate product that contains a color-imparting component (such as a pigment) in a matrix (usually a binder, a solvent, and optionally additives). Compared to the final coating material formulation, the initial coating material formulation typically contains a reduced amount of color-imparting components to avoid making the produced batch of coating material too dark due to the use of too high an amount of (multiple) color-imparting components. After production, the corresponding color data of the produced batch of coating material is measured under the same physical conditions as the reference coating, and compared with the color data of the reference coating that exists under the defined physical conditions (such as in the dry state) or has been produced by the defined application method (such as spray application). Instead of measuring the color data of the produced batch, the color data of a previously produced batch of the same coating material can be used for comparison with the reference coating, provided that the color deviation between different batches is assumed to be low. Due to the reduced amount of color-imparting components, the produced batch of coating material typically has a significant residual color difference compared to the reference coating. Therefore, the initial coating material formulation must be modified in a subsequent color adjustment process such that the residual color difference between the adjusted sample coating and the color data of the reference coating is below the defined threshold.

[0067] A color prediction model can be used to calculate the adjusted sample coating formulation from the sample coating formulation and the color data of the sample coating and the reference coating. However, the color data of the adjusted sample coating that exists in the wet state is significantly different from the color data of the adjusted sample coating that exists in the dry state. This also applies to using different application processes to apply the adjusted sample coating material to a substrate, for example, using spray application compared to roll application.

[0068] Due to the significant influence of physical conditions on color data, using color data of an adjusted sample coating that exists under physical conditions different from those of a reference coating (e.g., using color data obtained in a wet state after adjusting the produced batch of sample coatings) during color prediction or color adjustment processes generally results in a significant deviation between the color data of the adjusted sample coating predicted for the physical conditions associated with the reference coating and the color data of the adjusted sample coating measured for the physical conditions associated with the reference coating. Therefore, an adjusted sample coating that matches the physical conditions associated with the reference coating typically has to be prepared from the adjusted sample coating material, and the color data of the prepared adjusted sample coating has to be determined and compared with the color data of the reference coating to ensure a sufficient degree of color matching. However, this procedure is time-consuming, associated with high costs, and increases the production time of batches of colored coating materials.

[0069] Accordingly, there is a high desire to provide methods and apparatuses that produce more accurate color prediction and color matching results when using data of a sample coating or an adjusted sample coating that exists under physical conditions different from those of a reference coating for color prediction and / or color matching. Such methods and apparatuses would reduce or avoid the preparation of an adjusted sample coating that matches the physical conditions associated with the reference coating to ensure sufficient color matching.

[0070] These and other objects are solved by the subject matter of the independent claims, which will become apparent when reading the following description. The dependent claims relate to embodiments of the present disclosure.

[0071] In an embodiment, a color prediction model is configured to predict color data of a coating based on input data that includes coating formulation data and optical data of individual color components. The coating formulation data may include data on the components present in the coating material used to prepare the coating and the amounts of those components. The data on the components can be used to determine the corresponding optical data of the individual color components to be used for predicting the color data. Such color prediction models are well known in the prior art, for example as described in Georg A. Klein; Farbenphysik für industrielle Anwendungen; Chapter 7 - Farbrezept - Berechnung, June 2004.

[0072] The optical data of the individual color components may include the optical constants of these individual color components, such as their wavelength - dependent scattering and absorption properties. The optical constants may further include the orientation of individual color components (such as effect pigments) within the coating.

[0073] In an embodiment, the correction term includes the systematic error of the color prediction model when predicting the color data of the adjusted sample coating present under the second physical condition based on the input data associated with the adjusted sample coating present under the first physical condition. The systematic error may be caused by the fact that the physical condition of the coating significantly affects the color and thus the color data, as previously described. The correction term can be taken into account, for example, by adding the correction term to the color of the corresponding coating formulation predicted by the color prediction model based on the input data.

[0074] When using the input data associated with the second physical condition to predict the color data of the first physical condition or vice versa, the dependence of the color data on the physical condition may result in a strong deviation between the predicted color data and the observed color data. The correction term can be used to at least partially correct the difference in color data caused by using different physical conditions, such that when the correction term is used, the color data predicted by the color prediction model for the physical condition is more accurate than without the correction term. Thus, the correction term can allow for an improvement in the accuracy of the color data predicted by the color prediction model, even if the input data is associated with a physical condition different from the "target coating" or reference coating. For example, when using data associated with the adjusted sample coating present under wet conditions as input, the use of the correction term can allow for a more accurate prediction of the color data of the adjusted sample coating present under dry conditions. This may result in fewer coatings having to be prepared from the adjusted sample coating material to allow for sufficiently correct calculations for further adjustment of the adjusted sample coating (such as further adjustment of the formulation) such that the color of the coating produced from the further adjusted sample coating material sufficiently matches the color of the reference coating used for comparison.

[0075] In an embodiment, the first physical condition includes a wet state or a physical condition associated with a first application process. The first application process can be an application process generally used to apply a coating material to at least a portion of the surface of a substrate. Suitable application processes include, for example, dipping, bar coating, spraying or roll coating. Spraying can include spray application methods such as compressed air spraying (pneumatic application), airless spraying, high-speed rotation, electrostatic spray application (ESTA), optionally associated with thermal spray application (such as hot air spraying).

[0076] In an embodiment, the second physical condition includes a dry state or a physical condition associated with a second application process. The second application process is different from the first application process. For example, the first application process can be a bar coating or dipping process, and the second application process can be a spraying process, and vice versa.

[0077] In an embodiment, the color data includes: reflectance data; color space data, such as CIEL*a*b* values or CIEL*C*h* values; glossiness data; texture parameters, such as texture characteristics and / or roughness characteristics; or a combination thereof. A multi-angle spectrometer can be used to determine the color data, such as the reflectance data. The color space data (e.g., CIEL*a*b* values) can be calculated from the acquired reflectance data and the radiation function of the light source (see, for example, ASTM E2194-14(2017) and ASTM E2539-14(2017)). The texture parameters can be determined based on texture images acquired under defined light conditions and at defined angles. The texture parameters can be calculated based on the acquired images. Examples of such calculated texture parameters include the texture value Gdiff or Gdiff (so-called graininess or roughness or roughness value or roughness characteristic) that describes the roughness characteristics of the coating under diffuse illumination conditions, Si (flash intensity), and Sa (flash area) that describes the flash characteristics of the coating under directional illumination conditions, as introduced by Byk-Gardner (“Den Gesamtfarbeindruck objektivmessen”, Byk-Gardner, JOT 1.2009, Vol. 49, No. 1, pp. 50-52). The texture parameters introduced by Byk-Gardner are determined from grayscale images. It is also possible to determine the texture parameters from color images, as introduced, for example, by X-Rite with the MA-T6 or MA-T12 multi-angle spectrophotometer.

[0078] In an embodiment, providing the predicted color data of the adjusted sample coating present under the first physical condition includes

[0079] - receiving model input data, the model input data including adjusted sample coating formulation data and optical data of individual color components associated with the first physical condition,

[0080] - receiving a color prediction model, the color prediction model being configured to use the coating formulation data and the optical data of individual color components to predict the color data of the coating,

[0081] - using the received color prediction model and the received model input data to predict the color data.

[0082] Model input data can be received via a communication interface. The model input data can be stored on a data storage medium (such as a database) and can be retrieved by the at least one processor based on data associated with the adjusted sample coating (such as the ID of the adjusted sample coating). The adjusted sample coating formulation data can include data on the components present in the adjusted sample coating material and the amounts of the components. The optical data can be retrieved from the data storage medium based on the components present in the adjusted sample coating formulation.

[0083] The color prediction model can use the formulation data and the optical data associated with the components present in the adjusted sample coating material to predict the color data associated with the adjusted sample coating material. The predicted color data can be associated with a first physical condition because the optical data used for color prediction is also associated with the first physical condition. For example, if the optical data is associated with a wet condition (i.e., the data has been determined from a coating present under wet conditions), then the color data predicted by the color prediction model is also associated with the wet condition, i.e., the color prediction model predicts the color data of the adjusted sample coating present under wet conditions. The predicted color data can be reflectance data. The predicted color data can be color space data, such as CIEL*a*b* values or CIEL*C*H* values.

[0084] Providing the predicted color data of the adjusted sample coating present under the first physical condition can further include taking into account the systematic error of the color prediction model associated with the first physical condition. During color prediction performed by the color prediction model, the systematic error of the color prediction model can be considered a constant. Taking into account the systematic error of the color prediction model can allow for an improvement in the accuracy of the predicted color data.

[0085] The systematic error of the color prediction model associated with the first physical condition can be obtained by determining the difference between:

[0086] - the measured color data of the sample coating present under the first physical condition, and

[0087] - the predicted color data of the sample coating present under the first physical condition.

[0088] The measured color data of the sample coating present under the first physical condition can be obtained by preparing a sample coating from the corresponding sample coating material and measuring the color data of the prepared sample coating (e.g., using a multi-angle spectrophotometer as previously described).

[0089] The color prediction model mentioned previously, along with the sample coating formulation and the optical data associated with the first physical condition, can be used as input data for the color prediction model to predict the color data of the sample coating present under the first physical condition. The predicted color data of the sample coating can then be compared with the measured color data of the sample coating present under the first physical condition. For example, the color data of the sample coating can be measured under wet conditions. Suitable measurement methods can include using a measurement unit for liquid sample coating materials (such as a glass cuvette or a glass plate).

[0090] The systematic error associated with the first physical condition for the color prediction model can be obtained by determining the difference between:

[0091] - the measured color data of the adjusted sample coating present under the first physical condition, and

[0092] - the predicted color data of the adjusted sample coating present under the first physical condition.

[0093] The measured color data of the adjusted sample coating can be determined as previously described. As previously described, the color prediction model, the adjusted sample coating formulation data, and the optical data can be used to predict the color data of the adjusted sample coating.

[0094] In an embodiment, providing the predicted color data of the adjusted sample coating present under the second physical condition includes

[0095] - receiving model input data, which includes adjusted sample coating formulation data and optical data of individual color components associated with the second physical condition, or includes adjusted sample coating formulation data, optical data of individual color components associated with the first physical condition, and a condition adaptation parameter associated with the difference between the first physical condition and the second physical condition of the sample coating,

[0096] - receiving a color prediction model configured to predict the color data of a coating using coating formulation data, optical data of individual color components, and optionally a condition adaptation parameter,

[0097] - using the received color prediction model and the received model input data to predict the color data.

[0098] As previously described, model input data can be received via a communication interface. For example, adjusted sample coating formulation data can be stored on a data storage medium and retrieved by the at least one processor based on data associated with the adjusted sample coating, such as the ID of the adjusted sample coating. The adjusted sample coating formulation data can include data regarding the components present within the adjusted sample coating material and the amounts of the components. Optical data can be retrieved from the data storage medium based on the components present in the adjusted sample coating formulation.

[0099] The optical data can be associated with a second physical condition, such as a dry state. In such a case, the color prediction model can use the formulation data and the optical data associated with the components present within the adjusted sample coating material to predict color data associated with the adjusted sample coating material present in the dry state. The predicted color data can be associated with the second condition because the optical data used for color prediction is also associated with the second condition. The predicted color data can be reflectance data. The predicted color data can be color space data, such as CIEL*a*b* values or CIEL*C*H* values.

