Improved accuracy color prediction and color matching method and apparatus

Abstract

The present invention relates to a method and apparatus for determining correction terms for a color prediction model to enable reliable color prediction and color matching operations using input data determined under physical conditions different from 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 with improved accuracy due to the use of correction terms determined in accordance with the present disclosure.

Description

[Technical Field]

[0001] The present invention relates to a computer-implemented method for providing correction terms for a color prediction model, a computer-implemented method and apparatus for determining the color of an adjusted sample coating present under second physical conditions based on color data of the adjusted sample coating present under first physical conditions, an apparatus for determining a formula for a second adjusted sample coating based on color data of the first adjusted sample coating present under first physical conditions to match the color of a reference coating present under second physical conditions, and uses of the correction terms determined by the methods of the present invention, as well as computer program elements. [Background technology]

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

[0003] Adjusting the color of a sample coating formulation to match the color of a reference coating is an iterative process: starting with a preliminary sample coating formulation, the preliminary sample coating formulation must typically be adjusted several times until a tailored sample coating is found whose color sufficiently matches that of the reference coating, making the color adjustment process time-consuming and costly.

[0004] To reduce the time and costs associated with color tuning, computer-aided color prediction and color matching methods are now being used that are based on physical models that describe the interaction of light with scattering or absorbing media, such as colorants or pigments contained in coatings. The physical models can predict the light reflectance properties (e.g., color data) of a coating based on information about the coating material formulation used to prepare each coating, along with optical constants that describe the absorption and scattering properties of the formulation components, such as colorants or pigments, in the context of each physical model. The specific optical properties of the colorants can be determined from known coating formulation data and measured coating reflectance data based on the coating being present under defined physical conditions, such as dry physical conditions (e.g., dried and / or cured) or wet physical conditions (e.g., dried and uncured). Thus, color prediction and color matching methods that use the physical models and optical constants are always related to the physical conditions of the coating used to determine the optical constants.

[0005] However, the color tolerance of a reference coating is defined for a specific physical condition of the reference coating, such as a dry state (e.g., a dried and / or cured state), whereas a manufactured sample coating material may exist in a different physical condition, such as a wet state (e.g., a dry and uncured state). Because the optical properties, such as the reflectance characteristics, of a coating are highly dependent on the physical condition of the coating, for example, whether the coating is in a wet or dry state or the application process used to apply the coating material onto a substrate, color prediction and color matching methods that use the physical models and optical constants typically do not achieve high accuracy when using data from a sample coating that exists under a different physical condition than the reference coating.

[0006] Because of this lack of precision, the color of each adjusted coating associated with each adjusted sample coating formulation obtained in the color matching process must still be measured under the same physical conditions as the reference coating. Thus, for example, if the color data of a dry reference coating is to be used for comparison, each adjusted sample coating formulation must be applied to a substrate using the same application process as the reference coating and dried and / or cured to the same physical conditions before the color data of that adjusted sample coating is determined.

[0007] Therefore, there is a need to provide a color prediction and color matching method that provides more accurate results, thereby eliminating the need to prepare cured adjusted sample coatings each time a sample coating formula is adjusted during a color matching operation. Summary of the Invention [Problem to be solved by the invention]

[0008] It is therefore an object of the present disclosure to provide color prediction and color matching methods and apparatus that provide more accurate color prediction and color matching results, for example, when data from a sample coating or adjusted sample coating that exists under different physical conditions than a reference coating is used within the color prediction and / or color matching method. [Means for solving the problem]

[0009] In one aspect, the present disclosure relates to a computer-implemented method for providing a correction term to 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 the steps of: receiving, by at least one processor, via a communications interface, a request to provide: 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; 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, wherein the sample coating is relative to the adjusted sample coating; and 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.

[0010] determining, by the at least one processor in response to the request, a correction term for a color prediction model using the provided color differences (CD1) to (CD3); and Providing the determined correction terms for the color prediction model via the communication interface.

[0011] In a further aspect, the present disclosure relates to a computer-implemented method for determining the color of a conditioned sample coating present under a second physical condition based on color data of the conditioned sample coating present under a first physical condition, the method comprising the steps of: receiving, by at least one processor, via a communications interface, a request to provide: a color difference between the measured color data of the sample coating present under the second physical conditions and the predicted color data of the sample coating present under the second physical conditions, wherein the sample coating is relative to an adjusted sample coating; optical data of the individual color components related to a first physical condition; adjusted sample coating data, including adjusted sample coating recipes; a condition adaptation parameter related to the difference between the first physical condition and the second physical condition of the conditioned sample coating; a correction term for a color prediction model determined according to the computer-implemented method for providing a correction term for a color prediction model disclosed herein; and A color prediction model configured to predict the color of the adjusted sample coating present under a second physical condition by using the color difference, the optical data of the individual color components, the condition adaptation parameters, the adjusted sample coating data, and the correction terms as input data.

[0012] In response to the received request, determining, with the at least one processor, color data for the adjusted sample coating present under the second physical conditions using the color prediction model and the data provided in step (a); and Providing, via the communication interface, the determined color data of the adjusted sample coating present under the second physical conditions.

[0013] In a further aspect, the present disclosure relates to a computer-implemented method for determining a formula for a second adjusted sample coating to match the color of a reference coating present under second physical conditions based on color data of a first adjusted sample coating present under first physical conditions, the method comprising the steps of: receiving, by at least one processor, via a communications interface, a request to provide: a 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, said sample coating being relative to the first adjusted sample coating; optical data of the individual color components related to a first physical condition; reference coating data, including color data of the reference coating present under a second physical condition; first adjusted sample coating data including a formulation for the first adjusted sample coating; a condition adaptation parameter related to the difference between the first physical condition and the second physical condition of the first conditioned sample coating; a correction term for a color prediction model determined according to the computer-implemented method for providing a correction term for a color prediction model disclosed herein; and A color prediction model configured to predict the color of a second adjusted sample coating present under second physical conditions 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 terms as input data.

[0014] In response to the request, determining with at least one processor a second adjusted sample coating formula using the color prediction model and the data provided in step (a); and Providing the determined second adjusted sample coating formula via the communication interface.

[0015] In a further 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 thereon that, when executed by the one or more computing nodes, cause the apparatus to perform a computer-implemented method disclosed herein.

[0016] In a further aspect, the present disclosure relates to the use of correction terms determined in accordance with the computer-implemented methods disclosed herein to improve the accuracy of color data of an adjusted sample coating present under second physical conditions, the color data being predicted by a color prediction model based on color data of an adjusted sample coating present under first physical conditions.

[0017] In yet another aspect, the present disclosure relates to a computer program element, such as a computer-readable storage medium, computer program, or computer program product, that includes instructions that, when executed by one or more computing nodes, or computing systems, direct the computing nodes or computing systems to perform the steps of the computer-implemented methods disclosed herein.

[0018] In yet another aspect, the present disclosure relates to a computer program element, such as a computer-readable storage medium, computer program, or computer program product, that includes instructions that, when executed by an apparatus disclosed herein, direct the apparatus to perform the steps that the apparatus disclosed herein is configured to perform.

[0019] All disclosures and embodiments described herein relate to methods, apparatus, and computer program elements lined out above and below. Advantageously, benefits provided by any of the embodiments and examples apply equally to all other embodiments and examples.

[0020] The disclosed methods, devices, and computer program elements enable more accurate prediction of optical properties, such as the color of a prepared sample coating formulation, e.g., a prepared sample coating formulation that has already been applied at least once (e.g., by coloring a manufactured batch of the sample coating formulation at least once), 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 prepared sample coating present under a second physical condition, such as a wet state (e.g., dry and uncured). Thus, for example, the predicted color of the prepared sample coating present in the dry state more accurately matches the color of the reference coating present in the dry state, despite being based on data of the prepared sample coating present in the wet state.

[0021] The same is true for the color matching methods of the present disclosure, where an adjusted formulation of a sample coating can be more accurately calculated to match the optical properties of a reference coating present under a first physical condition (e.g., a dry condition) based on data related to the sample coating or previous adjustments of the sample coating present under a second physical condition (e.g., a wet condition), or vice versa.

[0022] The improved accuracy of the disclosed color prediction and color matching methods is obtained by determining a correction term for a physical model used in the color prediction and / or color matching operations. The correction term converts a systematic error of the physical model for a second state (e.g., a wet state) into a systematic error of the physical model for a first physical condition (e.g., a dry state), or vice versa. The conversion of the systematic error from the physical condition of the sample coating or adjusted sample coating to the respective physical condition of the reference coating can take into account the strong influence of the physical condition of the respective coating on optical properties such as reflectance characteristics, thereby significantly improving prediction and matching results.

[0023] The significantly improved prediction and matching results allow for a reduction in the amount of coated substrate (hereafter referred to as spray-outs) that must be prepared during color matching operations to ensure that the adjusted sample coating formulation results in optical properties within a predetermined tolerance range relative to the reference coating. Reducing the amount of spray-out required can save costs and increase the efficiency of the coating material manufacturing process. Furthermore, reducing the amount of spray-out improves the reproducibility of the optical properties of the adjusted sample coating by avoiding the impact of spray-out preparation on the optical properties of the resulting coating.

[0024] Furthermore, the color prediction and color matching method according to the present disclosure enables the automation of the coloring process in coating material production, where manufactured batches typically need to be colored to ensure sufficient color matching with their respective reference coatings. Because manufactured coating materials are typically in a wet state, the coloring process is also performed in a wet state. By accurately predicting the required coloring of a produced coating material batch using the color prediction and color matching method according to the present disclosure, production efficiency can be significantly improved by reducing or avoiding spray-out preparation to ensure a sufficient degree of color matching between the produced coating material batch and the reference coating, thereby reducing the cost and time associated with the production of pigmented coating materials. DETAILED DESCRIPTION OF THE INVENTION

[0025] In the following, the terms used in this specification and / or the technical field of the present disclosure will be outlined by means of embodiments and / or examples.When examples are provided, it should be understood that the present disclosure is not limited to these examples.All terms and definitions used in this specification are broadly understood and have common meanings.

[0026] In one embodiment, a correction term may refer to a term introduced into a physical model, such as a color prediction model, that is necessary to make the results obtained by the physical model match the measured results.

[0027] In one embodiment, a color prediction model may refer to a deterministic model based on physical laws configured to predict color data for a coating. The color prediction model may be based on physical laws that describe the light absorption and scattering properties of a pigment system, such as a pigment coating.

[0028] In embodiments, a coating may refer to the entire layer of coating material that is or has been applied to a substrate. Coatings can be characterized in more detail according to various references, such as the type of coating material (painting, lacquering, powder coating) or the type of application process (painting, spray coating, dip coating, casting coating, filler coating, etc.). Multiple coating layers can be prepared by applying each coating material to the substrate, for example, using one of the aforementioned application processes. After application, the coating material may form a continuous layer (e.g., a coating film) on the substrate, which may be dried and / or cured. When more than one coating material is applied to a 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.

[0029] In one embodiment, a reference coating may refer to a coating having defined properties, such as defined colorimetric properties. The reference coating may be prepared by applying at least one defined coating material, e.g., 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 include at least one colorant. In one embodiment, a sample coating may refer to a coating that is evaluated in comparison to a reference coating for at least one defined property, e.g., a colorimetric property. The sample coating can be prepared as described for the reference coating, e.g., by using the respective sample coating materials.

[0030] In one embodiment, an adjusted sample coating may refer to a sample coating in which at least one component present in the sample coating formulation has been altered at least once relative to the sample coating formulation (e.g., an unaltered sample coating formulation), e.g., by altering the amount and / or type of that component. The sample coating used as the basis for preparing an adjusted sample coating may be referred to as the "sample coating associated with the adjusted sample coating." A sequential number may be used in conjunction with the term "adjusted sample coating" to indicate the number of adjustments associated with the sample coating. For example, the term "first adjusted sample coating" refers to the first adjustment of the sample coating formulation, the term "second adjusted sample coating" refers to the second adjustment of the sample coating formulation, and so on. As used herein, the terms "formula," "color formula," and "coating formula" are used interchangeably.

[0031] In one embodiment, the physical condition may refer to the state of each coating, such as the reference coating, the sample coating, the adjusted sample coating of the first adjusted sample coating, or the second adjusted sample coating. The state may be a wet state or a dry state. The wet state may refer to a state in which each coating has not been dried and / or cured, for example, by using high temperatures. Thus, the wet state may refer to the formed coating material, for example, present in a measurement cell, and the dry state may refer to the dried and / or cured state of a coating formed from each coating material. The dry state may refer to the state of the coating after the organic solvent and / or water present in the coating material or film has evaporated after application of the coating material to a substrate. Drying may be performed at temperatures, for example, 15 to 35°C and / or at elevated temperatures, for example, 40 to 90°C. The coating material is fluid at least immediately after application and can form a uniform, smooth coating film by leveling. However, when the formed coating film is dried, the film no longer becomes fluid. However, the resulting coating may still be soft and / or tacky and undergo further significant changes in its properties, such as hardness or adhesion to a substrate, upon further exposure to curing conditions, as described below. The cured state may refer to a coating that undergoes no further significant changes in properties, such as hardness or adhesion to a substrate, upon exposure to curing conditions, such as elevated temperatures (e.g., 80-200°C) for 10-60 minutes. A cured coating, in contrast to a dried coating, is no longer soft or tacky but has been conditioned as a solid coating. This state may also be associated with certain application processes, such as spray coating, roll coating, brush coating, and spin coating.