[0100] The optical data can be associated with a first physical condition, such as a wet state. In such a case, condition adaptation parameters can be used to adapt the color prediction performed by the color prediction model using the optical data associated with the wet state to the dry state. This can allow the same optical data to be used regardless of the physical condition under which the color prediction is performed, thereby reducing the amount of samples that need to be prepared to determine the optical data and the amount of data that needs to be acquired and processed to determine the optical data.

[0101] The condition adaptation parameters can be pre-configured (i.e., predefined) and / or can be calculated based on sample coating input data using a method configured to optimize the condition adaptation parameters by starting from a given set of initial condition adaptation parameters and minimizing a cost function, as well as a color prediction model configured to predict color data of a sample coating present in the first physical condition using the formulation of the sample coating, optical data of individual color components associated with the first physical condition, and the condition adaptation parameters generated by the method as input data. The color prediction model can be the previously described color prediction model. The condition adaptation parameters determined for the sample coating can correspond to the condition adaptation parameters associated with the adjusted sample coating. This allows the condition adaptation parameters to be determined from data of sample coatings that are readily available, thereby avoiding providing further input data and / or performing further calculations to obtain the input data required to determine the condition adaptation parameters of the adjusted sample coating.

[0102] The cost function may include a color distance between the measured color data of a sample coating present under a second physical condition and the color data of the sample coating predicted using a color prediction model.

[0103] A condition adaptation parameter may be calculated by comparing the recursively predicted color data of a sample coating for a second physical condition with the measured color data of the sample coating until a given cost function drops below a given threshold. This allows determination of the condition adaptation parameter required to consider using optical data associated with a first physical condition when predicting the color data of an adjusted sample coating present under a second physical condition. For example, when predicting the color data of an adjusted sample coating present in a dry state, the condition adaptation parameter may be used to account for the use of optical data associated with a wet condition (i.e., determined from a coating in a wet state).

[0104] Providing the predicted color data of the adjusted sample coating present under the second physical condition may further include accounting for a systematic error of the color prediction model associated with the second physical condition. During use of the color prediction model to predict the color data of an adjusted sample coating present under a second physical condition, the systematic error may be considered constant. The systematic error may be accounted for, for example, by adding the systematic error to the predicted color of the adjusted sample coating present under the second physical condition.

[0105] A systematic error of the color prediction model associated with a second physical condition may be obtained by determining the difference between:

[0106] - the measured color data of a sample coating present under a second physical condition, and

[0107] - the predicted color data of a sample coating present under a second physical condition.

[0108] The measured color data of a sample coating present under a second physical condition may be obtained by preparing a sample coating from a corresponding sample coating material and measuring the color data of the prepared sample coating (e.g., using a multi - angle spectrophotometer as previously described). For example, a sample coating in a dry state may be prepared by applying the sample coating material to a substrate and drying and / or curing the applied sample coating material to obtain a sample coating in a dry state.

[0109] As previously described, a color prediction model may be used to predict the color data of a sample coating present under a second physical condition.

[0110] In an embodiment, a correction term of the color prediction model is determined using the provided color differences (CD1) to (CD3) according to formula (I):

[0111]

[0112] (I). In this formula (I), the numerator of the fraction thus corresponds to the color difference CD2, and the denominator of the fraction thus corresponds to the color difference CD3.

[0113] CD1 in formula (I) can be determined according to formula (Ia):

[0114]

[0115] In an embodiment, the color difference can correspond to the difference between the measured data and / or the predicted data. The color difference can correspond to the color difference (CD1), the color difference (CD2), and / or the color difference (CD3). For example, the color differences (CD1) to (CD3) can be determined using the corresponding color data (such as the measured color data and the predicted color data (e.g., for color differences (CD1) and (CD2)) and / or the predicted color data of the first physical condition and the second physical condition (e.g., for color difference (CD3))).

[0116] In an embodiment, the adjusted sample coating data further includes data indicating the adjusted sample coating, the layer structure of the adjusted sample coating, instructions for preparing the (multiple) adjusted sample coating formulations, price, or a combination thereof. The adjusted sample coating data can be retrieved from a data storage medium. For example, data indicating the adjusted sample coating can be provided to the at least one processor, and the processor uses the received data to retrieve the data. The data indicating the adjusted sample coating can include a color number, a color code, a barcode, a unique database ID associated with the adjusted sample coating, or a combination thereof. The instructions for preparing the (multiple) adjusted sample coating formulations can include mixing instructions.

[0117] In an embodiment, providing the determined color data of the adjusted sample coating present under the second physical condition includes providing the determined color data (optionally combined with additional data) via a communication interface for display. The determined color data can be provided to a display device including a screen. Examples of additional data displayed together with the determined color data can include data contained in the adjusted sample coating data, condition adaptation parameters, correction terms, or a combination thereof.

[0118] The display device can include a housing that houses at least one processor that executes the methods disclosed herein and a screen. The housing can be made of plastic, metal, glass, or a combination thereof.

[0119] The display device and the at least one processor may be configured as separate components, i.e., the display device may include a housing that houses the screen but does not house the at least one processor that performs the steps of the method disclosed herein. Thus, the at least one processor may exist separately from the display device, for example, in another computing device that is connected to the display device via a communication interface to allow data exchange. Using another computer processor that exists outside the display device allows the use of a higher computing power than that provided by the processor of the display device, thereby reducing the computing time required to perform the method disclosed herein and thus reducing the total time until the computed color data is displayed on the screen of the display device. This allows for the immediate display of the computed color data without the need for a display device with high computing power. The other computer processor may be located on a server such that the method disclosed herein may be performed in a cloud computing environment. In this case, the display device may be used as a client device that is connected to the server via a network and is used to provide input data.

[0120] The display device may be a mobile or a fixed display device. Fixed display devices include computer monitors, television screens, projectors, etc. Mobile display devices include laptop computers or handheld devices such as smartphones and tablet computers.

[0121] The screen of the display device can be constructed according to any emissive or reflective display technology with a suitable resolution and color gamut. A suitable resolution is, for example, 72 dots per inch (dpi) or higher, such as 300 dpi, 600 dpi, 1200 dpi, 2400 dpi or higher. This ensures that the generated appearance data can be displayed in high quality. A suitably wide color gamut is the standard red-green-blue (sRGB) or a larger color gamut. In various embodiments, a screen with a color gamut similar to the color gamut perceptible by human vision can be selected. In one aspect, the screen of the display device is constructed according to liquid crystal display (LCD) technology, particularly according to liquid crystal display (LCD) technology further including a touch screen panel. The LCD can be backlit by any suitable light source. However, the color gamut of the LCD screen can be widened or otherwise improved by selecting one or more light-emitting diode (LED) backlights. In another aspect, the screen of the display device is constructed according to light-emitting polymer or organic light-emitting diode (OLED) technology. In yet another aspect, the screen of the display device can be constructed according to reflective display technology (such as electronic paper or ink). Known manufacturers of electronic ink / paper displays include EINK and XEROX. Preferably, the screen of the display device also has a suitably wide viewing field, which allows it to generate images that do not fade or change severely when the user views the screen from different angles. Since LCD screens work with polarized light, some models exhibit a high degree of viewing angle dependence. However, various LCD structures have a relatively wide viewing field and may therefore be preferred. For example, an LCD screen constructed according to thin film transistor (TFT) technology can have a suitably wide viewing field. In addition, screens constructed according to electronic paper / ink and OLED technology may have a wider viewing field than many LCD screens and can therefore be selected.

[0122] The display device can include interaction elements to facilitate user interaction with the display device. The interaction elements can be physical interaction elements, such as input devices or input / output devices, particularly a mouse, keyboard, trackball, touch screen, or a combination thereof. The interaction elements can be used to provide input data or mimic further actions, as described later.

[0123] A color prediction model can be used to determine the color data of an adjusted sample coating present under a second physical condition based on the color data of the adjusted sample coating present under a first physical condition. The color prediction model can receive the following as input data:

[0124] · The color difference between the measured color data of a sample coating present under the second physical condition and the predicted color data of the sample coating present under the second physical condition, the sample coating being associated with the adjusted sample coating,

[0125] ·Optical data of individual color components associated with the first physical condition,

[0126] ·Adjusted sample coating data, which includes the formulation of the adjusted sample coating,

[0127] ·Condition adaptation parameters associated with the difference between the first physical condition and the second physical condition of the adjusted sample coating,

[0128] ·Correction terms of the color prediction model as previously described.

[0129] The color prediction model can be configured to predict the color of the adjusted sample coating in the following manner:

[0130] -Predict the color data of the adjusted sample coating based on the optical data of individual color components, condition adaptation parameters, and adjusted sample coating data, and

[0131] -Add the color difference and correction terms to the predicted color data.

[0132] The color difference and correction terms can relate to the systematic error of the color prediction model associated with predicting the color of the adjusted sample coating existing under the second physical condition based on the color data of the adjusted sample coating existing under the first physical condition. Such a systematic error can be added to the color (e.g., color data) predicted by the physical model based on the formulation of the adjusted sample coating, the optical data of individual color components, and condition adaptation parameters.

[0133] In an embodiment, a computer-implemented method for determining the color of the adjusted sample coating existing under the second physical condition based on the color data of the adjusted sample coating existing under the first physical condition further includes

[0134] -Providing the color data of a reference coating existing under the second physical condition,

[0135] -Calculating the color difference between the determined color data of the adjusted sample coating existing under the second physical condition and the provided color data of the reference coating existing under the second physical condition, and

[0136] -Optionally providing the calculated color difference via a communication interface.

[0137] The color data of the reference coating can be provided by retrieving the color data from a data storage medium. For example, data indicating the reference coating can be provided, and the reference coating color data can be retrieved based on the provided data. The data indicating the reference coating can include a color number, a color code, a barcode, a unique database ID associated with the reference coating, or a combination thereof.

[0138] Color tolerance equations can be used to calculate the color difference. The color tolerance equations can be selected from Delta E (CIE 1994) color tolerance equation, Delta E (CIE 2000) color tolerance equation, Delta E (DIN 99) color tolerance equation, Delta E (CIE 1976) color tolerance equation, Delta E (CMC) color tolerance equation, Delta E (Audi95) color tolerance equation, Delta E (Audi2000) color tolerance equation, or other color tolerance equations.

[0139] As previously described, the calculated color difference can be provided via the communication interface for display.

[0140] In an embodiment, a computer-implemented method for determining the color of an adjusted sample coating present under a second physical condition based on color data of the adjusted sample coating present under a first physical condition further includes initiating at least one action associated with the calculated color difference. This can include comparing the calculated color difference with a predefined threshold and initiating an action based on the calculation. For example, if the calculated color difference is higher or lower than the predefined threshold, an action can be initiated. The initiated action can depend on the result of the comparison. For example, one or more actions can be associated with the calculated color difference being lower than the predefined threshold, while (multiple) different actions can be associated with the calculated color difference being higher than the predefined threshold. An action associated with the calculated color difference being higher than the predefined threshold can be to initiate modifying the formulation of the adjusted sample coating to minimize the color difference relative to a reference coating, such as described later with respect to the method for determining the formulation of a second adjusted sample coating. The at least one action can be initiated by the user or can be initiated by the at least one processor.