[0032] In one embodiment, the coating process may refer to the application of a coating material to a substrate. The application of a coating material to a substrate may further include post-treatment of the applied coating material, for example, by drying and / or curing at elevated temperatures and / or extended periods of time. The application of a coating material to a substrate may be accomplished by various methods known in the art, such as spray coating, dip coating, roll coating, spin coating, electrocoating, etc.

[0033] In one embodiment, individual color components may refer to separate components 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 color pigments and effect pigments, binders, solvents, and additives, such as, for example, matting pastes.

[0034] 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 the individual color component are parameters of a physical model that can be determined by preparing a coating with a defined batch of pigment paste and determining the optical properties by measuring the reflectance spectrum of the prepared coating, for example, using a spectrophotometer. From the reflectance spectrum and corresponding formulation data, specific optical properties, such as the K / S constant, can be determined and assigned to each individual color component as optical data. The terms “individual color component optical data,” “individual color component optical data,” or “colorant optical data” are used interchangeably.

[0035] In one embodiment, the systematic error of a color prediction model may refer to limitations of the physical model and / or systematic errors in the optical data of the individual color components included in each coating formulation. Systematic errors in the optical data of the individual color components may result from differences in the colorant intensity characteristics of the pigment paste due to deviations in said characteristics from batch to batch due to variations in the raw materials (e.g., pigments) used to prepare the pigment paste. In one example, the systematic error of a color prediction model may represent the difference between the color data of a coating predicted by the color prediction model and the measured color data of that coating. In another example, the systematic error may 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 a coating / coating material predicted by the color prediction model for a second physical condition. The systematic error of a color prediction model may be adjusted to account for systematic errors associated with the color prediction of a sample coating or previous adjustments of the sample coating (e.g., previous systematic errors). Previous systematic errors can be accounted for, for example, by adding the systematic error to the predicted color of each adjusted sample coating. For example, when adjusting for systematic errors associated with the color prediction of an adjusted sample coating, the systematic errors associated with the sample coating used to prepare the adjusted sample coating (e.g., the difference between the measured color data of the sample coating and the predicted color data of the sample coating) are taken into account, for example, by adding the systematic errors to the predicted color data of the adjusted sample coating.

[0036] In one embodiment, the condition adaptation parameter may refer to a difference, such as a specific transfer function, between a first physical condition compared to a second physical condition (e.g., the difference between the wet and dry states of the respective coatings, or the difference between a first application process and a second application process). The condition adaptation parameter may include differences related to pigments, differences related to different physical conditions, and / or differences related to changes in appearance with changing physical conditions. Pigment-related differences may include effect flake orientation adaptation, color pigment effectiveness, and / or effect pigment effectiveness. Effect flake orientation adaptation allows for better or worse flake orientation in effect coatings (e.g., coatings consisting of at least one coating layer containing effect pigments) to be considered and can be used to adjust their lightness / color flop behavior. Color pigment effectiveness allows for consideration of high or low color pigment effectiveness to adjust for differences in color intensity of solid colorants that may be caused, for example, by shear effects or agglomerates. The effectiveness of an effect pigment can be used to account for whether it is more effective at adjusting for differences in the reflectivity of the effect pigment, which may be caused by, for example, overspray loss or settling / separation effects. Differences associated with different physical conditions can include light loss adaptations for coating materials present under wet conditions in a cuvette or measurement cell, and / or refractive index conversion terms between different physical conditions, such as wet and dry conditions. Differences associated with changes in appearance with changes in physical conditions can include corrections for components, such as mixing clears in coating materials present under wet conditions, that have a certain degree of opacity and become transparent with changes in physical conditions, such as upon drying and / or curing of the coating. The condition adaptation parameter can relate to the systematic error of a color prediction model associated with predicting the color of a coating formulation under one physical condition compared to predicting the color of the coating formulation under a second physical condition. This systematic error can be accounted for, for example, by adding the systematic error to the predicted color of each coating formulation.For example, when considering conditioned parameters related to the color prediction of the adjusted sample coating, this systematic error can be added to the predicted color data of the adjusted sample coating.

[0037] In one embodiment, a computing node may refer to any device or system that includes at least one physical, tangible processor and physical, tangible memory that can have computer-executable instructions executed by the processor thereon. A computing node may be, for example, a handheld device, production equipment, sensor, monitoring system, control system, home appliance, laptop computer, desktop computer, mainframe, data center, or even a device not traditionally considered a computing node, such as a wearable (e.g., eyeglasses, watch, etc.). The memory may be in any form, depending on the nature and form of the computing node.

[0038] In embodiments, a processor may refer to any circuit, such as any logic or quantum circuit, configured to perform the basic operations of a computer or system, and / or generally to a device configured to perform computations or logical operations. In particular, a processor or computer processor may be configured to process the basic instructions that run a computer or system. It may be a semiconductor-based processor, a quantum processor, or other type of processor configured to process instructions. As an example, a processor may be or include a central processing unit ("CPU"). A processor may also be a graphics processing unit ("GPU"), a tensor processing unit ("TPU"), a complex instruction set computing ("CISC") microprocessor, a reduced instruction set computing ("CISC") microprocessor, a very long instruction word ("VLIW") microprocessor, or a processor implementing other instruction sets or a combination of instruction sets. The processing means may also be one or more special-purpose 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"), or a network processor. The methods, systems, and devices described herein may be implemented as software within a DSP, microcontroller, or other side processor, or as hardware circuitry within an ASIC, CPLD, or FPGA. The term processor may also refer to one or more processing devices, such as a distributed system of processing devices located across multiple computer systems (e.g., cloud computing), and is not limited to a single device unless otherwise specified.

[0039] In one embodiment, memory or data storage medium refers to physical system memory, which may be volatile, nonvolatile, or a combination thereof. Memory may include nonvolatile mass storage devices such as physical storage media. Memory may be a computer-readable storage medium such as RAM, ROM, EEPROM, CD-ROM, or other optical disk storage, magnetic disk storage, or other magnetic storage, non-magnetic disk storage such as solid-state disks, or any other physical and tangible storage medium that can be used to store desired program code means in the form of computer-executable instructions or data structures and that can be accessed by a computing system. Furthermore, memory may be a computer-readable medium (also called a transmission medium) that transmits computer-executable instructions. Furthermore, program code means in the form of computer-executable instructions or data structures may be automatically transferred from a transmission medium to a storage medium (or vice versa) upon reaching various computing system components. For example, computer-executable instructions or data structures received over a network or data link may be buffered in RAM in a network interface module (e.g., a "NIC") and then ultimately transferred to the computing system's RAM and / or a less volatile storage medium in the computing system. Thus, it should be understood that storage media can be included in computing components that also (or primarily) utilize transmission media.

[0040] In one embodiment, the computer-readable program instructions for carrying out the operations of the present disclosure may be either assembler instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source 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 execute entirely on the user's computer, partially on the user's computer as a standalone 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 scenario, the remote computer may be connected to the user's computer via 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., via the Internet using an Internet Service Provider). In some embodiments, electronic circuits, including, for example, programmable logic circuits, field programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), can utilize the state information of the computer-readable program instructions to execute the computer-readable program instructions and personalize the electronic circuit to carry out aspects of the present invention. In one embodiment, the computer-readable program instructions may be downloaded from a computer-readable storage medium to a respective computing / processing device, or may be downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network.The network may include copper transmission cables, optical fiber transmission cables, wireless transmission cables, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device can receive computer-readable program instructions from the network and forward the computer-readable program instructions for storage in a computer-readable storage medium in each computing / processing device.

[0041] In one embodiment, a communication interface may refer to a software and / or hardware interface for establishing communication, such as the transfer or exchange of signals or data. The software interface may be, for example, a function call or an API. The communication interface may include a transceiver and / or a receiver. 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, such as, for example, a short-range communication protocol, such as Bluetooth® or WiFi, or a long-range communication protocol, such as, for example, a cellular or mobile network, such as a second-generation cellular network (“2G”), 3G, 4G, LTE (Long-Term Evolution), or 5G. Alternatively, or in addition, the communication interface may be based on a proprietary short-range or long-range protocol. The communication interface may support any one or more standard and / or proprietary protocols.

[0042] In one embodiment, a database may refer to a collection of related information that can be searched and retrieved. A database may be a retrievable electronic document, such as a numeric, alphanumeric, or text document, a retrievable PDF document, a Microsoft Excel® spreadsheet, or any other database commonly known in the art. A database may be a collection of electronic documents, photographs, images, diagrams, data, or drawings residing on a computer-readable storage medium that can be searched and retrieved. A database may be a single database, a collection of related databases, or a collection of unrelated databases. Related databases may include databases that contain at least one common information element that can be used to associate such databases in related databases.

[0043] The manufacturing process for a coating of a given color typically begins with an initial or sample coating material formula, such as a formula loaded from a database. Next, an initial batch of coating material is manufactured according to this initial coating material formula by adding at least one pigment paste (hereinafter also referred to as colorant) to a base varnish containing a binder, a solvent, and optionally additives. The pigment paste is an intermediate product containing color-imparting components (such as pigments) in a matrix (typically a binder, a solvent, and optionally additives). The initial coating material formula typically contains a smaller amount of color-imparting components than the final coating material formula to prevent the resulting batch of coating material from being too dark due to the use of too many color-imparting components. After manufacturing, the corresponding color data of the manufactured coating material batch is measured under the same physical conditions as the reference coating and compared with the color data of a reference coating that exists under defined physical conditions, such as a dry state, or is manufactured by a defined application method, such as spray application. Instead of measuring the color data of the manufactured batch, the color data of a previously manufactured batch of the same coating material may be used for comparison with the reference coating, as long as 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 usually has a significant residual color difference compared to the reference coating. Therefore, in a subsequent color adjustment process, the initial coating material formula must be modified so that the residual color difference between the adjusted color data of the sample coating and the color data of the reference coating is below a defined threshold.

[0044] The adjusted sample coating formula can be calculated from the sample coating formula and the color data of the sample coating and reference coating using a color prediction model. However, the color data of the adjusted sample coating in the wet state can differ significantly from the color of the adjusted sample coating in the dry state. This also applies when the adjusted sample coating is applied to a substrate using different application processes, such as spray application and roll application.

[0045] When color data of a sample coating adjusted under different physical conditions from the reference coating, such as color data obtained in a wet state immediately after adjusting a manufactured batch of sample coatings, is used in a color prediction or color adjustment process, the physical conditions typically have a significant effect on the color data, resulting in a significant discrepancy between the color data predicted for the adjusted sample coating under the physical conditions associated with the reference coating and the color data measured for the adjusted sample coating under the physical conditions associated with the reference coating. Therefore, it is usually necessary to prepare an adjusted sample coating from the adjusted sample coating material that matches the physical conditions associated with the reference coating, measure the color data of the prepared adjusted sample coating, and compare it with the color data of the reference coating to ensure a satisfactory color match. However, this procedure is time-consuming, involves high costs, and increases the manufacturing time of the colored coating material.

[0046] Therefore, it is highly desirable to provide methods and apparatus that provide more accurate color prediction and color matching results when data from sample coatings or adjusted sample coatings that exist under different physical conditions than the reference coating is used for color prediction and / or color matching. Such methods and apparatus can reduce or avoid the need to prepare adjusted sample coatings that match the physical conditions associated with the reference coating to ensure adequate color matching.

[0047] These and other objects that will become apparent on reading the following description are solved by the subject matter of the independent claims. The dependent claims refer to embodiments of the present disclosure.

[0048] In one embodiment, the color prediction model is configured to predict color data of a coating based on input data, the input data including coating formulation data and optical data of individual color components. The coating formulation data may include data regarding the components and amounts of the components present in the coating material used to prepare the coating. The component-related data can be used to determine the optical data of each individual color component for use in predicting the color data. Such color prediction models are well known in the art, as described, for example, in Georg A. Klein; Farbenphysik fuer industrielle Anwendungen; Chapter 7 - Farbrezept-Berechnung, June 2004.

[0049] The optical data for the individual color components may include the optical constants of the individual color components, such as the wavelength-dependent scattering and absorption properties of the individual color components, which may further include the orientation of the individual color components, such as effect pigments in a coating.

[0050] In one embodiment, the correction term includes a systematic error of the color prediction model when predicting the color data of the adjusted sample coating under a second physical condition based on input data related to the adjusted sample coating under a first physical condition. The systematic error may be due to the fact that, as mentioned above, the physical conditions of the coating significantly affect the color, and therefore the color data. The correction term can be taken into account, for example, by adding the correction term to the color of each coating formulation predicted by the color prediction model based on the input data. When input data related to a second physical condition is used to predict color data for a first physical condition, or vice versa, the predicted color data may deviate significantly from the observed color data due to the dependency of the color data on the physical condition. The correction term serves to at least partially correct for differences in color data resulting from the use of different physical conditions, such that the color data predicted by a color prediction model for a physical condition is more accurate when the correction term is used than when the correction term is not used. Thus, the correction term can improve the accuracy of the color data predicted by a color prediction model, even when the input data relates to physical conditions different from those of the "target coating" or reference coating. For example, the use of the correction term may result in more accurate predictions when the color data of a prepared sample coating present under dry conditions is used as input data related to a prepared sample coating present under wet conditions. This may result in fewer coatings being prepared from the prepared sample coating material in order to accurately calculate further adjustments to the prepared sample coating, further formulation adjustments, etc., so that the color of the resulting coating from the prepared sample coating material sufficiently matches the color of the reference coating used for comparison.

[0051] In one embodiment, the first physical condition includes a wet state or a physical condition associated with a first application process. The first application process may be a commonly used application process for applying a coating material to at least a portion of a substrate surface. Suitable application processes include, for example, dipping, bar coating, spraying, or rolling. Spray application includes spray application methods such as compressed air spray (pneumatic application), airless spray, high-speed spin, electrostatic spray application (ESTA), and optionally hot spray application, such as hot air spray application.

[0052] In one embodiment, the second physical conditions include dry conditions or physical conditions associated with a second coating process. The second coating process is different from the first coating process. For example, the first coating process may be a bar coating or dip coating process, and the second coating process may be a spray coating process, or vice versa.

[0053] In one embodiment, the color data includes reflectance data, color space data such as CIEL*a*b* values ​​or CIEL*C*h* values, gloss data, texture parameters such as texture and / or roughness characteristics, or a combination thereof. Color data such as reflectance data can be determined using a multi-angle spectrometer. Color space data, such as CIEL*a*b* values, may be calculated from the acquired reflectance data and an illuminant radiance function (see, e.g., ASTM E2194-14(2017) and ASTM E2539-14(2017)). Texture parameters may be determined from texture images acquired under defined lighting conditions and at defined angles. Texture parameters may be calculated from the acquired images. Examples of such calculated texture parameters include the texture values ​​Gdiff (also known as graininess or roughness or roughness value or roughness characteristic) that describe the roughness characteristics of a coating layer under diffuse lighting conditions, and the Si (glow intensity) and Sa (glow area) that describe the brilliance characteristics of a coating layer under directional lighting conditions, as introduced by Byk-Gardner ("The Gesamtfarbeindruck objektiv messen", Byk-Gardner GmbH, JOT 1.2009, vol. 49, issue 1, pp. 50-52). The texture parameters introduced by Byk-Gardner are determined from grayscale images. Texture parameters can also be determined from color images, as introduced by X-Rite with their multi-angle spectrophotometers MA-T6 and MA-T12.

[0054] In one embodiment, providing predicted color data of the adjusted sample coating present under the first physical conditions includes:

[0055] receiving model input data including adjusted sample coating formulation data and optical data for individual color components associated with a first physical condition; receiving a color prediction model configured to predict color data of the coating using coating formulation data and optical data of individual color components; Predicting the color data using the received color prediction model and the received model input data.

[0056] The model input data may be received via a communications interface. The model input data may be stored in a data storage medium, such as a database, and may be acquired by the at least one processor based on data associated with the prepared sample coating, such as the ID of the prepared sample coating. The prepared sample coating formulation data may include data regarding components and amounts of components present in the prepared sample coating material. The optical data may be acquired from the data storage medium based on the components present in the prepared sample coating material.

[0057] The color prediction model can predict color data associated with the adjusted sample coating material using the formula data as well as optical data associated with components present in 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 wet conditions (i.e., the data was determined from a coating present under wet conditions), the color data predicted by the color prediction model is also associated with wet conditions, 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.

[0058] Providing predicted color data for the adjusted sample coating present under the first physical condition may further include considering a systematic error of the color prediction model associated with the first physical condition. The systematic error of the color prediction model may be considered as a constant between color predictions performed by the color prediction model. By considering the systematic error of the color prediction model, the accuracy of the predicted color data may be improved. The systematic error of the color prediction model associated with the first physical condition can be determined by determining the difference between:

[0059] measured color data of the sample coating present under a first physical condition; Predicted color data for a sample coating present under a first physical condition.

[0060] The measured color data of the sample coatings present under the first physical conditions can be obtained by preparing sample coatings from each sample coating material and measuring the color data of the prepared sample coatings, for example, using a multi-angle spectrophotometer as described above.

[0061] The color data of the sample coating present under the first physical condition can be predicted using the aforementioned color prediction model and the sample coating's formulation and optical data associated with the first physical condition as input data for the color prediction model. 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 include the use of a measurement cell for the liquid sample coating material, such as a glass cuvette or glass pane.

[0062] The systematic error of the color prediction model associated with the first physical condition can be determined by determining the difference between:

[0063] Measured color data of the adjusted sample coating present under a first physical condition; and Predicted color data for the adjusted sample coating present under a first physical condition.

[0064] The measured color data of the adjusted sample coating can be determined as described above. The color data of the adjusted sample coating can be predicted using a color prediction model, the formulation data of the adjusted sample coating, and the optical data, as described above.

[0065] In one embodiment, providing predicted color data of the adjusted sample coating present under the second physical conditions includes:

[0066] receiving model input data including formulation data of the adjusted sample coating and optical data of the individual color components associated with a second physical condition, or including formulation data of the adjusted sample coating, optical data of the individual color components associated with the first physical condition, and condition adaptation parameters associated with a difference between the first physical condition and the second physical condition of the sample coating; receiving a color prediction model configured to predict color data of the coating using coating formulation data, optical data of individual color components, and optionally condition adaptation parameters; Predicting the color data using the received color prediction model and the received model input data.

[0067] The model input data may be received via a communications interface, as described above. For example, the adjusted sample coating formula data may be stored in 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 formula data may include data regarding the components and amounts of the components present in the adjusted sample coating material. Optical data may be retrieved from the data storage medium based on the components present in the adjusted sample coating material.

[0068] The optical data may be associated with a second physical condition, such as a dry state. In this case, the color prediction model can use the formulation data, as well as optical data associated with components present in the prepared sample coating material, to predict color data associated with the prepared sample coating material existing in a dry state. Because the optical data used for color prediction also relates to the second state, the predicted color data may relate to the second state. The predicted color data may be reflectance data. The predicted color data may be color space data, such as CIEL*a*b* values ​​or CIEL*C*H* values.

[0069] The optical data may be associated with a first physical condition, such as a wet condition. In this case, the condition adaptation parameter may be used to adapt the color prediction performed by the color prediction model using the optical data associated with the wet condition to a dry condition. This allows the same optical data to be used regardless of the physical condition in which the color prediction is performed, thereby reducing the amount of sample that needs 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.

[0070] The condition adaptation parameters may be preset (i.e., predefined) and / or calculated based on input data of the sample coating using a method configured to optimize the condition adaptation parameters by minimizing a cost function starting from a predetermined set of initial condition adaptation parameters, and a color prediction model configured to predict color data of the sample coating present under the first physical condition using as input data the sample coating formulation, optical data of individual color components associated with the first physical condition, and the condition adaptation parameters obtained from the method. The color prediction model may be a color prediction model described above. The condition adaptation parameters determined for the sample coating may correspond to the condition adaptation parameters associated with the adjusted sample coating. This allows the condition adaptation parameters to be determined from readily available data for the sample coating, avoiding the need to provide additional input data and / or perform additional calculations to obtain the input data necessary to determine the condition adaptation parameters of the adjusted sample coating.

[0071] The cost function can include a color distance between measured color data of the sample coating present under the second physical condition and color data of said sample coating predicted by the color prediction model.

[0072] The condition adaptation parameters can be calculated by recursively comparing the predicted color data of the sample coating for a second physical condition with the measured color data of the sample coating until a predetermined cost function falls below a predetermined threshold. This can determine the condition adaptation parameters necessary to account for the use of optical data associated with the first physical condition when predicting the color data of the adjusted sample coating present under the second physical condition. For example, the condition adaptation parameters can be used to account for the use of optical data associated with a wet state (i.e., determined from the coating being in a wet state) when predicting the color data of the adjusted sample coating present under a dry state.

[0073] Providing predicted color data of the adjusted sample coating present under the second physical conditions may further include considering a systematic error of the color prediction model associated with the second physical conditions. The systematic error may be considered as a constant while predicting the color data of the adjusted sample coating present under the second physical conditions using the color prediction model. The systematic error may be considered, for example, by adding the systematic error to the predicted color of the adjusted sample coating present under the second physical conditions.

[0074] The systematic error of the color prediction model associated with the second physical condition can be determined by determining the difference between:

[0075] measured color data of the sample coating present under a second physical condition; and Predicted color data for the sample coating present under a second physical condition.

[0076] The measured color data of the sample coatings present under the second physical condition can be obtained by preparing sample coatings from the respective sample coating materials and measuring the color data of the prepared sample coatings, for example, using a multi-angle spectrophotometer as described above. For example, the dried sample coatings can be prepared by applying the sample coating material to a substrate and drying and / or curing the applied sample coating material to obtain the dried sample coating.

[0077] The color data of the sample coating as it exists under the second physical condition can be predicted using a color prediction model as described above.

[0078] In one embodiment, a correction term for a color prediction model using the provided color differences (CD1) to (CD3) is determined according to formula (I):

[0079]

number

[0080] In this formula (I), the numerator of the fraction corresponds to the color difference CD2 and the denominator of said fraction corresponds to the color difference CD3.

[0081] CD1 in formula (I) can be determined according to formula (Ia):

[0082]

number

[0083] In one embodiment, the color difference may correspond to a difference between measured data and / or predicted data. The color difference may correspond to color difference (CD1), color difference (CD2), and / or color difference (CD3). For example, color differences (CD1)-(CD3) may be determined using respective color data, such as measured color data and predicted color data (e.g., for color differences (CD1) and (CD2)), and / or predicted color data for first and second physical conditions (e.g., for color difference (CD3)).

[0084] In one embodiment, the adjusted sample coating data further includes data indicative of the adjusted sample coating, the layer structure of the adjusted sample coating, instructions for preparing the adjusted sample coating formula, price, or a combination thereof. The adjusted sample coating data can be obtained from a data storage medium. For example, data indicative of the adjusted sample coating can be provided to at least one processor, and the processor can obtain the data using the received data. The data indicative of 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 adjusted sample coating formula can include mixing instructions.

[0085] In one embodiment, providing determined color data of the adjusted sample coating present under the second physical conditions includes providing the determined color data, optionally in combination with additional data, for display via a communications interface. The determined color data may be provided to a display device including a screen. Examples of additional data displayed with the determined color data may include data included in the adjusted sample coating data, condition adaptation parameters, correction terms, or a combination thereof.

[0086] The display device may include a housing that houses at least one processor that performs the methods disclosed herein and a screen. The housing may be made of plastic, metal, glass, or a combination thereof.

[0087] The display device and the at least one processor may be configured as separate components; i.e., the display device may include a housing containing a screen but not the at least one processor that executes the steps of the methods disclosed herein. Thus, the at least one processor may reside separately from the display device, e.g., in an additional computer device connected to the display device via a communication interface to enable data exchange. The use of an additional computer processor external to the display device allows for the use of higher computing power than that provided by the display device's processor, thereby reducing the computation time required to execute the methods disclosed herein and thus the overall time it takes for the calculated color data to be displayed on the display device screen. This allows for ad-hoc display of calculated color data without requiring a display device with high computing power. The additional computer processor may be located on a server, allowing the methods disclosed herein to be executed in a cloud computing environment. In this case, the display device may function as a client device connected to the server via a network and used to provide input data.

[0088] Display devices can be mobile or stationary. Stationary display devices include computer monitors, television screens, and projectors. Mobile display devices include laptops or handheld devices such as smartphones and tablets.

[0089] The display device screen can be constructed according to any emissive or reflective display technology with an appropriate resolution and color gamut. Suitable resolutions include, for example, 72 dots per inch (dpi) or higher, such as 300 dpi, 600 dpi, 1200 dpi, 2400 dpi, or higher. This ensures high-quality display of the generated appearance data. A suitable wide color gamut is the standard red-green-blue (sRGB) color gamut or higher. In various embodiments, the screen can be selected to have a color gamut that is close to the color gamut perceptible by human vision. In one aspect, the display device screen is constructed according to liquid crystal display (LCD) technology, particularly a liquid crystal display (LCD) technology that further includes a touchscreen panel. The LCD may be backlit by any suitable illumination source. However, the color gamut of an LCD screen can be expanded or otherwise improved by selecting a light-emitting diode (LED) backlight or backlight. In another aspect, the display device screen is constructed according to light-emitting polymer or organic light-emitting diode (OLED) technology. In yet another aspect, the display device screen can be constructed according to a reflective display technology, such as electronic paper or ink. Known manufacturers of electronic ink / paper displays include E INK and XEROX. Preferably, the display device screen also has a reasonably wide field of view so as to produce an image that does not wash out or change significantly when a user views the screen from different angles. Because LCD screens operate using polarized light, some models exhibit a high degree of viewing angle dependency. However, various LCD structures have relatively wide fields of view and may be preferred for this reason. For example, LCD screens constructed according to thin-film transistor (TFT) technology may have a suitably wide field of view. Also, screens constructed according to electronic paper / ink or OLED technology may have a wider field of view than many LCD screens and may be selected for this reason.