[0141] Initiating at least one action can include optionally providing the adjusted sample coating formulation to a printing device and / or data storage medium and / or filling production line after determining whether the calculated color difference is lower than a predefined threshold. For example, the determined color difference being lower than the predefined threshold can indicate that the color difference between the reference coating and the sample coating is low enough, i.e., the quality of the sample coating in terms of color / appearance is high enough for the sample coating to meet a predefined standard. This can trigger generating an adjusted sample coating material according to the adjusted sample coating formulation for determining the color data. The generated adjusted sample coating material can be filled into a packaging unit for transporting the material to a customer.

[0142] In an embodiment, determining the formulation of a second adjusted sample coating includes

[0143] - Provide a method configured to adjust the concentration of at least one individual color component present in a first adjusted sample coating formulation by minimizing a given cost function starting from the concentrations of the individual color components included in the provided first adjusted sample coating data, and

[0144] - Use the provided method to modify the concentration of at least one individual color component present in the first adjusted sample coating formulation by comparing the color data recursively predicted by a color prediction model using the first adjusted sample coating formulation recursively modified by the method with the provided color data of a reference coating until the color difference drops below a given threshold or until the number of iterations reaches a predefined limit.

[0145] The first adjusted sample coating may correspond to the previously mentioned adjusted sample coating. The first adjusted sample coating is associated with or related to the sample coating. The relationship between the sample coating and the first adjusted sample coating may arise from the fact that the first adjusted sample coating formulation associated with the first adjusted sample coating is obtained by modifying the sample coating formulation associated with the sample coating. The second adjusted sample coating may correspond to the adjusted sample coating obtained after modifying the adjusted sample coating formulation (e.g., by modifying the (multiple) components and / or the amount of the (multiple) components of the adjusted sample coating formulation).

[0146] The provided data may correspond to the data provided to the at least one computer processor via a communication interface before determining the second adjusted sample coating formulation.

[0147] The method configured to adjust the concentration of at least one individual color component present in the first adjusted sample coating may be selected from the Levenberg–Marquardt algorithm (referred to as LMA or LM), also known as the damped least squares method (DLS). The method may be stored on a data storage medium (such as the internal memory of a computing device including the at least one processor), or stored in a database connected to the at least one processor via a communication interface. The at least one processor may retrieve the method from the data storage medium when determining the second adjusted sample coating formulation.

[0148] During the adjustment of the concentration of at least one individual color component, the color difference between the measured color data and the predicted color data of the sample coating may be considered constant. This allows for taking into account the remaining systematic error of the color prediction model, thus improving the accuracy of calculating the second adjusted sample coating formulation.

[0149] The cost function can be the color difference between the predicted color data of the first adjusted sample coating that is recursively modified and the provided color data of the reference coating. The color difference can be calculated using the previously described color tolerance equation. In the case where the cost function is the color difference, the given threshold can preferably be a given or predefined color difference.

[0150] The color data can be recursively predicted by the provided physical model using the provided color difference, the optical data of the provided individual color components, the provided condition adaptation parameters, the provided correction terms, and the recursively modified first adjusted sample coating formulation as input data. The color difference and the correction terms can be added as systematic errors of the color prediction model to the preliminary color data predicted by the color prediction model based on the optical data of the individual color components, the condition adaptation parameters, and the recursively modified first adjusted sample coating formulation. The provided physical model can predict the color data of the first adjusted sample coating formulation or the recursively modified first adjusted sample coating formulation based on input parameters, such as reflectance data. This prediction can be performed each time the first adjusted sample coating formulation is modified, until the cost function drops below a given threshold or reaches a maximum iteration limit.

[0151] In an embodiment, providing the determined second adjusted sample coating formulation includes providing the determined formulation (optionally combined with additional data) via a communication interface for display. As previously described, the provided data can be displayed on the screen of a display device.

[0152] In an embodiment, the computer-implemented method for determining a second adjusted sample coating formulation to match the color of a reference coating that exists under a second physical condition based on the color data of a first adjusted sample coating that exists under a first physical condition further includes initiating at least one action associated with the determined second adjusted sample coating formulation. The at least one action can be initiated by a user or can be initiated by the at least one processor.

[0153] Initiating the at least one action can include providing the second adjusted sample coating formulation to a printing device and / or a data storage medium and / or a mixing device. Providing the second adjusted sample coating formulation to the mixing device can allow for the automatic preparation of the second adjusted sample coating material based on the received second adjusted sample coating formulation.

[0154] In an embodiment, the apparatus further includes at least one of the following:

[0155] - A display device having a screen;

[0156] - At least one database, the at least one database including at least one of the following: a color prediction model, optical data of individual color components associated with the first physical condition, reference coating data, first adjusted sample coating data, condition adaptation parameters associated with the difference between the first physical condition and the second physical condition of the first adjusted sample coating, determined correction terms of the color prediction model,

[0157] - A measurement device configured to measure color data of a sample coating and / or a reference coating present under a second physical condition,

[0158] - A measurement device configured to measure color data of the sample coating and / or the adjusted sample coating present under the first physical condition.

[0159] A display device may be connected to the one or more computing nodes of the device via a communication interface. The display device may be configured to display data determined or calculated by the one or more computing nodes of the device. For example, the display device may be configured to display correction terms determined according to the methods disclosed herein. In another example, the display device may be configured to display color data of an adjusted sample coating determined according to the methods herein. In yet another example, the display device may be configured to display a second adjusted sample coating formulation determined by the methods disclosed herein.

[0160] The at least one database may be connected to the one or more computing nodes of the device via a communication interface. The (one or more) measurement devices may be connected to the one or more computing nodes of the device via a communication interface.

[0161] The measurement device configured to measure color data of a sample coating and / or an adjusted sample coating present under the first physical condition may include a measurement unit that may be filled with a coating material present in a wet state as previously described.

[0162] The measurement device configured to measure color data of a sample coating and / or a reference coating present under the second physical condition may be a multi-angle spectrophotometer as previously described. BRIEF DESCRIPTION OF THE DRAWINGS

[0163] These and other features of the present invention will be more fully set forth in the following description of exemplary embodiments of the invention. To facilitate identification of the discussion of any particular element or act, one or more of the most significant digits in the reference numerals refer to the drawing number in which the element is first introduced. In the drawings and this disclosure, like reference numerals are intended to refer to the same or similar elements, components, and / or parts. The description is made with reference to the drawings, in which:

[0164] Figure 1A flowchart of a method for providing a correction term for a color prediction model according to an exemplary embodiment of the present disclosure;

[0165] Figure 2A Shows an exemplary embodiment according to the present disclosure Figure 1 A flowchart of an aspect of block 102;

[0166] Figure 2B Shows an exemplary embodiment according to the present disclosure Figure 2A A flowchart of an aspect of block 210;

[0167] Figure 3A , Figure 3B Shows an exemplary embodiment according to the present disclosure Figure 1 A flowchart of another aspect of block 102;

[0168] Figure 3C Shows an exemplary embodiment according to the present disclosure Figure 3B A flowchart of an aspect of block 318;

[0169] Figure 4A A flowchart of a method for determining the color of an adjusted sample coating present under a second physical condition based on color data of an adjusted sample coating present under a first physical condition according to an exemplary embodiment of the present disclosure;

[0170] Figure 4B Shows an exemplary embodiment according to the present disclosure Figure 4A A flowchart of another aspect of the method;

[0171] Figure 5 A flowchart of a method for determining a second adjusted sample coating formulation to match the color of a reference coating present under a second physical condition based on color data of a first adjusted sample coating present under a first physical condition according to an exemplary embodiment of the present disclosure;

[0172] Figure 6 Shows an exemplary embodiment according to the present disclosure Figure 5 A flowchart of an aspect of block 504;

[0173] Figure 7A Shows an exemplary embodiment according to the present disclosure Figure 4A A schematic diagram of an aspect of the method;

[0174] Figure 7B Shows an exemplary embodiment according to the present disclosure Figure 5 A schematic diagram of an aspect of the method;

[0175] Figure 8 Illustrates that can be used to implementFigures 1 to 7B An illustrative type of computing device for any aspect of the features shown;

[0176] Figure 9 Shows a client - server organization according to an example embodiment of the present disclosure;

[0177] Figure 10A Shows a graph that includes a reference coating present in a dry state, measured reflection spectra of an adjusted sample coating batch present in a liquid state and a dry state, and the reflection spectrum of the adjusted sample coating batch predicted for the dry state based on color data of the adjusted sample coating batch present in the liquid state according to a color prediction method known in the prior art;

[0178] Figure 10B Shows a graph that includes a reference coating present in a dry state, measured reflection spectra of an adjusted sample coating batch present in a liquid state and a dry state, and the reflection spectrum of the adjusted sample coating batch predicted for the dry state according to a color prediction method of an example embodiment of the present disclosure;

[0179] Figure 10C Shows a table including Figure 10A and Figure 10B a color difference comparison of the color data shown in;

[0180] Figure 11A Shows a graph that includes another reference coating present in a dry state and measured reflection spectra of another adjusted sample coating batch present in a liquid state and a dry state, and the reflection spectrum of the adjusted sample coating batch predicted for the dry state based on color data of the adjusted sample coating batch present in the liquid state according to a color prediction method known in the prior art;

[0181] Figure 11B Shows a graph that includes the other reference coating present in a dry state and measured reflection spectra of the other adjusted sample coating batch present in a liquid state and a dry state, and the reflection spectrum of the adjusted sample coating batch predicted for the dry state according to a color prediction method of an example embodiment of the present disclosure;

[0182] Figure 11C Shows a table including Figure 11A and Figure 11B a color difference comparison of the color data shown in;

[0183] Figure 12Ashows a graph that includes the measured reflection spectra of yet another reference coating present in the dry state and yet another batch of adjusted sample coating present in both the liquid state and the dry state, and the reflection spectrum of the batch of adjusted sample coating predicted for the dry state based on the color data of the batch of adjusted sample coating present in the liquid state according to a color prediction method known in the prior art;

[0184] Figure 12B shows a graph that includes the measured reflection spectra of the other reference coating present in the dry state and the other batch of adjusted sample coating present in both the liquid state and the dry state, and the reflection spectrum of the batch of adjusted sample coating predicted for the dry state according to the color prediction method of the exemplary embodiments of the present disclosure;

[0185] Figure 12C shows a table that includes Figure 12A and Figure 12B a color difference comparison of the color data shown in DETAILED DESCRIPTION

[0186] The following detailed description is intended as a description of various aspects of the subject matter of the present invention and is not intended to represent the only configuration in which the subject matter of the present invention may be practiced. The accompanying drawings are incorporated herein and constitute a part of the detailed description. The detailed description includes specific details for providing a thorough understanding of the subject matter of the present invention. However, it will be apparent to those skilled in the art that the subject matter of the present invention may be practiced without these specific details.

[0187] In one case, the division of the various parts shown in the drawings into different units may reflect the use of corresponding different physical and tangible parts in the actual implementation. Alternatively or additionally, any single part shown in the figures may be implemented by a plurality of actual physical parts. Alternatively or additionally, the depiction of any two or more separate parts in the figures may reflect different functions performed by a single actual physical part.

[0188] Other figures describe these concepts in the form of flowcharts. In this form, certain operations are described as constituting different boxes that are executed in a specific order. Such embodiments are illustrative and not restrictive. Certain boxes described herein may be combined and executed in a single operation, certain boxes may be divided into multiple component boxes, and the order of execution of certain boxes may be different from that shown herein (including executing these boxes in parallel). In one embodiment, the boxes shown in the flowchart that relate to processing-related functions may be implemented by the hardware logic circuits described with respect to Figure 8 which may in turn be implemented by one or more hardware processors and / or other logic components including a set of task-specific logic gates.