[0090] The display device may include interaction elements to facilitate user interaction with the display device. The interaction elements may be input or input / output devices, particularly physical interaction elements such as a mouse, keyboard, trackball, touchscreen, or combinations thereof. The interaction elements may be used to provide input data or to mimic further actions, as described below.

[0091] Based on the color data of the adjusted sample coating present under a first physical condition, the color data of the adjusted sample coating present under a second physical condition can be determined using a color prediction model. The color prediction model can receive as input data:

[0092] a color difference between the measured color data of the sample coating present under the second physical conditions and the predicted color data of the sample coating present under the second physical conditions, wherein the sample coating is relative to an adjusted sample coating; optical data of the individual color components related to a first physical condition; adjusted sample coating data, including adjusted sample coating recipes; a condition adaptation parameter related to the difference between the first physical condition and the second physical condition of the conditioned sample coating; Correction term for the color prediction model mentioned above.

[0093] The color prediction model can be configured to predict the color of the adjusted sample coating by the following method.

[0094] predicting color data of the adjusted sample coating based on the optical data of the individual color components, the condition adaptation parameters, and the adjusted sample coating data; Adding color differences and correction terms to the predicted color data.

[0095] The color difference and correction term may relate to a systematic error of the color prediction model associated with predicting the color of the adjusted sample coating present under a second physical condition based on color data of the adjusted sample coating present under a first physical condition. Such systematic error may be added to the color (e.g., color data) predicted by the physical model based on the adjusted sample coating's formula, the optical data of the individual color components, and the condition adaptation parameters.

[0096] In one embodiment, the 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 comprises the steps of:

[0097] providing color data of the reference coating present under a second physical condition; calculating a color difference between the determined color data of the adjusted sample coating present under the second physical conditions and the provided color data of the reference coating present under the second physical conditions; and Optionally, providing the calculated color difference via a communication interface.

[0098] The color data of the reference coating may be provided by retrieving the color data from a data storage medium. For example, data indicative of the reference coating may be provided, and the color data of the reference coating may be retrieved based on the provided data. The data indicative of the reference coating may include a color number, a color code, a barcode, a unique database ID associated with the reference coating, or a combination thereof.

[0099] The color difference can be calculated using a color tolerance equation, which may be selected from the Delta E (CIE 1994) color tolerance equation, the Delta E (CIE 2000) color tolerance equation, the Delta E (DIN 99) color tolerance equation, the Delta E (CIE 1976) color tolerance equation, the Delta E (CMC) color tolerance equation, the Delta E (Audi 95) color tolerance equation, the Delta E (Audi 2000) color tolerance equation, or other color tolerance equations.

[0100] The calculated color differences may be provided for display via a communications interface, as previously described.

[0101] In one embodiment, the computer-implemented method for determining the color of an adjusted sample coating present under second physical conditions based on color data of the adjusted sample coating present under first physical conditions further includes initiating at least one action related to the calculated color difference. This may include comparing the calculated color difference to a predefined threshold and initiating an action based on the calculation. For example, an action may be initiated if the calculated color difference is above or below the predefined threshold. The action initiated may depend on the result of the comparison. For example, one or more actions may be associated with the calculated color difference being less than the predefined threshold, while a different action may be associated with the calculated color difference being equal to or greater than the predefined threshold. The action associated with the calculated color difference being equal to or greater than the predefined threshold may be initiating a modification of the adjusted sample coating formula to minimize the color difference relative to the reference coating, as described later in connection with the method for determining a second adjusted sample coating formula. The at least one action may be initiated by a user or by at least one processor.

[0102] Initiating at least one operation may optionally include providing the adjusted sample coating formula to a printing device and / or a data storage medium and / or a filling line after determining whether the calculated color difference is equal to or less than a predefined threshold. For example, a determined color difference equal to or less than a predefined threshold may indicate that the color difference between the reference coating and the sample coating is sufficiently low, i.e., that the quality of the sample coating in terms of color / appearance is sufficiently high for the sample coating to meet the predefined reference. This initiates production of the adjusted sample coating according to the adjusted sample coating formula used to determine the color data. The produced adjusted sample coating material can be filled into a packaging unit used to transport the material to customers.

[0103] In one embodiment, determining the second adjusted sample coating formula comprises the following steps.

[0104] providing a method configured to adjust the concentration of at least one individual color component present in the first adjusted sample coating formula by minimizing a predetermined cost function starting from the concentrations of the individual color components included in the provided first adjusted sample coating data; and correcting the concentration of at least one individual color component present in the first adjusted sample coating formula using the provided method by comparing color data recursively predicted by the color prediction model using the first adjusted sample coating formula recursively corrected by the method with provided color data of the provided reference coating until the color difference falls below a predetermined threshold or the number of iterations reaches a predefined limit.

[0105] The first adjusted sample coating can correspond to the adjusted sample coating described above. The first adjusted sample coating is related to or associated with the sample coating. The relationship between the sample coating and the first adjusted sample coating can 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 can correspond to an adjusted sample coating obtained after modifying the adjusted sample coating formulation, for example, by changing the components and / or the amounts of the components of the adjusted sample coating formulation.

[0106] The provided data can correspond to data provided to the at least one computer processor via the communications interface prior to determining the second adjusted sample coating formula.

[0107] The method configured to adjust the concentration of at least one individual color component present in the first adjusted sample coating can be selected from the Levenberg-Marquardt algorithm (also known as LMA or LM), also known as the damped least squares (DLS) method. The method can be stored in a data storage medium, such as an internal memory of a computing device including at least one processor, or in a database connected to the at least one processor via a communication interface. The at least one processor can retrieve the method from the data storage medium when determining the second adjusted sample coating formula.

[0108] The color difference between the measured color data of the sample coating and the predicted color data of the sample coating can be considered as a constant during the adjustment of the concentration of at least one individual color component, thereby allowing the remaining systematic error of the color prediction model to be taken into account and improving the accuracy of the calculation of the second adjusted sample coating formula.

[0109] The cost function may be the color difference between the predicted color data of the recursively corrected first adjusted sample coating and the color data of the provided reference coating. The color difference may be calculated using the color tolerance equation described above. When the cost function is color difference, the predetermined threshold may preferably be a predetermined or predefined color difference.

[0110] The color data may be recursively predicted by a provided physical model using the provided color difference, the provided optical data of the individual color components, the provided condition adaptation parameters, the provided correction terms, and the recursively corrected first adjusted sample coating formula as input data. The color difference and correction terms may be added as systematic errors of the color prediction model to 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 corrected first adjusted sample coating formula. The provided physical model may predict color data, such as reflectance data of the first adjusted sample coating formula or the recursively corrected first adjusted sample coating formula, based on the input parameters. This prediction may be performed for each modification of the first adjusted sample coating formula until the cost function falls below a predetermined threshold or until a maximum limit of iterations is reached.

[0111] In one embodiment, providing the determined second adjusted sample coating formula comprises providing the determined formula, optionally in combination with further data, for display via a communications interface, which data may be displayed on a screen of a display device, as described above.

[0112] In one embodiment, the computer-implemented method for determining a second adjusted sample coating formula to match the color of a reference coating present under second physical conditions based on color data of a first adjusted sample coating present under first physical conditions further includes initiating at least one action associated with the determined second adjusted sample coating formula, the at least one action being initiated by a user or by the at least one processor.

[0113] Initiating the at least one operation can include providing the second adjusted sample coating formula to the printing device and / or the data storage medium and / or the mixing device. Providing the second adjusted sample coating formula to the mixing device can automatically prepare the second adjusted sample coating material based on the received second adjusted sample coating formula.

[0114] In one embodiment, the apparatus further comprises at least one of the following: a display device having a screen; at least one database including at least one of the color prediction model, optical data of the individual color components associated with the first physical condition, the reference coating data, the first adjusted sample coating data, condition adaptation parameters associated with a difference between the first physical condition and the second physical condition of the first adjusted sample coating, and determined correction terms for the color prediction model; a measurement device configured to measure color data of the sample coating and / or the reference coating present under a second physical condition; and A measurement device configured to measure color data of the sample coating and / or the conditioned sample coating present under a first physical condition.

[0115] The display device may be connected to one or more computing nodes of the device via a communications interface. The display device may be configured to display data determined or calculated by 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 disclosed herein. In yet another example, the display device may be configured to display a second adjusted sample coating formula determined according to the methods disclosed herein.

[0116] The at least one database may be connected to one or more computing nodes of the device via a communication interface. The measurement device may be connected to one or more computing nodes of the device via a communication interface.

[0117] The measurement device configured to measure color data of the sample coating and / or adjusted sample coating present under the first physical conditions may include a measurement cell that may be filled with the coating material present in a wet state as described above.

[0118] The measurement device configured to measure color data of the sample coating and / or the reference coating present under the second physical conditions may be a multi-angle spectrophotometer as described above. [Brief explanation of the drawings]

[0119] These and other features of the present invention are more fully described in the following description of exemplary embodiments of the invention. To easily identify the discussion of any particular element or act, the most significant digit or digits of a reference number refer to the figure number in which that element is first introduced. The same reference numbers in the drawings and this disclosure are intended to refer to the same or similar elements, components, and / or parts. This specification is presented with reference to the accompanying drawings. [Figure 1] FIG. 1 shows a flowchart of a method for providing a correction term to a color prediction model according to an exemplary embodiment of the present disclosure. [Figure 2A] FIG. 2A illustrates a flow chart of an aspect of block 102 of FIG. 1, according to an exemplary embodiment of the present disclosure. [Figure 2B] FIG. 2B illustrates a flowchart of an aspect of block 210 of FIG. 2A, according to an exemplary embodiment of the present disclosure. [Figure 3A] 3A and 3B show a flowchart of further aspects of block 102 of FIG. 1, according to an exemplary embodiment of the present disclosure. [Figure 3B] 3A and 3B show a flowchart of further aspects of block 102 of FIG. 1, according to an exemplary embodiment of the present disclosure. [Figure 3C] FIG. 3C illustrates a flowchart of an aspect of block 318 of FIG. 3B, according to an exemplary embodiment of the present disclosure. [Figure 4A] FIG. 4A shows 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 the adjusted sample coating present under a first physical condition, according to an exemplary embodiment of the present disclosure. [Figure 4B] FIG. 4B shows a flowchart of a further aspect of the method of FIG. 4A, according to an exemplary embodiment of the present disclosure. [Figure 5]FIG. 5 shows a flowchart of a method for determining a formula for a second adjusted sample coating to match the color of a reference coating present under second physical conditions based on color data of a first adjusted sample coating present under first physical conditions, according to an exemplary embodiment of the present disclosure. [Figure 6] FIG. 6 illustrates a flowchart of an aspect of block 504 of FIG. 5, according to an exemplary embodiment of the present disclosure. [Figure 7A] FIG. 7A shows a schematic diagram of an aspect of the method of FIG. 4A, according to an exemplary embodiment of the present disclosure. [Figure 7B] FIG. 7B shows a schematic diagram of an aspect of the method of FIG. 5, according to an exemplary embodiment of the present disclosure. [Figure 8] FIG. 8 illustrates an exemplary type of computing device that can be used to implement any aspect of the features illustrated in FIGS. 1 through 7B. [Figure 9] FIG. 9 is a diagram illustrating a client-server setup according to an exemplary embodiment of the present disclosure. [Figure 10AB] Figure 10A shows a graph including measured reflectance spectra of a reference coating present in a dry state, an adjusted sample coating batch present in a liquid state, an adjusted sample coating batch present in a liquid and dry state, and a reflectance spectrum of the adjusted sample coating batch present in a dry state predicted according to a color prediction method known in the art based on color data of the adjusted sample coating batch present in a liquid state. Figure 10B shows a graph including measured reflectance spectra of a reference coating present in a dry state, an adjusted sample coating batch present in a liquid and dry state, and a reflectance spectrum of the adjusted sample coating batch present in a dry state predicted according to a color prediction method of an exemplary embodiment of the present disclosure. [Figure 10C] FIG. 10C shows a table containing a comparison of the color differences of the color data shown in FIGS. 10A and 10B. [Figure 11AB]Figure 11A shows a graph including measured reflectance spectra of an additional reference coating present in a dry state, an additional adjusted sample coating batch present in a liquid state and a dried state, and a predicted reflectance spectrum of said adjusted sample coating batch in a dry state according to a color prediction method known in the art based on color data of said adjusted sample coating batch in a liquid state. Figure 11B shows a graph including measured reflectance spectra of an additional reference coating present in a dry state, an additional adjusted sample coating batch present in a liquid state and a dried state, and a predicted reflectance spectrum of said adjusted sample coating batch in a dry state according to a color prediction method of an exemplary embodiment of the present disclosure. [Figure 11C] FIG. 11C shows a table containing a comparison of the color differences of the color data shown in FIGS. 11A and 11B. [Figure 12AB] Figure 12A shows a graph including measured reflectance spectra of an additional reference coating present in a dry state, an additional adjusted sample coating batch present in a liquid state and a dried state, and a predicted reflectance spectrum of said adjusted sample coating batch in a dry state according to a color prediction method known in the art based on color data of said adjusted sample coating batch in a liquid state. Figure 12B shows a graph including measured reflectance spectra of an additional reference coating present in a dry state, an additional adjusted sample coating batch present in a liquid state and a dried state, and a predicted reflectance spectrum of said adjusted sample coating batch in a dry state according to a color prediction method of an exemplary embodiment of the present disclosure. [Figure 12C] FIG. 12C shows a table containing a comparison of the color differences of the color data shown in FIGS. 12A and 12B. [Example]

[0120] The detailed description set forth below is intended to describe various aspects of the present subject matter and is not intended to represent the only configurations in which the present subject matter 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 present subject matter. However, it will be apparent to those skilled in the art that the subject matter may be practiced without these specific details.