[0189] Regarding terminology, the phrase "configured to" encompasses various physical and tangible mechanisms for performing the identified operations. These mechanisms can be configured to perform operations using the hardware logic circuits described with respect to Figure 8 The term "logic" likewise encompasses various physical and tangible mechanisms for performing tasks. For example, each processing-related operation shown in a flowchart corresponds to a logic component for performing that operation. The logic component can perform its operations using the hardware logic circuits described with respect to Figure 8 When implemented by a computing device, regardless of the manner of implementation, the logic component represents an electrical component that is a physical part of the computing system.

[0190] The following explanations may identify one or more features as "optional". Statements of this type should not be construed as an exhaustive indication of features that may be considered optional; that is, other features may be considered optional even though not explicitly indicated in the text. Further, any description of a single entity is not intended to exclude the use of multiple such entities; similarly, a description of multiple entities is not intended to exclude the use of a single entity. Further, although the specification may interpret certain features as alternative ways of performing the identified functions or implementing the identified mechanisms, these features may also be combined together in any combination. Finally, the term "exemplary" or "illustrative" refers to one implementation among potentially multiple implementations.

[0191] Figure 1Depicts an example of method 100 for determining a correction term for a color prediction model, the correction term being associated with an adjusted sample coating present under at least two different physical conditions. The correction term can be used to transform the systematic error of the color prediction model from a first condition of the adjusted sample coating to a second condition of the adjusted sample coating. The correction term can be taken into account when predicting color data by the color prediction model by adding the correction term to the color data predicted by the color prediction model. If input data for the color prediction model of the adjusted sample coating present under the first physical condition is used, this allows for more accurate prediction of the color data of the adjusted sample coating present under the second physical condition. The first physical condition can be a wet state. The second physical condition can be a dry state. The adjusted sample coating can be associated with an adjusted sample coating material that can be used to prepare the adjusted sample coating. The adjusted sample coating material can be associated with an adjusted sample coating formulation. The adjusted sample coating formulation can be obtained by modifying the sample coating formulation at least once. For example, the adjusted sample coating formulation can be obtained using generally known color matching operations (such as the methods described in the aforementioned Georg Klein, Farbenphysik für industrielle Anwendungen), using the sample coating formulation and the color data of the reference coating as input data. The sample coating material can correspond to a batch of coating material prepared according to a defined formulation scheme.

[0192] Method 100 can be executed by a computing system (e.g., the system described with respect to Figure 8 ), or can be executed by server 902 of the client-server organization described with respect to Figure 9 .

[0193] In block 102, the computing system implementing method 100 can receive a request providing the following data:

[0194] · The color difference (CD1) between the measured color data and the predicted color data of the adjusted sample coating present under the first physical condition,

[0195] · The color difference (CD2) between the measured color data of the sample coating present under the second physical condition and the measured color data of the sample coating present under the first physical condition, the sample coating being associated with the adjusted sample coating, and

[0196] · The color difference (CD3) between the predicted color data of the adjusted sample coating present under the second physical condition and the predicted color data of the adjusted sample coating present under the first physical condition.

[0197] The request can include data indicating the method 100 of initiation (i.e., the method for determining the correction term), and the computing system can be configured to provide the above data in response to the request. The request can be received by the computing system from an input / output device (such as Figure 8 the I / O device 814 of Figure 9 or the client 908 of

[0198] The computing system can be configured to determine a color difference (CD1), for example, as described with respect to Figure 2A The computing system can be configured to determine the color difference (CD2) by calculating the color difference based on the provided color data. The color data required to calculate the color difference (CD2) can be provided to the computing system via a communication interface. The color data required to calculate the color difference (CD2) can be retrieved by the computing system based on the received identifier associated with the sample coating. The computing system can be configured to determine a color difference (CD3), for example, as described with respect to Figure 3A and Figure 3B

[0199] In block 104, the computing system implementing method 100 can use the color difference provided in block 102 to determine a correction term for the color prediction model in response to the received request. The correction term can be determined according to the previously described formulas (I) and (Ia). The correction term can take into account the systematic error of the color prediction model when predicting color data using input data (such as the previously described input data). The correction term can take into account the differences in color data between different physical conditions.

[0200] In block 106, the computing system can provide the determined correction term via a communication interface. For example, the computing system can provide the determined correction term to an I / O device having a display for display. In another example, if the determined correction term is to be used in a later color prediction or color adjustment method described with respect to Figure 4A and Figure 5 then the computing system can provide the correction term to a data storage medium.

[0201] Figure 2A Shows an example method 200a of providing the color difference (CD1) between the measured color data of the adjusted sample coating present under the first physical condition and the predicted color data of the adjusted sample coating present under the first physical condition (e.g., the color difference (CD1) mentioned in block 102 above with respect to Figure 1 The method 200a can be executed by a computing system (such as the computing system implementing the method 100 described with respect to Figure 1

[0202] ​​In block 202, color data of an adjusted sample coating determined under a first physical condition can be provided. The first physical condition can be a wet state. A suitable measuring device (such as a multi-angle spectrophotometer configured to determine color data of a liquid coating material present in a measuring unit) can be used to determine the color data. The acquired data can be used to determine corresponding color data. For example, the acquired reflectance data can be used to determine color space data as previously described. The color data can be determined by a computing system that controls the measuring device or by a computing system implementing method 200a. The determined color data can be retrieved from a data storage medium by the computing system implementing method 200a. For example, the computing system can receive data (such as an ID) indicating the adjusted sample coating, and can retrieve the color data based on the received data.

[0203] In block 204, model input data can be provided. The model input data can include adjusted sample coating formulation data and optical data of individual color components. The optical data can be associated with the first physical condition. The adjusted sample coating formulation data can include data on the components present in the adjusted sample coating material used to prepare the adjusted sample coating and their corresponding amounts. The optical data can be stored on a data storage medium and can be retrieved by a computing system based on the adjusted sample coating formulation data. For example, the computing system can be configured to determine the components present in the adjusted sample coating material according to the formulation data, and can retrieve the optical data associated with the determined components from the data storage medium.

[0204] In block 206, a color prediction model can be provided, which is configured to predict color data of a coating using the coating formulation data and optical data of individual color components. The color prediction model can be stored on a data storage medium and can be retrieved by a computing system.

[0205] In block 208, the model provided in block 206 and the model input data provided in block 204 can be used to determine color data of the adjusted sample coating. The color prediction model can use the formulation data and the optical data associated with the components present in the adjusted sample coating material to predict color data associated with the adjusted sample coating material. The predicted color data can be associated with the first physical condition because the optical data used for color prediction is also associated with the first physical condition.

[0206] In block 210, a systematic error of the color prediction model associated with the first physical condition can be provided, and this block is generally optional. The systematic error associated with the first physical condition can be determined as described later with respect to Figure 2B Providing the systematic error can include retrieving the error from a data storage medium.

[0207] In block 212, the systematic error provided in block 210 can be added to the color data of the predicted adjusted sample coating in block 208, which is typically optional. The use of the systematic error can improve the accuracy of the correction term and thus also improve the accuracy of the color prediction or color matching method using the correction term.

[0208] In block 214, the color difference (CD1) between the color data provided in block 202 and the color data predicted in block 208 or the color data obtained in block 212 can be determined. Then, method 200a can proceed to block 104 of method 100 as described Figure 1 above.

[0209] Figure 2B An example method 200b is shown that provides the systematic error of the color prediction model mentioned in block 210 above. Method 200b can be executed by a computing system (e.g., the computing system implementing method 100 as described Figure 2A above). Figure 1 above).

[0210] In block 216, the color data of the sample coating determined under a first physical condition can be provided. The sample coating can be associated with the adjusted sample coating. For example, the adjusted sample coating can be obtained by modifying the sample coating, e.g., by modifying at least one compound present in the sample coating formulation and / or the amount of at least one compound to obtain an adjusted sample coating formulation. The sample coating can correspond to a batch of coating material produced according to a given scheme or formulation. The sample coating material can be a liquid sample coating material. The color data can be determined as described for Figure 2A block 202 above.

[0211] In block 218, model input data can be provided. The model input data can include sample coating formulation data and optical data of individual color components. The optical data can be associated with the first physical condition. The sample coating formulation data can include data on the components present in the sample coating material used to prepare the sample coating and their corresponding amounts. The optical data can be stored on a data storage medium and can be retrieved as described for Figure 2A block 204 above.

[0212] In block 220, the color data of the sample coating can be determined using the color prediction model provided in Figure 2A block 206 above and the model input data provided in block 218. The prediction of the color data can be performed as described for Figure 2A block 208 above.

[0213] In block 222, a systematic error in the color prediction model may be determined by determining the difference between the color data provided in block 216 and the color data predicted in block 222. Figure 2A The systematic error determined in block 222 can be used to determine the difference as described in block 214 of FIG. Figure 2A The use of the systematic errors allows improving the accuracy of the determined correction terms and thus also improving the accuracy of the color prediction and color matching methods using the correction terms.

[0214] Figure 3A and Figure 3B The color difference (CD3) between the predicted color data of the adjusted sample coating under the second physical condition and the predicted color data of the adjusted sample coating under the first physical condition is shown (e.g., as described above with respect to Figure 1 The method 300a may be implemented by a computing system (e.g., a computer system implementing Figure 1 The described method 100 is performed by a computing system).

[0215] In block 302, adjusted sample coating recipe data and optical data associated with a first physical condition may be provided. Figure 2A The data is provided as described in block 204 of .

[0216] In block 304, the use of conditional adaptation may be determined. This may be performed based on a physical condition associated with the available optical data. The available optical data may be stored on a data storage medium. The computing system implementing method 300a may be configured to determine the physical condition associated with the available optical data. For example, if the available optical data is associated with the second physical condition, conditional adaptation is not required, and method 300a proceeds to block 306. Otherwise, that is, if the available optical data is associated only with the first physical condition, conditional adaptation is required, and method 300a proceeds to block 308.

[0217] In block 306, optical data of the individual color components associated with the second physical condition may be provided. For example, this may be as described with respect to Figure 2A The process is performed as described in block 202 of FIG.

[0218] In block 308, a condition adaptation parameter associated with a difference between a first physical condition and a second physical condition of the adjusted sample can be provided. For example, the condition adaptation parameter can be determined by a computing system implementing method 300a. The condition adaptation parameter can be pre-configured and / or the condition adaptation parameter can be determined using an optimization method and a color prediction model. The optimization method can be configured to optimize the condition adaptation parameter by minimizing a cost function starting from a set of initial condition adaptation parameters. The color prediction model can use the condition adaptation parameter optimized by the optimization method to predict color data of the adjusted sample coating. The cost function can be a color difference between the color data predicted by the color prediction model for the sample coating present under the second physical condition and the measured color data of the sample coating present under the second physical condition. The optimization method can optimize the condition adaptation parameter until the color difference drops below a given threshold. The condition adaptation parameter determined using input data associated with the sample coating can correspond to the condition adaptation parameter associated with the adjusted sample coating, i.e., the condition adaptation parameter determined using input data associated with the sample coating can be used for the adjusted sample coating without causing significant errors. This allows for determining the condition adaptation parameter required to account for using optical data associated with the first physical condition when predicting the color data of the adjusted sample coating present under the second physical condition. The determined condition adaptation parameter can be stored on a data storage medium. The determined condition adaptation parameter can be provided as input data to the color prediction model.

[0219] In block 310, a color prediction model can be provided, e.g., as described with respect to Figure 2A block 206. The color prediction model can be configured to predict the color of the adjusted sample coating using the adjusted sample coating formulation data, optical data of individual color components, and optionally the condition adaptation parameter as input data.

[0220] In block 312, the color prediction model provided in block 310 and the model input data provided in block 302 can be used to determine the color data of the adjusted sample coating present under the first physical condition. The color data can be predicted as described with respect to Figure 2A block 208.

[0221] In block 314, the color data of the adjusted sample coating existing under the second physical condition can be determined using the color prediction model provided in block 310, the adjusted sample coating formulation provided in block 302, and the optical data provided in block 306. The color data of the adjusted sample coating existing under the second physical condition can be predicted using the color prediction model provided in block 310, the data provided in block 302, and the condition adaptation parameters provided in block 308. The parameters can be considered by adding the condition adaptation parameters as systematic errors to the color data predicted by the color prediction model. The color data can be predicted as described for block 208 with respect to Figure 2A .

[0222] In block 316 (see Figure 3B ), the systematic error associated with the first physical condition of the color prediction model can be provided, and this block is generally optional. The error can be provided as described for Figure 2B . The use of the systematic error can improve the accuracy of the correction term and thus also improve the accuracy of the color prediction or color matching method using the correction term.

[0223] In block 318 (see Figure 3B ), the systematic error associated with the second physical condition of the color prediction model can be provided, and this block is generally optional. The error can be provided as described later for Figure 3C . The use of the systematic error can improve the accuracy of the correction term and thus also improve the accuracy of the color prediction or color matching method using the correction term.

[0224] In block 320 (see Figure 3B ), the systematic error provided in block 316 can be added to the color data of the adjusted sample coating predicted in block 312, and this block is generally optional.

[0225] In block 322 (see Figure 3B ), the systematic error provided in block 318 can be added to the color data of the adjusted sample coating predicted in block 314, and this block is generally optional.

[0226] In block 324, the color difference (CD3) between the color data predicted in block 314 and the color data predicted in block 312 can be determined. The color difference (CD3) between the color data obtained in block 322 and the color data obtained in block 320 can be determined. If the systematic error is to be considered, the latter can be performed. As previously described, considering the systematic error allows improving the accuracy of the correction term and thus also improving the accuracy of the color prediction and color matching operations using the correction term.

[0227] Figure 3C shows an example method 300c for providing the systematic error of the color prediction model mentioned in box 318 above. Method 300c can be executed by a computing system (e.g., the computing system implementing method 300a described regarding Figure 3B ). Figure 3A

[0228] In box 326, color data of a sample coating determined under a second physical condition can be provided. The sample coating can be associated with an adjusted sample coating as described regarding Figure 2B . The color data can be determined as described in box 202 regarding Figure 2A .

[0229] In box 328, the use of condition adaptation can be determined. This can be performed based on the result of the determination executed in box 304 described regarding Figure 3A . If condition adaptation is not used, method 300c can proceed to box 330. Otherwise, method 300c can proceed to box 332 described later.

[0230] In box 330, model input data can be provided. The model input data can include sample coating formulation data and optical data of individual color components. The optical data can be associated with the second physical condition. The optical data can be provided as described in box 306 regarding Figure 3A .

[0231] In box 332, model input data can be provided. The model input data can include sample coating formulation data, optical data of individual color components, and a condition adaptation parameter associated with the difference between the first physical condition and the second physical condition of the adjusted sample coating. The optical data is associated with the first physical condition. The condition adaptation parameter can be provided as described in box 308 regarding Figure 3A .

[0232] In box 334, the color prediction model provided in box 310 of Figure 3A and the model input data provided in box 330 or box 332 can be used to determine the color data of the sample coating. The prediction of the color data can be performed as described in box 208 regarding Figure 2A .

[0233] In box 336, the systematic error of the color prediction model can be determined by determining the difference between the color data provided in box 326 and the color data predicted in box 334. The difference can be determined as described in box 214 regarding Figure 2A . The systematic error determined in box 336 can be used for Figure 3B ​in the frame 318. Using the system error allows improving the accuracy of the determined correction term and thus also improving the accuracy of color prediction and color matching methods using the correction term.

[0234] Figure 4A An example of a method 400 is depicted for determining color data of an adjusted sample coating present under a second physical condition based on color data of an adjusted sample coating present under a first physical condition. The first physical condition may be a wet state. The second physical condition may be a dry state. The method may use a correction term, such as the correction term determined as described above with respect to Figures 1 to 3C The correction term allows transforming the systematic error of a color prediction model from a first condition of the adjusted sample coating to a second condition of the adjusted sample coating. This enables more accurate determination of color data of an adjusted sample coating present under a second physical condition using input data for the color prediction model of an adjusted sample coating present under a first physical condition. The correction term may be taken into account by adding it to the color data predicted by the color prediction model.

[0235] Method 400 may be executed by a computing system (e.g., the system described with respect to Figure 8 ), or may be executed by a server 902 of a client - server organization described with respect to Figure 9 .

[0236] In block 402, a computing system implementing method 400 may receive a request providing the following data:

[0237] · The color difference between the measured color data and the predicted color data of a sample coating present under a second physical condition,

[0238] · Optical data of individual color components associated with the first physical condition,

[0239] · Adjusted sample coating data, which includes the formulation of the adjusted sample coating,

[0240] · A condition adaptation parameter associated with the difference between the first physical condition and the second physical condition of the adjusted sample coating,

[0241] · A correction term of a color prediction model determined according to the methods disclosed herein (e.g., the method described above with respect to Figures 1 to 3C ), and

[0242] · A color prediction model configured to predict the color of an adjusted sample coating present under a second physical condition by using the color difference, optical data of individual color components, the condition adaptation parameter, the adjusted sample coating data, and the correction term as input data.

[0243] The sample coating is associated with an adjusted sample coating. For example, as previously described, an adjusted sample coating can be obtained by modifying the sample coating formulation associated with the sample coating at least once. The sample coating material associated with the sample coating can correspond to a batch of coating material prepared according to a defined formulation scheme.

[0244] The request can include data indicating the initiation of method 400 (i.e., a method for determining color data of an adjusted sample coating present under a second physical condition), and the computing system can be configured to provide or retrieve the above data in response to the request. The request can be received by the computing system from an input / output device (such as Figure 8 I / O device 814 or Figure 9 client 908).

[0245] For example, as described with respect to Figure 3C the computing system can be configured to determine the color difference between the measured color data of the sample coating present under a second physical condition and the predicted color data of the sample coating present under a second physical condition. For example, as described with respect to Figure 3A the computing system can be configured to determine condition adaptation parameters.

[0246] In block 404, as previously described, the computing system implementing method 400 can use the data provided in block 402 in response to the received request to determine the color data of the adjusted sample coating present under a second physical condition. The color prediction model can be configured to predict the color of the adjusted sample coating by:

[0247] - Predicting the color data of the adjusted sample coating based on the optical data of individual color components and the adjusted sample coating data, and

[0248] - Adding the color difference, condition adaptation parameters, and correction terms to the predicted color data.

[0249] The color difference, condition adaptation parameters, and correction terms can relate to the systematic error associated with the color prediction model for predicting the color of the adjusted sample coating present under a second physical condition based on the color data of the adjusted sample coating present under a first physical condition. Such systematic error can be added to the color (e.g., color data) predicted by the physical model based on the formulation of the adjusted sample coating and the optical data of individual color components.

[0250] In block 406, the computing system may provide the determined color data via a communication interface. For example, the computing system may provide the determined color data to an I / O device having a display for display. In another example, if the determined color is to be used later, the computing system may provide the color data to a data storage medium. This may include correlating the color data with an adjusted sample coating identifier to allow retrieval of the color data using the identifier. After block 406 ends, the routine implementing method 400 may return to block 402 or may end method 400.

[0251] Figure 4B An example of another aspect of the method described with respect to Figure 4A is shown. In addition to the steps described with respect to Figure 4A the steps shown in Figure 4B may also be performed. Figure 4B The steps of Figure 4B may allow comparison of the determined color data with the color data of a reference coating, thereby allowing determination of the degree of color match between the adjusted sample coating and the reference coating. Figure 4B The method described in Figure 4A may be implemented using a computing system (such as the computing system described with respect to Figure 4B For example, Figure 4A the method of

[0252] In block 408, color data of a reference coating present under a second physical condition may be provided. The color data may be provided from a data storage medium such as a database. For example, the computing system may receive data (such as an ID) indicating the reference coating and may use the received data to retrieve the color data. In another example, the computing system may use data indicating the adjusted sample coating to retrieve the color data of the reference coating associated with the adjusted sample coating.

[0253] In block 410, a color difference between the color data of the adjusted sample coating determined in block 404 of Figure 4A and the color data of the reference coating provided in block 408 may be calculated. One of the above color tolerance equations may be used to calculate the color difference.

[0254] In block 412, the calculated color difference may be provided, which block is generally optional. For example, the color difference may be provided via a communication interface to a display device for display, such as described in block 406 of Figure 4A

[0255] In block 414, at least one action associated with the calculated color difference can be initiated, which block is generally optional. The at least one action can be associated with the determined color difference being higher or lower than a defined threshold. The threshold can be a predefined color difference. For example, if the determined color difference is higher than the predefined threshold, i.e., if there is not a sufficient color match between the color of the adjusted sample coating and the color of the reference coating, the calculation system can initiate the calculation of a further adjusted sample coating formulation, e.g., as described with respect to Figure 5 and Figure 6 described. In another example, the calculation system can initiate providing the adjusted sample coating formulation to a printing device and / or a data storage medium and / or a filling production line. After block 414 ends, the method can end, or the method can return to block 402.

[0256] Figure 5 FIG. depicts an example of method 500 for determining a second adjusted sample coating formulation to match the color of a reference coating existing under a second physical condition based on color data of a first adjusted sample coating existing under a first physical condition. The first physical condition can be a wet state. The second physical condition can be a dry state. The second adjusted sample coating formulation can be obtained by modifying the first adjusted sample coating formulation at least once. The first adjusted sample coating formulation can correspond to the adjusted sample coating formulation described above with respect to Figures 1 to 4B described. The method can use a correction term, such as the correction term determined as described above with respect to Figures 1 to 3C described. The correction term allows transformation of the systematic error of the color prediction model from the first condition of the adjusted sample coating to the second condition of the adjusted sample coating. This enables more accurate determination of the color data of the adjusted sample coating existing under the second physical condition using the input data for the color prediction model of the adjusted sample coating existing under the first physical condition.

[0257] Method 500 can be performed by a calculation system (e.g., the system described with respect to Figure 8 described), or can be performed by server 902 of the client-server organization described with respect to Figure 9 described.

[0258] In block 502, the calculation system implementing method 500 can receive a request providing the following data:

[0259] · The color difference between the measured color data of a sample coating existing under the second physical condition and the predicted color data of the sample coating existing under the second physical condition, where the sample coating is associated with the first adjusted sample coating,

[0260] · Optical data of individual color components associated with the first physical condition,

[0261] ·Reference coating data, which includes color data of a reference coating present under a second physical condition,

[0262] ·First adjusted sample coating data, which includes the formulation of a first adjusted sample coating,

[0263] ·A condition adaptation parameter associated with the difference between the first physical condition and the second physical condition of the first adjusted sample coating,

[0264] ·A correction term for a color prediction model determined according to the methods disclosed herein (such as the methods described above regarding Figures 1 to 3C ),

[0265] ·A color prediction model configured to predict the color of a second adjusted sample coating present under a second physical condition by using color difference, optical data of individual color components, reference coating data, first adjusted sample coating data, condition adaptation parameter, and correction term as input data.