[0121] In some cases, the depiction of various components in a figure as separate units may reflect the use of corresponding separate physical and tangible components in an actual implementation. Alternatively, or in addition, any single component depicted in a figure may be implemented by multiple actual physical components. Alternatively, or in addition, the depiction of two or more separate components in a figure may reflect different functions performed by a single actual physical component.

[0122] Other figures illustrate concepts in flowchart form. In this format, certain operations are described as constituting separate blocks that are performed in a certain order. Such embodiments are exemplary and non-limiting. Certain blocks described herein may be performed together in a single operation, certain blocks may be broken down into multiple component blocks, and certain blocks may be performed in a different order than illustrated herein (including aspects in which blocks are performed in parallel). In one embodiment, blocks shown in the flowcharts associated with processing-related functions may be implemented by hardware logic circuitry, as described in connection with FIG. 8, which may in turn be implemented by one or more hardware processors and / or other logic components that include collections of task-specific logic gates.

[0123] With regard to terminology, the phrase "configured to" encompasses various physical and tangible mechanisms for performing a specified operation. The mechanisms may be configured to perform the operation using hardware logic circuitry, such as that described in connection with FIG. 8. The term "logic" similarly encompasses various physical and tangible mechanisms for performing a task. For example, each processing-related operation illustrated in a flowchart corresponds to a logical component for performing that operation. The logical component may perform that operation using hardware logic circuitry, such as that described in connection with FIG. 8. When implemented by a computing device, a logical component represents an electrical component that is a physical part of the computing system, however implemented.

[0124] The following description may identify one or more features as "optional." This type of statement should not be construed as an exhaustive list of features that may be considered optional. That is, other features may also be considered optional, even though not explicitly identified in the text. Moreover, a statement referring to a single entity is not intended to exclude the use of multiple such entities. Similarly, a statement referring to multiple entities is not intended to exclude the use of a single entity. Furthermore, while the specification may describe particular features as alternative ways of performing a specified function or implementing a specified mechanism, the features may also be combined together in any combination. Finally, the terms "exemplary" or "exemplary" refer to one embodiment of potentially multiple embodiments.

[0125] FIG. 1 illustrates an example method 100 for determining a correction term for a color prediction model, the correction term being associated with an adjusted sample coating under at least two different physical conditions. The correction term can be used to convert a systematic error of the color prediction model from a first adjusted sample coating condition to a second adjusted sample coating condition. The correction term may be taken into account when predicting color data using the color prediction model by adding the correction term to color data predicted by the color prediction model. This allows for more accurate prediction of color data for an adjusted sample coating under a second physical condition when input data for the color prediction model of an adjusted sample coating under a first physical condition is used. The first physical condition may be a wet condition. The second physical condition may be a dry condition. The adjusted sample coating may be associated with an adjusted sample coating material used to prepare the adjusted sample coating. The adjusted sample coating material may be associated with an adjusted sample coating formulation. The adjusted sample coating formula is obtained by modifying the sample coating formula at least once. For example, an adjusted sample coating formulation can be obtained using commonly known color matching operations using the color data of the sample coating formulation and the reference coating as input data, e.g., using the methods described in Georg Klein, "Farbenphysik fuer industrielle Anwendungen," supra. The sample coating material can correspond to a batch of coating material prepared according to a defined formulation recipe.

[0126] The method 100 may be performed by a computing system such as the system described in connection with FIG. 8, or may be performed by the server 902 of a client-server setup described in connection with FIG.

[0127] At block 102, a computing system performing the method 100 may receive a request to provide the following data: 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; 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, wherein the sample coating is relative to the adjusted sample coating; and 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.

[0128] The request may include data indicating initiation of method 100, i.e., determining a correction term, and the computing system may be configured to provide the data in response to the request. The request may be received by the computing system from an input / output device, such as I / O device 814 of FIG. 8 or client 908 of FIG. 9.

[0129] The computing system may be configured to determine the color difference (CD1), for example, as described in connection with FIG. 2A. The computing system may be configured to determine the color difference (CD2) by calculating said color difference from provided color data. The color data necessary to calculate the color difference (CD2) may be provided to the computing system via a communication interface. The color data necessary to calculate the color difference (CD2) may be obtained by the computing system based on a received identifier associated with the sample coating. The computing system may be configured to determine the color difference (CD3), for example, as described in connection with FIG. 3A and FIG. 3B.

[0130] In block 104, the computing system performing method 100 may, in response to the received request, determine a correction term for the color prediction model using the color differences provided in block 102. The correction term may be determined according to equations (I) and (Ia) above. The correction term may account for systematic errors in the color prediction model when predicting color data using input data, such as the input data ( ), previously described. The correction term may account for differences in color data between different physical conditions.

[0131] In block 106, the computing system may provide the determined correction terms via a communications interface. For example, the computing system may provide the determined correction terms to an I / O device having a display for display. In another example, the computing system may provide the determined correction terms to a data storage medium, for example, when the correction terms are used in a color prediction or color adjustment method described later in connection with FIGS. 4A and 5.

[0132] 2A illustrates an exemplary method 200a for providing a color difference (CD1) between measured color data of a conditioned sample coating present under a first physical condition and predicted color data of the conditioned sample coating present under the first physical condition, such as the color difference (CD1) mentioned in connection with block 102 of FIG. 1 above. Method 200a may be performed, for example, by a computing system implementing method 100 described in connection with FIG. 1.

[0133] In block 202, color data of the adjusted sample coating determined under a first physical condition may be provided. The first physical condition may be a wet condition. The color data may be determined using a suitable measurement device, such as a multi-angle spectrophotometer configured to determine color data of the liquid coating material present in the measurement cell. The acquired data may be used to determine the respective color data. For example, the acquired reflectance data may be used to determine color space data, as described above. The color data may be determined by a computing system controlling the measurement device or by a computing system performing method 200a. The determined color data may be obtained from a data storage medium by the computing system performing method 200a. For example, the computing system may receive data indicative of the adjusted sample coating, such as an ID, and may obtain the color data based on the received data. In block 204, model input data is provided. The model input data may include adjusted sample coating formula data and optical data of individual color components. The optical data may be associated with a first physical condition. The adjusted sample coating formula data may include data regarding components and their respective amounts present in the adjusted sample coating material used to prepare the adjusted sample coating. The optical data may be stored in a data storage medium and retrieved by the computing system based on the adjusted sample coating formula data. For example, the computing system may determine the components present in the adjusted sample coating material from the formula data and may be configured to retrieve optical data related to the determined components from the data storage medium.

[0134] A color prediction model configured to predict color data of the coating using the coating formulation data and the optical data of the individual color components may be provided at block 206. The color prediction model may be stored on a data storage medium or retrieved by a computing system.

[0135] In block 208, color data for the adjusted sample coating can be determined using the model provided in block 206 and the model input data provided in block 204. The color prediction model may predict color data associated with the adjusted sample coating material using the formulation data and optical data related to components present in the adjusted sample coating material. Because the optical data used for color prediction also relates to the first physical condition, the predicted color data can relate to the first physical condition.

[0136] In block 210, a systematic error of the color prediction model associated with the first physical condition may be provided; this block is generally optional. The systematic error associated with the first physical condition may be determined as described below in connection with FIG. 2B. Providing the systematic error may include obtaining the error from a data storage medium.

[0137] In block 212, the systematic errors provided in block 210 can be added to the adjusted sample coating color data predicted in block 208, although this block is generally optional. The use of systematic errors can improve the accuracy of the correction terms and, consequently, the accuracy of the color prediction or color matching method that uses them.

[0138] In block 214, a color difference (CD1) may be determined between the color data provided in block 202 and the color data predicted in block 208 or obtained in block 212. Method 200a may then proceed to block 104 of method 100 described in connection with FIG.

[0139] 2B illustrates an exemplary method 200b for providing a systematic error for the color prediction model described in connection with block 210 of FIG. 2A above. Method 200b may be performed by a computing system implementing, for example, method 100 described in connection with FIG.

[0140] In block 216, color data of the sample coating determined under the first physical conditions may be provided. The sample coating may be associated with an adjusted sample coating. For example, the adjusted sample coating may be obtained by modifying the sample coating, e.g., by modifying at least one compound and / or the amount of at least one compound present in the sample coating formulation to obtain an adjusted sample coating formulation. The sample coating may correspond to a batch of coating material manufactured according to a predetermined recipe or formula. The sample coating material may be a liquid sample coating material. The color data may be determined as described in connection with block 202 of FIG. 2A.

[0141] In block 218, model input data is provided. The model input data may include sample coating formulation data and optical data of individual color components. The optical data may be associated with a first physical condition. The sample coating formulation data may include data regarding components and their respective amounts present in the sample coating material used to prepare the sample coating. The optical data may be stored in a data storage medium or may be acquired as described in connection with block 204 of FIG. 2A.

[0142] In block 220, color data for the sample coating may be determined using the color prediction model provided in block 206 of Figure 2A and the model input data provided in block 218. Prediction of the color data may be performed as described in connection with block 208 of Figure 2A.

[0143] In block 222, a systematic error of 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. The difference may be determined as described in connection with block 214 of Figure 2A. The systematic error determined in block 222 may be used in block 212 of Figure 2A. Using the systematic error may improve the accuracy of the determined correction terms, and therefore the accuracy of color prediction and color matching methods that use the correction terms.

[0144] 3A and 3B illustrate an exemplary method 300a for providing a color difference (CD3) between predicted color data of a sample coating adjusted under second physical conditions and predicted color data of a sample coating adjusted under first physical conditions, such as the color difference (CD3) mentioned in connection with block 102 of FIG. 1 above. Method 300a may be performed by a computing system implementing, for example, method 100 described in connection with FIG. 1.

[0145] In block 302, adjusted sample coating formulation data and optical data associated with a first physical condition may be provided, for example, as described in connection with block 204 of FIG.

[0146] At block 304, a determination may be made to use condition adaptation. This may be performed based on the physical condition with which the available optical data is associated. The available optical data may be stored on a data storage medium. A computing system performing method 300a may be configured to determine the physical condition with which the available optical data is associated. For example, if the available optical data is associated with a second physical condition, condition adaptation is not required, and method 300a proceeds to block 306. Otherwise, i.e., if the available optical data is associated only with the first physical condition, condition adaptation is required, and method 300a proceeds to block 308.

[0147] In block 306, optical data for the individual color components associated with the second physical condition may be provided, which may be performed, for example, as described in connection with block 202 of FIG.

[0148] In block 308, condition adaptation parameters related to the difference between the first physical condition and the second physical condition of the conditioned specimen may be provided. The condition adaptation parameters may be determined, for example, by a computing system performing method 300a. The condition adaptation parameters may be preset and / or determined using an optimization method and a color prediction model. The optimization method may be configured to optimize the condition adaptation parameters by minimizing a cost function starting from a set of initial condition adaptation parameters. The color prediction model may predict color data of the conditioned sample coating using the condition adaptation parameters optimized by the optimization method. The cost function may be the color difference between color data predicted by the color prediction model for the sample coating present under the second physical condition and measured color data of the sample coating present under the second physical condition. The optimization method may optimize the condition adaptation parameters until the color difference is below a predetermined threshold. The condition adaptation parameters determined using the input data related to the sample coating may correspond to the condition adaptation parameters related to the conditioned sample coating, i.e., the condition adaptation parameters determined using the input data related to the sample coating may be used for the conditioned sample coating without significant error. This allows for determining condition adaptation parameters necessary to account for the use of optical data associated with the first physical condition when predicting color data for the adjusted sample coating present under the second physical condition. The determined condition adaptation parameters may be stored in a data storage medium. The determined condition adaptation parameters may be provided as input data to a color prediction model.

[0149] In block 310, a color prediction model may be provided, for example, as described in connection with block 206 of Figure 2A. The color prediction model may be configured to predict the color of the adjusted sample coating using the adjusted sample coating formulation data, the optical data of the individual color components, and optionally the condition fit parameters as input data.

[0150] In block 312, color data for the adjusted sample coating present under the first physical conditions may be determined using the color prediction model provided in block 310 and the model input data provided in block 302. The color data may be predicted as described in connection with block 208 of FIG.