[0266] The sample coating is associated with the first adjusted sample coating. For example, as previously described, the first adjusted sample coating can be obtained by modifying the sample coating formulation associated with the sample coating at least once. The sample coating material associated with the sample coating can correspond to a batch of coating materials prepared according to a defined formulation scheme.

[0267] The request can include data indicating the initiation of method 500 (i.e., the method for determining the color data of an adjusted sample coating present under a second physical condition), and the computing system can be configured to provide or retrieve the above data in response to the request. The request can be received by the computing system from an input / output device (such as Figure 8 the I / O device 814 or Figure 9 the client 908).

[0268] For example, as described regarding Figure 3C , the computing system can be configured to determine the color difference between the measured color data of the sample coating present under a second physical condition and the predicted color data of the sample coating present under a second physical condition. For example, as described regarding Figure 3A , the computing system can be configured to determine the condition adaptation parameter.

[0269] In block 504, a second adjusted sample coating formulation can be determined by using the color prediction model and additional data provided in block 402. The second adjusted sample coating formulation can be determined as described regarding Figure 6 .

[0270] In block 506, the determined second adjusted sample coating can be provided via a communication interface. For example, a computing system can provide the determined formulation to an I / O device having a display for display. In another example, if the determined formulation is to be used later, the computing system can provide the formulation to a data storage medium.

[0271] In block 508, at least one action associated with the second adjusted sample coating formulation determined in block 504 can be initiated, which block is generally optional. Initiating the at least one action can include providing the second adjusted sample coating formulation to a printing device and / or a data storage medium and / or a mixing device. After block 508 ends, method 500 can return to block 502 or can end.

[0272] Figure 6 A flowchart showing aspects of Figure 5 block 504 of an example embodiment in accordance with the present disclosure. Figure 6 The method described in Figure 5 can be performed by a computing system implementing method 500.

[0273] In block 602, a method is provided that is configured to adjust the concentration of at least one individual color component present in a first adjusted sample coating formulation. Suitable methods can include the Levenberg-Marquardt algorithm (referred to as LMA or LM), also known as the damped least squares (DLS) method. The adjustment of the concentration can be performed by minimizing a given cost function starting from the concentration of the individual color components included in the first adjusted sample coating data provided in Figure 5 block 502. The cost function can be the color difference between the predicted color data of the recursively modified first adjusted sample coating and the provided color data of a reference coating. The color difference can be calculated using the color tolerance equations described previously.

[0274] In block 604, the method provided in block 602 can be used to modify the concentration of at least one individual color component present in the first adjusted sample coating formulation.

[0275] In block 606, the color data of the modified first adjusted sample coating formulation resulting from performing block 604 can be determined using the color prediction model, color difference, optical data of the individual color components, condition adaptation parameters, and correction terms provided in Figure 5 block 502. The color data can be predicted by the color prediction model using the optical data of the individual color components and the modified adjusted sample coating formulation. The color difference, condition adaptation parameters, and correction terms can be added as systematic errors of the color prediction model to the color data predicted by the color prediction model based on the optical data of the individual color components and the recursively modified first adjusted sample coating formulation.

[0276] In block 608, the color data determined in block 606 can be compared with the color data of the reference coating provided in block 602. This can include, for example, determining the color difference by using the previously mentioned color tolerance equation.

[0277] In block 610, it can be determined whether the color difference determined in block 608 has dropped below a predefined threshold or whether the number of iterations has reached a predefined limit. If the determined color difference has dropped below the predefined threshold or the iteration limit has been reached, the method proceeds to Figure 6 block 506. Otherwise, the method repeats the previously described blocks 604 to 608.

[0278] Figure 7A A schematic diagram of a method 700a for determining the color data of an adjusted sample coating present under a second physical condition based on the color data of an adjusted sample coating present under a first physical condition according to an embodiment disclosed herein is shown. The method can be performed using a color prediction model 704 (e.g., a physical model describing the interaction of light with a scattering or absorbing medium (e.g., colorants in a coating)). The model can be implemented and run on at least one processor of a computing system 702. The model 704 can access optical data 706 of individual color components, such as optical data associated with the first physical condition. The optical data can include optical constants of individual color components. Each individual color component can be associated with a set of constants, such as wavelength-dependent K values and S values. The model 704 can access condition adaptation parameters 708 associated with the difference between the first physical condition and the second physical condition. The method described regarding Figure 3A can be used to determine the condition adaptation parameters.

[0279] For example, as previously described regarding Figure 4A the color difference 710 between the measured color data of a sample coating present under a second physical condition and the predicted color data of a sample coating present under a second physical condition is provided to the computing system 702. Compared with the color prediction methods described in the prior art (such as those described in WO 2022 / 122777 A1), a correction term 712 reflecting the difference in color data associated with different physical conditions is provided to the computing system 702. The correction term can be related to the systematic error of the color prediction model 704 and can be taken into account during the prediction of color data by adding the correction term to the color data predicted by the color prediction model 704 based on the optical data 706 and the adjusted sample coating data 716. The correction term can be determined according to the method disclosed herein (e.g., as regarding Figures 1 to 3Cdetermined as described). Compared to methods known in the prior art, using the correction term allows for a more accurate prediction of the color data of the adjusted sample coating, as the correction term allows for taking into account the deviation of the color data associated with different physical conditions. This allows for using the input data associated with the first physical condition and accurately predicting the color data associated with the second physical condition. If the color data of the reference coating used as the target is only available for the second physical condition and it is difficult to generate the input data for said physical condition, it may be appropriate to use the input data associated with a physical condition different from the color data to be predicted. For example, the resulting liquid coating material is colored in the wet state such that the color data of the coating produced by the resulting liquid coating material matches the color data of the reference coating that has been dried and / or cured. However, this requires an accurate prediction of the color data of the coating produced by the liquid coating material in order to generate accurate coloring instructions, i.e., in order to determine the adjustments for obtaining a sufficient color match between the colored coating and the reference coating.

[0280] The adjusted sample coating data 716 including the formula of the adjusted sample coating can be provided to the computing system 702. For example, the adjusted sample coating formula can be determined as described with respect to Figure 4A described. For example, as described with respect to Figure 4A and Figure 4B described, using the adjusted sample coating data, the received color difference, and the correction term as input data, the color prediction model 704 can use the optical data 706 and the condition adaptation parameter 708 to predict the color data of the adjusted sample coating. Then, for example, the predicted color data of the adjusted sample coating present under the second physical condition (such as the dry state) is provided via the communication interface for display on the screen. If the color difference between the predicted color data and the reference coating is to be determined, the color data 714 of the reference coating present under the second physical condition (such as the dry state) can be provided to the computing system 702, and the computing system can be configured to determine the color difference between the predicted color data and the received reference coating color data, for example, as described with respect to Figure 4B described. The computing system 702 can be configured to provide the determined color difference. The computing system 702 can be configured to initiate at least one action associated with the calculated color difference (see, for example, Figure 4B ).

[0281] Figure 7BShows a schematic diagram of method 700b for determining a second adjusted sample coating formulation to match the color of a reference coating present under a second physical condition based on color data of a first adjusted sample coating present under a first physical condition. The second adjusted sample coating formulation can be obtained by modifying the first adjusted sample coating formulation provided as input data. The first adjusted sample coating formulation can correspond to the adjusted sample coating formulation described previously. The first adjusted sample coating formulation can be obtained by modifying the sample coating formulation using commonly known color matching operations. The sample coating formulation can correspond to a batch of sample coating material prepared by mixing various coating material components according to a given scheme or formulation. Method 700b can be performed by color prediction model 704 and optimization method 718. The model and the optimization method can be implemented and run on at least one processor of computing system 702. Model 704 can access optical data 706 of individual color components, such as optical data associated with the first physical condition (see Figure 7A ). Model 704 can access condition adaptation parameters 708 associated with the difference between the first physical condition and the second physical condition. The condition adaptation parameters can be determined using the method described with respect to Figure 3A .

[0282] For example, as previously described with respect to Figure 7A , the color difference 710 between the measured color data of the sample coating present under the second physical condition and the predicted color data of the sample coating present under the second physical condition can be provided to computing system 702. In addition, a correction term 712 reflecting the difference in color data associated with different physical conditions can be provided to computing system 702. During the adjustment of the sample coating formulation using numerical method 718, the correction term 712 and the color difference 710 can be considered constants, for example, and can be added to the color data predicted by color prediction model 704.

[0283] Data 714 of the reference coating can be provided to computing system 702. The data can include color data of the reference coating prepared according to the reference coating formulation, such as reflectance data. The reference coating can be present in a dry state. The reference coating can be prepared by applying at least the corresponding reference coating material to a substrate and drying and / or curing the applied coating material.

[0284] Adjusted sample coating data 716 including the formulation of the adjusted sample coating can be provided to computing system 702. For example, the adjusted sample coating formulation can be determined as described with respect to Figure 4A .

[0285] For example, as described with respect to Figure 4A and Figure 4BAs described, using the adjusted sample coating data 716, the received color difference 710, and the correction term 712 as input data, the color prediction model 704 can use the optical data 706 and the condition adaptation parameter 708 to predict the color data of the adjusted sample coating. After determining the color data, the optimization method 718 can modify the concentration of at least one colorant present in the adjusted sample coating formulation by minimizing the color difference between the color data of the reference coating and the color data of the recursively modified adjusted sample coating predicted by the physical model 704. Each time the adjusted sample coating formulation is modified by the optimization method 718, the physical model 704 can be used to predict the color data based on the optical data 706, the condition adaptation parameter 708, and the modified adjusted sample coating formulation. The modification can be repeated by the optimization method 718 until the color difference between the color data of the reference coating and the predicted color data of the recursively modified adjusted sample coating reaches a given threshold, or until a predefined maximum iteration limit is reached. Then, the computing system 702 can provide, for example via a communication interface, a second adjusted sample formulation associated with the color difference reaching the given threshold or a second adjusted formulation associated with the maximum number of iterations for display on a screen. The computing system 702 can be configured to initiate at least one action associated with the calculated color difference (see, for example Figure 4B ).

[0286] Figure 8 FIG. shows a computing device 800 that can be used to implement any aspect of the mechanisms described above Figures 1 to 7B . For example, referring to Figures 1 to 6 , Figure 8 the type of computing device 800 shown therein can be used to implement any computing device associated with the methods disclosed in the said figures. In another example, Figure 8 the type of computing device 800 shown therein can be used to implement any computing device associated with Figure 7A and Figure 7B the computing system 702. In all cases, the computing device 800 represents a physical and tangible processing mechanism.

[0287] The computing device 800 can include one or more hardware processors 802. The (multiple) hardware processors can include, but are not limited to, one or more central processing units (CPUs), and / or one or more graphics processing units (GPUs), and / or one or more application-specific integrated circuits (ASICs), etc. More generally, any hardware processor can correspond to a general-purpose processing unit or a special-purpose processor unit.