[0151] In block 314, color data of the adjusted sample coating present under second physical conditions 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 present under second physical conditions 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 condition adaptation parameters may be taken into account by adding the parameters as systematic errors to the color data predicted by the color prediction model. The color data may be predicted as described in connection with block 208 of FIG. 2A.

[0152] In block 316 (see FIG. 3B), a systematic error of the color prediction model associated with the first physical condition may be provided; this block is generally optional. The error may be provided as described in connection with FIG. 2B. Using the systematic error may improve the accuracy of the correction term and, therefore, the accuracy of the color prediction or color matching method that uses the correction term.

[0153] In block 318 (see FIG. 3B), a systematic error of the color prediction model associated with a second physical condition may be provided; this block is generally optional. The error may be provided as described below in connection with FIG. 3C. The use of the systematic error may improve the accuracy of the correction term and, therefore, the accuracy of the color prediction or color matching method that uses the correction term.

[0154] In block 320 (see FIG. 3B), the systematic errors provided in block 316 may be added to the adjusted sample coating color data predicted in block 312, although this block is generally optional.

[0155] In block 322 (see FIG. 3B), the systematic errors provided in block 318 may be added to the adjusted sample coating color data predicted in block 314, although this block is generally optional.

[0156] In block 324, the color difference (CD3) between the color data predicted in block 314 and the color data predicted in block 312 may be determined. The color difference (CD3) between the color data obtained in block 322 and the color data obtained in block 320 may be determined. The latter may be performed when taking into account systematic errors. Taking into account said systematic errors can improve the accuracy of the correction terms and therefore the accuracy of the color prediction and color matching operations that use said correction terms, as described above.

[0157] Figure 3C illustrates an example method 300c for providing a systematic error for the color prediction model described in connection with block 318 of Figure 3B above. Method 300c may be performed by a computing system implementing, for example, method 300a described in connection with Figure 3A.

[0158] Color data for the sample coating determined under the second physical conditions may be provided in block 326. The sample coating may be related to the adjusted sample coating as described in connection with Figure 2B. The color data may be determined as described in connection with block 202 of Figure 2A.

[0159] At block 328, a decision may be made to use condition adaptation. This may be made based on the results of the determination made at block 304, described in connection with FIG. 3A. If condition adaptation is not used, the method 300c may proceed to block 330. Otherwise, the method 300c may proceed to block 332, described below.

[0160] In block 330, model input data is provided. The model input data may include sample coating formulation data and optical data for individual color components. The optical data may be related to a second physical condition. The optical data may be provided as described in connection with block 306 of FIG. 3A.

[0161] In block 332, model input data may be provided. The model input data may include sample coating formulation data, optical data for individual color components, and condition adaptation parameters related to differences between first and second physical conditions of the adjusted sample coating. The optical data is associated with the first physical condition. The condition adaptation parameters may be provided as described in connection with block 308 of FIG. 3A.

[0162] In block 334, color data for the sample coating may be determined using the color prediction model provided in block 310 of Figure 3A and the model input data provided in block 330 or block 332. Prediction of the color data may be performed as described in connection with block 208 of Figure 2A.

[0163] In block 336, a systematic error of the color prediction model may be determined by determining the difference between the color data provided in block 326 and the color data predicted in block 334. The difference may be determined as described in connection with block 214 of Figure 2A. The systematic error determined in block 336 may be used in block 318 of Figure 3B. Using the systematic error may improve the accuracy of the determined correction terms, and therefore the accuracy of color prediction and color matching methods that use the correction terms.

[0164] FIG. 4A illustrates an example method 400 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 condition. The second physical condition may be a dry condition. The method may use a correction term, such as the correction term determined as described in connection with FIGS. 1-3C. The correction term may convert systematic errors of the color prediction model from the adjusted sample coating's first condition to the adjusted sample coating's second condition. As a result, the input data of the color prediction model for the adjusted sample coating present under the first physical condition may be used to more accurately determine color data of the adjusted sample coating present under the second physical condition. The correction term may be taken into account by adding the correction term to the color data predicted by the color prediction model.

[0165] The method 400 may be performed by a computing system such as the system described in connection with FIG. 8, or may be performed by the server 902 of the client-server setup described in connection with FIG.

[0166] At block 402, a computing system performing the method 400 may receive a request to provide the following data: the color difference 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; optical data of the individual color components related to a first physical condition; adjusted sample coating data, including adjusted sample coating recipes; a condition adaptation parameter related to the difference between the first physical condition and the second physical condition of the conditioned sample coating; a correction term for the color prediction model determined according to a method disclosed herein, such as the method described in connection with FIGS. 1-3C; and A color prediction model configured to predict the color of the adjusted sample coating present under a second physical condition using the color difference, the optical data of the individual color components, the condition adaptation parameters, the adjusted sample coating data, and the correction terms as input data.

[0167] The sample coating is associated with a prepared sample coating. For example, the prepared sample coating is obtained by modifying the sample coating formulation associated with the sample coating at least once, as described above. The sample coating material associated with the sample coating can correspond to a batch of coating material prepared according to a defined formulation recipe.

[0168] The request may include data indicating initiating method 400, i.e., determining color data of the adjusted sample coating present under the second physical conditions, and the computing system may be configured to provide or obtain the data in response to the request. The request may be received by the computing system from an input / output device, such as input / output device 814 of Figure 8 or client 908 of Figure 9.

[0169] The computing system may be configured to determine a color difference between measured color data of the sample coating present under the second physical condition and predicted color data of the sample coating present under the second physical condition, for example, as described in connection with Figure 3C. The computing system may be configured to determine condition adaptation parameters, for example, as described in connection with Figure 3A.

[0170] At block 404, the computing system performing method 400 may, in response to the received request, determine color data for the adjusted sample coating present under the second physical conditions using the data provided in block 402, as described above. The color prediction model may be configured to predict the color of the adjusted sample coating by a method having the following steps:

[0171] predicting color data of the adjusted coating based on the optical data of the individual color components and the adjusted coating data; and Adding color differences, condition adaptive parameters, and correction terms to the predicted color data.

[0172] The color difference, condition adaptation parameters, and correction terms may be related to a systematic error of the color prediction model associated with predicting the color of the adjusted sample coating present under a second physical condition based on color data of the adjusted sample coating present under a first physical condition. Such systematic error may be additive to the color (e.g., color data) predicted by the physical model based on the adjusted sample coating's formulation and optical data of the individual color components.

[0173] In block 406, the computing system may provide the determined color data via a communications 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, the computing system may provide the determined color to a data storage medium, for example, if the color data is to be used later. This may include correlating the color data with an adjusted sample coating identifier so that the identifier can be used to retrieve the color data. After completing block 406, the routine implementing method 400 may return to block 402 or may end method 400.

[0174] FIG. 4B illustrates an example of a further embodiment of the method described in connection with FIG. 4A. The steps illustrated in FIG. 4B may be performed in addition to the steps described in connection with FIG. 4A. The steps of FIG. 4B may allow the determined color data to be compared with color data of a reference coating, thus allowing the degree of color matching between the adjusted sample coating and the reference coating to be determined. The method described in FIG. 4B may be implemented using a computing system such as the computing system described in connection with FIG. 4A. For example, the method of FIG. 4B may be performed using a computing system that executes method 400 described in connection with FIG. 4A.

[0175] At block 408, color data of the reference coating present under the 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 indicative of the reference coating, such as an ID, and use the received data to obtain the color data. In another example, the computing system may use data indicative of the adjusted sample coating to obtain color data of the reference coating associated with the adjusted sample coating.

[0176] In block 410, the color difference may be calculated 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. The color difference may be calculated using one of the color tolerance equations described above.

[0177] In block 412, the calculated color differences may be provided, which is generally optional. For example, the color differences may be provided via a communications interface to a display device for display, such as described in connection with block 406 of FIG. 4A.

[0178] At least one action related to the calculated color difference may be initiated in block 414, which is generally optional. The at least one action may be related to the determined color difference being greater than or less than a defined threshold. The threshold may be a predefined color difference. For example, the computing system may initiate calculation of a further adjusted sample coating formula, e.g., as described in connection with FIGS. 5 and 6, if the determined color difference exceeds a predefined threshold, i.e., if there is not a sufficient color match between the adjusted sample coating color and the reference coating color. In another example, the computing system may initiate providing the adjusted sample coating formula to a printing device and / or a data storage medium and / or a fill line. After completing block 414, the method may end, or the method may return to block 402.

[0179] FIG. 5 illustrates an example of a method 500 for determining a formula for a second adjusted sample coating 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 first physical condition may be a wet condition. The second physical condition may be a dry condition. The second adjusted sample coating formula is obtained by modifying the first adjusted sample coating formula at least once. The first adjusted sample coating formula may correspond to the adjusted sample coating formula described in connection with FIGS. 1-4B. The first adjusted sample coating formula corresponds to the adjusted sample coating formula described in connection with FIGS. 1-4B. The method may use a correction term, such as the correction term determined as described in connection with FIGS. 1-3C. The correction term can be used. The correction term can convert systematic errors of the color prediction model from the first adjusted sample coating condition to the second adjusted sample coating condition. As a result, the input data of the color prediction model for the adjusted sample coating present under the first physical condition can be used to more accurately determine color data of the adjusted sample coating present under the second physical condition.

[0180] The method 500 may be performed by a computing system such as the system described in connection with FIG. 8, or may be performed by the server 902 of the client-server setup described in connection with FIG.

[0181] At block 502, a computing system performing the method 500 may receive a request to provide the following data: a color difference between the measured color data of the sample coating present under the second physical conditions and the predicted color data of the sample coating present under the second physical conditions, the sample coating being relative to the first adjusted sample coating; optical data of the individual color components related to a first physical condition; reference coating data, including color data of the reference coating present under a second physical condition; first adjusted sample coating data including a formulation for the first adjusted sample coating; a condition adaptation parameter related to the difference between the first physical condition and the second physical condition of the first conditioned sample coating; a correction term for the color prediction model determined according to the methods disclosed herein, such as those described in connection with the figures; and A color prediction model configured to predict the color of a second adjusted sample coating present under second physical conditions 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 terms as input data.

[0182] The sample coating is associated with a first adjusted sample coating. For example, the first adjusted sample coating can be obtained by modifying the sample coating formulation associated with the sample coating at least once as described above. The sample coating material associated with the sample coating can correspond to a batch of coating material prepared according to a defined formulation recipe.

[0183] The request may include data indicating to initiate method 500, i.e., to determine color data of the adjusted sample coating present under the second physical conditions, and the computing system may be configured to provide or obtain said data in response to the request. The request may be received by the computing system from an input / output device, such as input / output device 814 of Figure 8 or client 908 of Figure 9.

[0184] The computing system may be configured to determine a color difference between measured color data of the sample coating present under the second physical condition and predicted color data of the sample coating present under the second physical condition, for example, as described in connection with Figure 3C. The computing system may be configured to determine condition adaptation parameters, for example, as described in connection with Figure 3A.

[0185] At block 504, a second adjusted sample coating formula may be determined using the color prediction model and the additional data provided at block 402. The second adjusted sample coating formula may be determined as described in connection with FIG.

[0186] In block 506, the determined second adjusted sample coating may be provided via a communications interface. For example, the computing system may provide the determined formulation to an I / O device having a display for display. In another example, the computing system may provide the determined formulation to a data storage medium, for example, if the formulation is to be used later.

[0187] At block 508, at least one operation related to the second adjusted sample coating formula determined at block 504 may be initiated; this block is generally optional. Initiating the at least one operation may include providing the second adjusted sample coating formula to a printing device and / or a data storage medium and / or a mixing device. After completing block 508, method 500 may return to block 502 or may end.

[0188] 6 illustrates a flowchart of an aspect of block 504 of FIG. 5, according to an exemplary embodiment of the present disclosure. The method described in FIG. 6 may be performed by a computing system implementing method 500 of FIG.

[0189] In block 602, a method is provided that is configured to adjust the concentration of at least one individual color component present in the first adjusted sample coating formula. A suitable method may include the Levenberg-Marquardt algorithm (LMA or LM), also known as the damped least squares (DLS) method. The concentration adjustment may be performed by minimizing a predetermined cost function starting from the concentrations of the individual color components included in the first adjusted sample coating data provided in block 502 of FIG. 5. The cost function may be the color difference between the predicted color data of the recursively modified first adjusted sample coating and the color data of the provided reference coating. The color difference may be calculated using the color tolerance equation described above.

[0190] In block 604, the concentration of at least one individual color component present in the first adjusted sample coating formulation can be altered using the method provided in block 602.

[0191] In block 606, color data of the modified first adjusted sample coating formula obtained after performing block 604 may be determined using the color prediction model, color difference, optical data of the individual color components, condition adaptation parameters, and correction terms provided in block 502 of Figure 5. The color data may be predicted by the color prediction model using the optical data of the individual color components and the modified adjusted sample coating formula. The color difference, condition adaptation parameters, and correction terms may 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 formula.

[0192] In block 608, the color data determined in block 606 may be compared to the color data of the reference coating provided in block 602. This may include determining color differences, for example, by using the color tolerance equations discussed above.