[0288] The computing device 800 may also include a computer-readable storage medium 804 corresponding to one or more computer-readable media hardware units. The computer-readable storage medium 804 stores any kind of information 806, such as machine-readable instructions, settings, data, etc. By way of non-limiting example, for instance, the computer-readable storage medium 804 may include one or more solid-state devices, one or more magnetic hard disks, one or more optical discs, magnetic tapes, etc. Any instance of the computer-readable storage medium 804 may use any technology for storing and retrieving information. Further, any instance of the computer-readable storage medium 804 may represent a fixed or removable component of the computing device 800. Further, any instance of the computer-readable storage medium 804 may provide volatile or non-volatile information retention.

[0289] The computing device 800 may utilize any instance of the computer-readable storage medium 804 in different ways. For example, any instance of the computer-readable storage medium 804 may represent a hardware memory unit (such as random access memory (RAM)) for storing transient information during the execution of a program in the computing device 800 and / or a hardware storage unit (such as a hard disk) for retaining / archiving information on a more permanent basis. In the latter case, the computing device 800 also includes one or more drive mechanisms 808 (such as a hard disk drive mechanism) for storing and retrieving information from an instance of the computer-readable storage medium 804.

[0290] When the (one or more) hardware processors 802 execute computer-readable instructions stored in any instance of the computer-readable storage medium 804, the computing device 800 may perform any of the above functions. For example, the computing device 800 may execute computer-readable instructions to perform each block of the method described with respect to Figures 1 to 6 each block of the method described.

[0291] Alternatively or additionally, the computing device 800 may rely on one or more other hardware logic components 810 to perform operations using a set of task-specific logic gates. For example, the (one or more) hardware logic components 810 may include a fixed configuration of hardware logic gates created and set at the time of manufacture and thereafter not changeable. Alternatively or additionally, the (one or more) other hardware logic components 810 may include a set of programmable hardware logic gates that can be set to perform different dedicated tasks. Devices of the latter category include, but are not limited to, programmable array logic devices (PALs), generic array logic devices (GALs), complex programmable logic devices (CPLDs), field programmable gate arrays (FPGAs), etc.

[0292] Figure 8Generally, the indicated hardware logic circuitry 812 includes any combination of (one or more) hardware processors 802, computer-readable storage media 804, and / or (one or more) other hardware logic components 810. That is, the computing device 800 may employ any combination of (one or more) hardware processors 802 that execute machine-readable instructions provided in the computer-readable storage media 804 and / or one or more other hardware logic components 810 that perform operations using a set of fixed and / or programmable hardware logic gates. More generally, the hardware logic circuitry 812 corresponds to one or more hardware logic components of any (multiple) type, the one or more hardware logic components performing operations based on logic stored in and / or otherwise embodied in the (one or more) hardware logic components.

[0293] In some cases, the computing device 800 may also include an input / output interface 814 for receiving various inputs (via input device 816) and for providing various outputs (via output device 818). For example, if the computing device 800 represents Figure 9 client devices 908.1 to 908.n, then the device 800 may include such input / output devices 814. Illustrative input devices include keyboard devices, mouse input devices, touchscreen input devices, digitizers, one or more still image cameras, one or more video cameras, one or more depth camera systems, one or more microphones, speech recognition mechanisms, any motion detection mechanisms (e.g., accelerometers, gyroscopes, etc.), and the like. One particular output mechanism may include a display device 820 and an associated graphical user interface rendering (GUI) 822. The display device 820 may correspond to a liquid crystal display device, a light-emitting diode display (LED) device, a cathode ray tube device, a projection mechanism, and the like. Other output devices include printers, one or more speakers, haptic output mechanisms, archival mechanisms (for storing output information), and the like. The computing device 800 may also include one or more network interfaces 824 for exchanging data with other devices via one or more communication conduits 826. One or more communication buses 828 may communicatively couple the above-described components together.

[0294] (One or more) communication conduits 826 may be implemented in any manner, e.g., by a local computer network, a wide area computer network (e.g., the Internet), a point-to-point connection, etc. or any combination thereof. (One or more) communication conduits 826 may include any combination of hardwired links, wireless links, routers, gateway functions, name servers, etc. governed by any protocol or combination of protocols.

[0295] Figure 8 The computing device 800 is shown as being composed of a collection of discrete individual units. In some cases, the collection of units may correspond to discrete hardware units provided in a computing device chassis having any form factor.

[0296] Go to Figure 9 which shows an Internet-based system 900 that can be used to implement the method described with respect to Figures 1 to 6 The system 900 can include a server 902 that can be accessed by one or more clients 908.1 to 908.n via a network 906 (such as the Internet). The server can correspond to the device described with respect to Figure 8 The server can be an HTTP server and can be accessed via traditional web-based Internet technologies. The server 902 can be connected to a database 904. The database 904 can store (a) color prediction model(s), optical data of individual color components, and / or condition adaptation parameters. The database 904 can also store correction terms determined by the server. The clients 908.1 to 908.n can be user-accessible computer terminals and can be custom devices such as data input kiosks or general-purpose devices such as personal computers. The clients 908.1 to 908.n can include a screen and can be used to display the determined correction terms and / or the determined color data and / or the determined second adjusted sample coating formulation. A printer 910 can be connected to the client terminal 908. The clients 908.1 to 908.n can be connected to a database 912. The database 912 can store reference coating data and / or first adjusted sample coating data and / or formulations associated with the adjusted sample coating or the second adjusted sample coating. The Internet-based system 900 can be particularly useful if serving customers or within a larger corporate organization. The client 908 can be used to provide reference coating data and adjusted sample coating data to the computer processor of the server.

[0297] Figure 10A shows a graph 1002 that includes the measured reflection spectrum 1004 of a green reference coating present in the dry state, the measured reflection spectrum 1006 of an adjusted green sample coating material present in the wet state, the predicted reflection spectrum 1008 of the adjusted green sample coating material for the dry state using the method described in WO 2022 / 122777A1, and the measured reflection spectrum 1010 of a green adjusted sample coating prepared from the adjusted green sample coating material and present in the dry state (as a control measurement result for determining the quality of color prediction accuracy). The adjusted green sample coating formulation can be determined using the method described in WO 2022 / 122777A1 and can be used to prepare, for example, the adjusted green sample coating in the dry state by applying the formulation to a substrate and drying and / or curing the applied formulation. The deviation between the reflection spectra 1004, 1010 of the green reference coating and the adjusted green sample coating is also reflected in Figure 10Cin the color data shown in Table 1014. The deviation seems to be caused by the fact that the systematic error of the color prediction model was determined for the wet state of the adjusted green sample coating using the method described in WO 2022 / 122777 A1, and this determined systematic error was assumed to correspond to the systematic error of the color prediction model for the dry state of the adjusted green sample coating. However, as Figure 10C is evidenced by the color data shown in Table 1014, this assumption seems inaccurate. Depending on the magnitude of the difference between the systematic errors associated with the wet and dry states of the color prediction model, the prediction of the color data can be rather inaccurate, as Figure 10C is evidenced.

[0298] Figure 10B shows graph 1012, which contains color data regarding Figure 10A the described green reference coating and the green adjusted sample coating. The graph contains the measured reflection spectrum 1004 of the green reference coating present in the dry state, the measured reflection spectrum 1006 of the adjusted green sample coating material present in the wet state, the predicted reflection spectrum 1008 of the adjusted green sample coating material for the dry state using the method described regarding Figures 1 to 6 , and the measured reflection spectrum 1010 of the adjusted green sample coating in the dry state (as a control measurement result for determining the quality of the color prediction accuracy). In graph 1012, there is no detectable deviation between the measured reflection spectrum 1004 of the green reference coating, the measured reflection spectrum 1010 of the adjusted green sample coating, and the predicted reflection spectrum 1008 of the adjusted green sample coating. The higher accuracy of the method disclosed herein compared to the method described in WO 2022 / 122777 A1 seems to be due to the use of a correction term that allows the use of input data associated with the wet state for the color prediction model to accurately predict color data, such as reflection spectra, in the dry state.

[0299] Figure 10C shows Table 1014, which contains Figure 10A and Figure 10BThe color difference comparison of the color data shown (i.e., the color data of the green reference coating measured in the dry state (i.e., for the cured green reference coating prepared by applying (a) reference coating material(s) to a substrate and drying and / or curing the applied (a) reference coating material(s)), and the color data predicted for the green sample coating (first row) or the adjusted green sample coating in the dry state using the methods disclosed herein (middle row) and the method disclosed in WO 2022 / 122777 A1 (last row)). As can be seen in the first row, there is a significant color difference between the green sample coating and the green reference coating. This is caused by the fact that a reduced amount of colorant is used to prepare the green sample coating material to avoid exceeding the colorant concentration. The second row illustrates that compared to a color prediction method (e.g., the color prediction method described in WO 2022 / 122777 A1) that does not use the correction term determined according to the method disclosed herein (e.g., determined according to Figures 1 to 3C ), if the correction term is used to predict color data using a color prediction model (e.g., as described with respect to Figure 4A and Figure 4B ), the use of the term results in a significant reduction in the color difference. The large color difference between the predicted color data and the color data of the green reference coating may lead to incorrect prediction of further necessary adjustments to bring the color difference below a predefined threshold. In contrast, the significantly lower color difference obtained with the methods disclosed herein allows for more reliable prediction of the color of a coating existing in a second physical condition (such as the dry state) using input data obtained in a first physical condition (such as the wet state). The improved accuracy allows for a significant reduction in the amount of ejecta (e.g., dried coating) that needs to be prepared to determine whether the adjustments calculated using the predicted color data are accurate enough.

[0300] Figure 11A Another graph 1102 is shown, which contains the measured reflection spectrum 1104 of the blue reference coating existing in the dry state, the measured reflection spectrum 1106 of the adjusted blue sample coating material existing in the wet state, the predicted reflection spectrum 1108 of the adjusted blue sample coating material for the dry state using the method described in WO 2022 / 122777 A1, and the measured reflection spectrum 1110 of the adjusted blue sample coating existing in the dry state and prepared from the adjusted blue sample coating material. The adjusted blue sample coating formulation can be determined using the method described in WO 2022 / 122777 A1 and can be used to prepare the adjusted blue sample coating, as described with respect to Figure 10A . The deviation between the reflection spectra 1104, 1110 of the blue reference coating and the adjusted blue sample coating is also reflected in the color data shown in Figure 11C Table 1114.

[0301] Figure 11B shows another graph 1112 that includes information about Figure 11A the color data of the described blue reference coating and the adjusted blue sample coating. The graph includes the measured reflection spectrum 1104 of the blue reference coating present in the dry state, the measured reflection spectrum 1106 of the adjusted blue sample coating material present in the wet state, the predicted reflection spectrum 1108 of the adjusted blue sample coating material for the dry state using the method described about Figures 1 to 6 and the measured reflection spectrum 1110 of the adjusted blue sample coating in the dry state. In graph 1112, there is no detectable deviation between the measured reflection spectrum 1104 of the blue reference coating, the measured reflection spectrum 1110 of the adjusted blue sample coating, and the predicted reflection spectrum 1108 of the adjusted blue sample coating.

[0302] Figure 11C shows another table 1114 that includes Figure 11A and Figure 11B the color data shown in (i.e., the color data of the blue reference coating measured in the dry state (i.e., for the cured blue reference coating prepared by applying the (multiple) blue reference coating materials to a substrate and drying and / or curing the applied (multiple) blue reference coating materials), and the color difference comparison of the color data predicted for the blue sample coating (first row) or for the adjusted blue sample coating in the dry state using the method disclosed herein (middle row) and the method disclosed in WO 2022 / 122777 A1 (last row)). As can be seen in the first row, the blue sample coating has a significant color difference compared to the blue reference coating. The second row illustrates that, compared to a color prediction method that does not use the correction term determined according to the method disclosed herein (e.g., the color prediction method described in WO 2022 / 122777 A1) (e.g., determined according to Figures 1 to 3C ), if the correction term is used for predicting color data using a color prediction model (e.g., as described about Figure 4A and Figure 4B ), the use of the term results in a significant reduction in the color difference.

[0303] Figure 12AShows yet another graph 1202 that includes the measured reflection spectrum 1204 of another green reference coating present in the dry state, the measured reflection spectrum 1206 of another adjusted green sample coating material present in the wet state, the predicted reflection spectrum 1208 of the adjusted green sample coating material using the method described in WO 2022 / 122777 A1, and the measured reflection spectrum 1210 of the adjusted green sample coating prepared from the adjusted blue sample coating material and present in the dry state. The adjusted blue sample coating formulation can be determined using the method described in WO 2022 / 122777 A1 and can be used to prepare the adjusted blue sample coating as described with respect to Figure 10A The deviation between the reflection spectra 1210, 1204 of the green reference coating and the adjusted green sample coating is also reflected in the color data shown in Figure 12C Table 1214.

[0304] Figure 12B Shows yet another graph 1212 that includes the color data for the green reference coating and the adjusted green sample coating described with respect to Figure 12A The graph includes the measured reflection spectrum 1204 of the green reference coating present in the dry state, the measured reflection spectrum 1206 of the adjusted green sample coating material present in the wet state, the predicted reflection spectrum 1208 of the adjusted green sample coating material for the dry state using the method described with respect to Figures 1 to 6 and the measured reflection spectrum 1210 of the adjusted green sample coating in the dry state. In graph 1212, there is no detectable visual deviation between the measured reflection spectrum 1204 of the green reference coating, the measured reflection spectrum 1210 of the adjusted green sample coating, and the predicted reflection spectrum 1208 of the adjusted green sample coating.

[0305] Figure 12C Shows yet another table 1214 that includes the color difference comparison of the color data shown in Figure 12A and Figure 12B (i.e., the color data of the green reference coating measured in the dry state (i.e., for the cured green reference coating prepared by applying the (multiple) green reference coating materials to the substrate and drying and / or curing the applied (multiple) green reference coating materials), and the color data predicted for the green sample coating (first row) or for the adjusted green sample coating in the dry state using the methods disclosed herein (middle row) and the method disclosed in WO 2022 / 122777 A1 (last row)). As can be seen in the first row, there is a significant color difference between the green sample coating and the green reference coating. The second row illustrates the comparison with the color difference without using the method determined according to the disclosure herein (e.g., according toFigures 1 to 3C Compared with a color prediction method for a determined correction term (e.g., the color prediction method described in WO 2022 / 122777A1), if the correction term is used to predict color data using a color prediction model (e.g., as described regarding Figure 4A and Figure 4B ), using the term results in a significant reduction in color difference.

[0306] In summary, when input data of a coating present under a first physical condition (such as a wet state) is used for color prediction, the methods, devices, and computer elements disclosed herein allow for a more accurate prediction of the color data of the same coating present under a second physical condition (such as a dry state). The more accurate prediction of color data using the correction term (which allows transformation of the systematic error of the color prediction model from one physical condition to another) allows for a more accurate determination of the adjusted sample coating formulation necessary to achieve a coating that meets the color matching requirements (e.g., the color difference between the color data associated with an adjusted sample coating prepared according to the determined adjusted sample coating formulation and the color data of a reference coating is below a defined threshold) when compared to a reference coating.

[0307] The present disclosure has also been described in connection with preferred embodiments by way of example. However, other variations can be understood and achieved by those skilled in the art and those practicing the claimed invention by studying the drawings, the present disclosure, and the claims.

[0308] Any steps presented herein can be performed in any order. The methods disclosed herein are not limited to a particular order of these steps. Nor is it required that different steps be performed in a particular location, i.e., each step can be performed at different computing nodes using different devices / data processing.

[0309] In the claims and the specification, the word “comprising” or “including” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. A single element or other unit can perform the functions of several entities or items recited in the claims. The fact that certain measures are recited only in mutually different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous embodiment.

[0310] As used herein, “determine” also includes “initiate or cause to determine”, “generate” also includes “initiate and / or cause to generate”, and “provide” also includes “initiate or cause to determine, generate, select, send, and / or receive”. “Initiate or cause to perform an action” includes any processing signal that triggers a computing node or device to perform the corresponding action.

[0311] Any disclosure and embodiment described herein relates to the methods, apparatus, and computer program elements listed above, and vice versa. Advantageously, the benefits provided by any embodiment and example apply equally to all other embodiments and examples, and vice versa.

Claims

1. A computer-implemented method for providing a correction term for a color prediction model, the correction term being associated with an adjusted sample coating present under at least two different physical conditions, the method comprising: - receiving, by at least one processor via a communication interface, a request for providing: · a color difference (CD1) between the measured color data of the adjusted sample coating present under a first physical condition and the predicted color data of the adjusted sample coating present under the first physical condition; · a color difference (CD2) between the measured color data of the sample coating present under the second physical condition and the measured color data of the sample coating present under the first physical condition, the sample coating being associated with the adjusted sample coating; and · a color difference (CD3) between the predicted color data of the adjusted sample coating present under the second physical condition and the predicted color data of the adjusted sample coating present under the first physical condition; and - in response to the received request, using the at least one processor to determine the correction term for the color prediction model using the provided color differences (CD1) to (CD3); and - providing, via the communication interface, the determined correction term for the color prediction model.

2. The computer-implemented method according to claim 1, wherein, The first physical condition includes a wet state or a physical condition associated with a first application process; and / or wherein the second physical condition includes a dry state or a physical condition associated with a second application process.

3. The computer-implemented method according to claim 1 or 2, wherein, The color data includes: reflectance data; color space data such as CIEL*a*b* values or CIEL*C*h* values; glossiness data; texture parameters such as texture characteristics and / or roughness characteristics; or a combination thereof.

4. The computer-implemented method according to any one of the preceding claims, wherein, Providing the predicted color data of the adjusted sample coating present under the first physical condition includes - receiving model input data, the model input data including adjusted sample coating formulation data and optical data of individual color components associated with the first physical condition, - receiving a color prediction model, the color prediction model being configured to predict the color data of the coating using the coating formulation data and the optical data of individual color components, and - using the received color prediction model and the received model input data to predict the color data.

5. The computer-implemented method according to claim 4, wherein, Providing the predicted color data of the adjusted sample coating present under the first physical condition further includes taking into account a systematic error of the color prediction model associated with the first physical condition.

6. The computer-implemented method according to any one of the preceding claims, wherein, Providing the predicted color data of the adjusted sample coating present under the second physical condition includes - receiving model input data, the model input data including adjusted sample coating formulation data and optical data of individual color components associated with the second physical condition, or including adjusted sample coating formulation data, optical data of individual color components associated with the first physical condition, and condition adaptation parameters associated with the difference between the first and second physical conditions of the sample coating, - A received color prediction model configured to predict color data of a coating using coating formulation data, optical data of individual color components, and optionally condition adaptation parameters, and - Using the received color prediction model and the received model input data to predict the color data.

7. The computer-implemented method according to claim 6, wherein, These condition adaptation parameters are pre-configured and / or calculated using a method configured to optimize the condition adaptation parameters by minimizing a cost function starting from a given set of initial condition adaptation parameters, and a color prediction model configured to predict the color data of these coatings present under the first physical condition by using the formulation of the coatings, the specific optical data of the individual color components present within these coatings' formulations, and the condition adaptation parameters generated by the method as input data.

8. The computer-implemented method according to claim 6 or 7, wherein, Providing the predicted color data of the adjusted sample coating present under the second physical condition further includes taking into account the systematic error of the color prediction model associated with the second physical condition.

9. The computer-implemented method according to any one of the preceding claims, wherein, Determining the correction of the color prediction model using the provided color differences (CD1) to (CD3) according to formula (I): (I), where the numerator of the fraction corresponds to the color difference (CD2), and the denominator of the fraction corresponds to the color difference (CD3).

10. A computer-implemented method for determining the color data of an adjusted sample coating present under a second physical condition based on the color data of the adjusted sample coating present under a first physical condition, the method comprising: - Receiving, by at least one processor via a communication interface, a request providing: · The color difference between the measured color data of a sample coating present under the second physical condition and the predicted color data of the sample coating present under the second physical condition, the sample coating being associated with the adjusted sample coating, · The optical data of individual color components associated with the first physical condition, · Adjusted sample coating data, the adjusted sample coating data including the formulation of the adjusted sample coating, · Condition adaptation parameters associated with the difference between the first physical condition and the second physical condition of the adjusted sample coating, · A correction term of the color prediction model determined according to the method of any one of claims 1 to 9, · A color prediction model configured to predict the color of the adjusted sample coating present under the second physical condition by using the color difference, the optical data of individual color components, these condition adaptation parameters, the adjusted sample coating data, and the correction term as input data; And - In response to the request, using the at least one processor to determine the color data of the adjusted sample coating present under the second physical condition by using the color prediction model and the data provided in step (a); - Providing via the communication interface the determined color data of the adjusted sample coating present under the second physical condition.

11. A computer-implemented method for determining a second adjusted sample coating formulation to match the color of a reference coating present under a second physical condition based on color data of a first adjusted sample coating present under a first physical condition, the method comprising: - receiving, by at least one processor via a communication interface, a request providing: · a color difference between measured color data of a sample coating present under the second physical condition and predicted color data of the sample coating present under the second physical condition, the sample coating being associated with the first adjusted sample coating, · optical data of individual color components associated with the first physical condition, · reference coating data, the reference coating data including color data of the reference coating present under the second physical condition, · first adjusted sample coating data, the first adjusted sample coating data including the formulation of the first adjusted sample coating, · a condition adaptation parameter associated with a difference between the first physical condition and the second physical condition of the first adjusted sample coating, · a correction term of a color prediction model determined according to the method of any one of claims 1 to 9, · a color prediction model configured to predict the color of a second adjusted sample coating present under the second physical condition by using the color difference, the optical data of the individual color components, the reference coating data, the first adjusted sample coating data, the condition adaptation parameters, and the correction term as input data; and - in response to the request, using the at least one processor to determine a second adjusted sample coating formulation by using the color prediction model and the provided data; - providing, via the communication interface, the determined second adjusted sample coating formulation.

12. An apparatus comprising: one or more computing nodes; and one or more computer-readable media having computer-executable instructions that, when executed by the one or more computing nodes, cause the apparatus to perform the method of any one of claims 1 to 11.

13. Use of a correction term determined according to the method of any one of claims 1 to 9 for improving the accuracy of color data of an adjusted sample coating present under a second physical condition, the color data being predicted by a color prediction model based on color data of the adjusted sample coating present under a first physical condition.

14. A computer program element comprising instructions that, when executed by one or more computing nodes or a computing system, cause the (one or more) computing nodes or the computing system to perform the steps of the method of any one of claims 1 to 11.

15. A computer program element comprising instructions that, when executed by the apparatus of claim 13, cause the apparatus to perform the steps of the method of any one of claims 1 to 11.

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