[0193] In block 610, it may be determined whether the color difference determined in block 608 is below a predefined threshold or whether the number of iterations has reached a predefined limit. If the determined color difference is below a predefined threshold or the iteration limit has been reached, the method proceeds to block 506 of Figure 6. Otherwise, the method repeats blocks 604 through 608 described above.

[0194] FIG. 7A shows a schematic diagram of a method 700a for determining color data of a prepared sample coating present under a second physical condition based on color data of the prepared sample coating present under a first physical condition, according to embodiments disclosed herein. The method may 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., a colorant in a coating layer. The model may be implemented and executed on at least one processor of a computing system 702. The model 704 may have access to optical data for individual color components 706, such as optical data associated with the first physical condition. The optical data may include optical constants for the individual color components. The individual color components may be associated with a set of constants, such as wavelength-dependent K and S values. The model 704 may have access to condition adaptation parameters 708 related to the difference between the first and second physical conditions. The condition adaptation parameters may be determined using the method described in connection with FIG. 3A.

[0195] A color difference 710 between the measured color data of the sample coating present under the second physical conditions and the predicted color data of the sample coating present under the second physical conditions is provided to a computing system 702, for example, as described above in connection with FIG. 4A . In contrast to color prediction methods described in the art, such as those described in WO 2022 / 122777 A1, a correction term 712 reflecting differences in color data associated with different physical conditions is provided to the computing system 702. The correction term may be related to a systematic error of the color prediction model 704 and may be taken into account during the prediction of the 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 may be determined according to the methods disclosed herein, for example, as described in connection with FIGS. 1-3C . The use of the correction term allows for a more accurate prediction of the color data of the adjusted sample coating compared to methods known in the art, since the correction term can account for deviations in color data associated with different physical conditions. This allows input data related to a first physical condition to be used to accurately predict color data related to a second physical condition. The use of input data related to a physical condition different from the predicted color data may be relevant when color data for a reference coating used as a target is only available for a second physical condition, and input data is difficult to generate for that physical condition. For example, a manufactured liquid coating material is colored in a wet state so that the color data of the coating obtained from the manufactured liquid coating material matches the color data of the dried and / or cured reference coating. However, in this case, accurate prediction of the color data of the coating produced from the liquid coating material is necessary to generate accurate color instructions, i.e., to determine adjustments that result in a sufficient color match of the colored coating to the reference coating.

[0196] The adjusted sample coating data, including a formula for an adjusted sample coating 716, may be provided to the computing system 702. The adjusted sample coating formula may be determined, for example, as described in connection with FIG. 4A. Using the adjusted sample coating data, the received color difference, and the correction terms as input data, the color prediction model 704 may predict color data for the adjusted sample coating using optical data 706 and condition adaptation parameters 708, for example, as described in connection with FIGS. 4A and 4B. The predicted color data for the adjusted sample coating under a second physical condition, such as a dry state, is then provided for display on a screen, for example, via a communications interface. When determining the color difference between the predicted color data and a reference coating, color data for the reference coating under a second physical condition, such as a dry state 714, may be provided to the computing system 702, which may be configured to determine the color difference between the predicted color data and the received reference coating color data, for example, as described in connection with FIG. 4B. The computing system 702 may be configured to provide the determined color difference. The computing system 702 may be configured to initiate at least one action related to the calculated color difference (see, eg, FIG. 4B).

[0197] FIG. 7B is a schematic diagram of a method 700b for determining a second adjusted sample coating formula that matches the color of a reference coating present under second physical conditions based on color data of a first adjusted sample coating present under first physical conditions. The second adjusted sample coating formula can be obtained by modifying the first adjusted sample coating formula provided as input data. The first adjusted sample coating formula may correspond to the adjusted sample coating formula described above. The first adjusted sample coating formula may be obtained by modifying the sample coating formula using a commonly known color matching operation. The sample coating formula may correspond to a batch of sample coating material prepared by mixing various coating material components according to a predetermined recipe or formula. Method 700b may be performed by a color prediction model 704 and an optimization method 718. The model and optimization method may be implemented and executed on at least one processor of the computing system 702. The model 704 may have access to optical data of individual color components 706, such as optical data associated with the first physical condition (see FIG. 7A). The model 704 can access condition adaptation parameters 708 related to the difference between the first physical condition and the second physical condition. The condition adaptation parameters may be determined using the method described in connection with FIG. 3A.

[0198] A color difference 710 between the measured color data of the sample coating present under the second physical conditions and the predicted color data of the sample coating present under the second physical conditions may be provided to the computing system 702, for example, as described above in connection with Figure 7A. Additionally, a correction term 712 reflecting the difference in color data associated with the different physical conditions may be provided to the computing system 702. The correction term 712 as well as the color difference 710 may be taken into account as a constant during adjustment of the sample coating formula using a numerical method 718, for example, and may be added to the color data predicted by the color prediction model 704.

[0199] Data for the reference coating 714 may be provided to the computing system 702. The data may include color data, such as reflectance data, of a reference coating prepared from a reference coating formulation. The reference coating may exist in a dry state. The reference coating may be prepared by applying at least the respective reference coating material to a substrate and drying and / or curing the applied coating material.

[0200] The adjusted sample coating data, including the adjusted sample coating 716 recipe, may be provided to the computing system 702. The adjusted sample coating recipe may be determined, for example, as described in connection with FIG. 4A.

[0201] 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 predict color data of the adjusted sample coating using the optical data 706 and the condition adaptation parameters 708, for example, as described in connection with FIGS. 4A and 4B. After determining the color data, the optimization method 718 may modify the concentration of at least one colorant present in the adjusted sample coating formula by minimizing the color difference between the color data of the reference coating and the color data of the recursively corrected adjusted sample coating predicted by the physical model 704. Upon each modification of the adjusted sample coating formula by the optimization method 718, the physical model 704 may be used to predict color data based on the optical data 706, the condition adaptation parameters 708, and the modified adjusted sample coating formula. The modifications may 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 corrected adjusted sample coating reaches a predetermined threshold or until a predefined maximum limit of iterations is reached. The second adjusted sample formula associated with the color difference that reaches the predetermined threshold, or the second adjusted formula associated with the maximum number of iterations, may then be provided by the computing system 702 for display on a screen, for example, via a communications interface. The computing system 702 may be configured to initiate at least one action associated with the calculated color difference (see, for example, FIG. 4B).

[0202] Figure 8 illustrates a computing device 800 that can be used to implement any aspect of the mechanisms described in Figures 1-7B above. For example, with reference to Figures 1-6, a computing device 800 of the type illustrated in Figure 8 can be used to implement any computing device associated with the methods disclosed therein. In another example, a computing device 800 of the type illustrated in Figure 8 can be used to implement any computing device associated with computing system 702 of Figures 7A and 7B. In all cases, computing device 800 represents a physical and tangible processing mechanism.

[0203] Computing device 800 may include one or more hardware processors 802. The hardware processors may include, but are not limited to, one or more central processing units (CPUs), one or more graphics processing units (GPUs), one or more application-specific integrated circuits (ASICs), etc. More generally, any hardware processor may correspond to a general-purpose processing unit or an application-specific processor unit.

[0204] 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 holds any type of information 806, such as machine-readable instructions, settings, data, etc. For example, and without limitation, computer-readable storage medium 804 may include one or more solid-state devices, one or more magnetic hard disks, one or more optical disks, magnetic tape, etc. Any example of computer-readable storage medium 804 may use any technology for storing and retrieving information. Furthermore, any example of computer-readable storage medium 804 may represent a fixed or removable component of computing device 800. Furthermore, any example of computer-readable storage medium 804 may provide volatile or non-volatile retention of information.

[0205] Computing device 800 may utilize any example of computer-readable storage medium 804 in different ways. For example, any example of computer-readable storage medium 804 may represent hardware storage (such as random access memory (RAM)) for storing temporary information during execution of a program by computing device 800, and / or hardware storage (such as a hard disk) for holding / archiving information on a more permanent basis. In the latter case, computing device 800 also includes one or more drive mechanisms 808 (such as a hard drive mechanism) for storing and retrieving information from the example of computer-readable storage medium 804.

[0206] Computing device 800 may perform any of the functions described above when hardware processor 802 executes computer-readable instructions stored on any example of computer-readable storage medium 804. For example, computing device 800 may execute computer-readable instructions to perform each block of the method described in connection with FIGS.

[0207] Alternatively, or in addition, computing device 800 may rely on one or more other hardware logic components 810 to perform operations using task-specific collections of logic gates. For example, hardware logic component 810 may include a fixed configuration of hardware logic gates, e.g., a configuration that is created and set at the time of manufacture and cannot be changed thereafter. Alternatively, or in addition, other hardware logic component 810 may include a programmable collection of hardware logic gates that can be configured to perform different application-specific tasks. Devices in 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.

[0208] 8 illustrates that hardware logic circuitry 812 generally includes any combination of hardware processor(s) 802, computer-readable storage media 804, and / or other hardware logic components 810. That is, computing device 800 may employ any combination of hardware processor(s) 802 that execute machine-readable instructions provided on computer-readable storage media 804, and / or one or more other hardware logic components 810 that perform operations using a fixed and / or programmable collection of hardware logic gates. More generally, hardware logic circuitry 812 corresponds to one or more hardware logic components of any type that perform operations based on logic stored in and / or embodied in the hardware logic components.

[0209] In some cases, computing device 800 may also include input / output interfaces 814 for receiving various inputs (via input devices 816) and providing various outputs (via output devices 818). For example, computing device 800 may include such input / output devices 814 if device 800 represents client devices 908.1-908.n of FIG. 9. Exemplary input devices include a keyboard device, a mouse input device, a touchscreen input device, a digitizing pad, one or more still image cameras, one or more video cameras, one or more depth camera systems, one or more microphones, a voice recognition mechanism, any motion detection mechanism (e.g., accelerometer, gyroscope, etc.), etc. A particular output mechanism may include a display device 820 and associated graphical user interface presentation (GUI) 822. 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, etc. Other output devices include a printer, one or more speakers, a haptic output mechanism, an archive mechanism (for storing output information), etc. Computing device 800 may also include one or more network interfaces 824 for exchanging data with other devices over one or more communication conduits 826. One or more communication buses 828 may communicatively couple the above-mentioned components.

[0210] The communications conduit 826 may be implemented in any manner, for example, by a local area computer network, a wide area computer network (e.g., the Internet), a point-to-point connection, etc., or any combination thereof. The communications conduit(s) 826 may include any combination of hardwired links, wireless links, routers, gateway functions, name servers, etc., governed by any protocol or combination of protocols.

[0211] 8 illustrates a computing device 800 that is made up of a discrete collection of separate units. In some cases, the collection of units may correspond to individual hardware units provided in the housing of a computing device having any form factor.

[0212] Turning to FIG. 9, an Internet-based system 900 is shown that can be used to implement the methods described in connection with FIGS. 1 through 6. System 900 may include a server 902 that can be accessed via a network 906, such as the Internet, by one or more clients 908.1 through 908.n. The server may be an HTTP server or may be accessed using conventional Internet web-based technology. Server 902 may be connected to a database 904. Database 904 may store color prediction models, optical data for individual color components, and / or condition adaptation parameters. Database 904 may also store correction terms determined by the server. Clients 908.1 through 908.n may be computer terminals accessible by users, and may be customized devices such as data entry kiosks or general-purpose devices such as personal computers. Clients 908.1 through 908.n may also include screens that can be used to display the determined correction terms, the determined color data, and / or the determined second adjusted sample coating formula. A printer 910 may be connected to client terminal 908. The clients 908.1-908.n may be connected to a database 912. The database 912 may store reference coating data and / or first adjusted sample coating data and / or recipes associated with the adjusted sample coating or the second adjusted sample coating. The internet-based system 900 may be particularly useful where services are provided to customers or in large corporate setups. The clients 908 may be used to provide the reference coating data and adjusted sample coating data to a computer processor of the server.

[0213] FIG. 10A shows a graph 1002 including a measured reflectance spectrum 1004 of a green reference coating in a dry state, a measured reflectance spectrum 1006 of an adjusted green sample coating material in a wet state, a reflectance spectrum 1008 of an adjusted green sample coating material in a dry state predicted using the method described in WO 2022 / 122777 A1, and a measured reflectance spectrum 1010 of a green adjusted sample coating in a dry state prepared from the adjusted green sample coating material (used as a control measurement to determine the quality of color prediction accuracy). An adjusted green sample coating formula can be determined using the method described in WO 2022 / 122777 A1 and used to prepare an adjusted green sample coating in a dry state, for example, by applying the formula to a substrate and drying and / or curing the applied formula. The deviation in reflectance spectra 1004, 1010 between the green reference coating and the adjusted green sample coating is also reflected in the color data shown in Table 1014 of FIG. 10C. This deviation appears to result from 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 it was assumed that this determined systematic error corresponded to the systematic error of the color prediction model for the dry state of the adjusted green sample coating. However, this assumption does not appear to be accurate, as demonstrated by the color data shown in Table 1014 of Figure 10C. Depending on the magnitude of the difference in the systematic error of the color prediction model associated with the wet and dry states, the prediction of the color data can be significantly inaccurate, as shown in Figure 10C.

[0214] Figure 10B shows a graph 1012 containing color data for the green reference coating and the green adjusted sample coating described in connection with Figure 10A. The graph includes a measured reflectance spectrum 1004 of the green reference coating as it exists in a dry state, a measured reflectance spectrum 1006 of the adjusted green sample coating material as it exists in a wet state, a predicted reflectance spectrum 1008 of the adjusted green sample coating material as it exists in a dry state using the method described in connection with Figures 1-6, and a measured reflectance spectrum 1010 of the adjusted green sample coating as it exists in a dry state (used as a control measurement to determine the quality of the color prediction accuracy). Graph 1012 shows no detectable deviations between the measured reflectance spectrum 1004 of the green reference coating, the measured reflectance spectrum 1010 of the adjusted green sample coating, and the predicted reflectance spectrum 1008 of the adjusted green sample coating. The increased accuracy of the method disclosed herein compared to the method described in WO 2022 / 122777 A1 is likely due to the use of correction terms that allow the wet-state related input data of the color prediction model to be used to accurately predict dry-state color data, e.g., reflectance spectra.

[0215] FIG. 10C shows a table 1014 containing a comparison of the color difference between the color data shown in FIGS. 10A and 10B. Specifically, the color data for the green reference coating measured in a dry state (i.e., a cured green reference coating prepared by applying a reference coating material to a substrate and drying and / or curing the applied reference coating material) and the color data predicted for the dry green sample coating (first row) or the adjusted green sample coating using the methods disclosed herein and the methods disclosed in WO 2022 / 122777 A1 (last row) (middle row). As can be seen in the first row, the green sample coating exhibits a significant color difference from the green reference coating. This is due to the fact that the green sample coating material was prepared with a reduced amount of colorant to avoid colorant concentration overshoot. The second row shows the use of correction terms determined according to the methods disclosed herein, e.g., the correction terms determined according to FIGS. 1-3C. When the correction term is used to predict color data using a color prediction model (e.g., as described in connection with FIGS. 4A and 4B), the color difference is significantly reduced compared to color prediction methods that do not use the term (e.g., the color prediction method described in WO 2022 / 122777 A1). A large color difference between the predicted color data and the color data of a green reference coating can lead to an erroneous prediction of further necessary adjustments, such that the color difference is below a predefined threshold. In contrast, the significantly lower color difference obtained with the method disclosed herein allows input data acquired under a first physical condition, such as a wet state, to more reliably predict the color of a coating present under a second physical condition, such as a dry state. This increased accuracy can significantly reduce the amount of spray (e.g., dried coating) that needs to be prepared to determine whether adjustments calculated using the predicted color data are sufficiently accurate.

[0216] FIG. 11A shows another graph 1102 including a measured reflectance spectrum 1104 of a blue reference coating present in a dry state, a measured reflectance spectrum 1106 of a prepared blue sample coating material present in a wet state, a reflectance spectrum 1108 of the prepared blue sample coating material present in a dry state predicted using the method described in WO 2022 / 122777 A1, and a measured reflectance spectrum 1110 of a prepared blue sample coating present in a dry state and prepared from the prepared blue sample coating material. The prepared blue sample coating formulation can be determined using the method described in WO 2022 / 122777 A1 and used to prepare the prepared blue sample coating as described in connection with FIG. 10A. The deviation in reflectance spectra 1104, 1110 between the blue reference coating and the prepared blue sample coating is also reflected in the color data shown in Table 1114 of FIG. 11C.

[0217] FIG. 11B shows another graph 1112 including the color data for the blue reference coating and the adjusted blue sample coating described in connection with FIG. 11A. The graph includes a measured reflectance spectrum 1104 of the blue reference coating as it exists in a dry state, a measured reflectance spectrum 1106 of the adjusted blue sample coating as it exists in a wet state, a predicted reflectance spectrum 1108 of the adjusted blue sample coating as it exists in a dry state using the method described in connection with FIGS. 1-6, and a measured reflectance spectrum 1110 of the adjusted blue sample coating as it exists in a dry state. Graph 1112 shows no detectable deviation between the measured reflectance spectrum 1104 of the blue reference coating, the measured reflectance spectrum 1110 of the adjusted blue sample coating, and the predicted reflectance spectrum 1108 of the adjusted blue sample coating.

[0218] FIG. 11C shows another table 1114 including a comparison of the color difference of the color data shown in FIGS. 11A and 11B. Specifically, the table shows color data measured in a dry state for a blue reference coating (i.e., a cured blue reference coating prepared by applying a blue reference coating material to a substrate and drying and / or curing the applied blue reference coating material) and color data predicted for the blue sample coating in a dry state (first row) or the prepared blue sample coating 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 significantly larger color difference compared to the blue reference coating. The second row shows the use of a correction term determined according to the method disclosed herein, e.g., the correction term determined according to FIGS. 1-3C. When the correction term is used to predict color data using a color prediction model (e.g., as described in connection with Figures 4A and 4B), it is shown that the color difference is significantly reduced compared to color prediction methods that do not include the use of the term (e.g., the color prediction method described in WO 2022 / 122777 A1).

[0219] FIG. 12A shows yet another graph 1202 including a measured reflectance spectrum 1204 of another green reference coating present in a dry state, a measured reflectance spectrum 1206 of another adjusted green sample coating material present in a wet state, a reflectance spectrum 1208 of the adjusted green sample coating material present in a dry state predicted using the method described in WO 2022 / 122777 A1, and a measured reflectance spectrum 1210 of an adjusted green sample coating present in a dry state and prepared from the adjusted blue sample coating material. The adjusted blue sample coating formula can be determined using the method described in WO 2022 / 122777 A1 and used to prepare the adjusted blue sample coating, as described in connection with FIG. 10A. The deviation in reflectance spectra 1210, 1204 between the green reference coating and the adjusted green sample coating is also reflected in the color data shown in table 1214 of FIG. 12C.

[0220] Figure 12B shows yet another graph 1212 including color data for the green reference coating and adjusted green sample coating described in connection with Figure 12A. The graph shows a measured reflectance spectrum 1204 of the green reference coating material as it exists in a dry state, a measured reflectance spectrum 1206 of the adjusted green sample coating material as it exists in a wet state, a predicted reflectance spectrum 1208 of the adjusted green sample coating material as it exists in a dry state using the method described in connection with Figures 1-6, and a measured reflectance spectrum 1210 of the adjusted green sample coating in a dry state. Graph 1212 shows no detectable visual deviation between the measured reflectance spectrum 1204 of the green reference coating, the measured reflectance spectrum 1210 of the adjusted green sample coating, and the predicted reflectance spectrum 1208 of the adjusted green sample coating.

[0221] FIG. 12C shows yet another table 1214 including a comparison of the color difference of the color data shown in FIGS. 12A and 12B. That is, the comparison is between the color data of the green reference coating measured in a dry state (i.e., a cured green reference coating prepared by applying a green reference coating material to a substrate and drying and / or curing the applied green reference coating material) and the color data predicted for the green sample coating in a dry state (first row) or the adjusted green sample coating using the method disclosed herein (middle row) as well as the method disclosed in WO 2022 / 122777 A1 (last row). As can be seen in the first row, the green sample coating has a significantly larger color difference compared to the green reference coating. The second row illustrates the use of a correction term determined according to the method disclosed herein, e.g., the correction term determined according to FIGS. 1-3C. When the correction term is used to predict color data using a color prediction model (e.g., as described in connection with Figures 4A and 4B), it is shown that the color difference is significantly reduced compared to color prediction methods that do not include the use of the term (e.g., the color prediction method described in WO 2022 / 122777 A1).

[0222] In summary, the methods, devices, and computer components disclosed herein enable more accurate prediction of color data of a coating present under a second physical condition, such as a dry state, when input data of the same coating present under a first physical condition, such as a wet state, is used for color prediction. The more accurate prediction of color data using the correction terms, which allow the systematic error of the color prediction model to be converted from one physical condition to another, enables more accurate determination of the adjusted sample coating formula needed to achieve a coating that meets color matching requirements when compared with a reference coating. For example, the color difference between the color data associated with the adjusted sample coating prepared from the determined adjusted sample coating formula and the color data of the reference coating is less than or equal to a defined threshold.

[0223] The present disclosure has also been described by way of example and in conjunction with preferred embodiments, however, other variations can be understood by those skilled in the art, from a study of the drawings, the disclosure, and the claims, and capable of practicing the claimed invention.

[0224] Any steps presented herein can be performed in any order. The methods disclosed herein are not limited to any particular order of these steps, nor are they required to be performed at any particular location. That is, each step may be performed at a different computing node using different equipment / data processing.

[0225] In the claims and the description, 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 may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used in accordance with advantageous embodiments.

[0226] As used herein, "determine" also includes "initiate or cause to be determined," "generate" also includes "initiate and / or cause to be generated," and "provide" also includes "initiate or cause to be initiated determining, generating, selecting, transmitting, and / or receiving." "Initiating or causing to be performed an operation" includes any processing signal that triggers a computing node or device to perform the respective operation.

[0227] The disclosures and embodiments described herein relate to the above-described methods, apparatus, and computer program elements, and vice versa. Advantageously, advantages provided by any of the embodiments and examples apply equally to all other embodiments and examples, and vice versa.

Claims

1. 1. A computer-implemented method for providing correction terms to a color prediction model, the correction terms being associated with adjusted sample coatings present under at least two different physical conditions, the method comprising the steps of: receiving, by at least one processor, via a communications interface, a request to provide: 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; 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, wherein the sample coating is relative to the adjusted sample coating; and 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; determining, by the at least one processor in response to the received request, a correction term for the color prediction model using the provided color differences (CD1)-(CD3); and providing the determined correction terms to the color prediction model via a communication interface; 11. A computer-implemented method comprising:

2. 2. The computer-implemented method of claim 1, wherein the first physical conditions include wet conditions, i.e., physical conditions associated with a first application step, and / or the second physical conditions include dry conditions, i.e., physical conditions associated with a second application step.

3. 3. The computer-implemented method of claim 1, wherein the color data includes reflectance data, color space data such as CIEL*a*b* values ​​or CIEL*C*h* values, gloss data, texture parameters such as texture characteristics and / or roughness characteristics, or a combination thereof.

4. Providing predicted color data for the adjusted sample coating present under the first physical conditions comprises the steps of: receiving model input data including adjusted sample coating formulation data and optical data for individual color components associated with the first physical condition; receiving a color prediction model configured to predict color data of the coating using formulation data of the coating and optical data of the individual color components; and Predicting the color data using the received color prediction model and the received model input data.

3. The computer-implemented method of claim 1 or 2, comprising:

5. 5. The computer-implemented method of claim 4, wherein providing predicted color data for the adjusted sample coating present under the first physical conditions further comprises accounting for systematic errors in the color prediction model associated with the first physical conditions.

6. Providing predicted color data for the adjusted sample coating present under the second physical conditions comprises the steps of: receiving model input data including formulation data of the adjusted sample coating and optical data of individual color components associated with a second physical condition, or including formulation data of the adjusted sample coating, optical data of individual color components associated with the first physical condition, and condition adaptation parameters associated with a difference between the first physical condition and the second physical condition of the sample coating; receiving a color prediction model configured to predict color data of the coating using coating prescription data, optical data of individual color components, and optionally condition adaptation parameters; and predicting said color data using the received color prediction model and the received model input data; 3. The computer-implemented method of claim 1 or 2, comprising:

7. 7. The computer-implemented method of claim 6, wherein the condition fit parameters are preset and / or calculated using a method configured to optimize the condition fit parameters by minimizing a cost function starting from a predetermined initial set of condition fit parameters, and a color prediction model configured to predict color data of the coating present under the first physical conditions by using as input data the coating formulation, specific optical data of individual color components present in the coating formulation, and the condition fit parameters obtained from the method.

8. 7. The computer-implemented method of claim 6, wherein providing predicted color data for the adjusted sample coating present under the second physical conditions further comprises considering a systematic error of the color prediction model associated with the second physical conditions.

9. A correction term of a color prediction model using the provided color differences (CD1) to (CD3) is determined according to formula (I): ・・・(I） 3. The computer-implemented method of claim 1 or 2, wherein the numerator of the fraction corresponds to the color difference (CD2) and the denominator of the fraction corresponds to the color difference (CD3).

10. 1. A computer-implemented method 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 method comprising the steps of: receiving, by at least one processor, via a communications interface, a request to provide: a color difference between the measured color data of the sample coating present under the second physical conditions and the predicted color data of the sample coating present under the second physical conditions, wherein the sample coating is relative to an adjusted sample coating; optical data for individual color components associated with the first physical condition; adjusted sample coating data, including adjusted sample coating recipes; a condition adaptation parameter related to the difference between the first physical condition and the second physical condition of the conditioned sample coating; a correction term for a color prediction model determined according to the method of claim 1; and a color prediction model configured to predict a color of the adjusted sample coating present under a second physical condition by using the color difference, the optical data of the individual color components, the condition adaptation parameters, the adjusted sample coating data, and the correction terms as input data; in response to the request, determining, by the at least one processor, color data for the adjusted sample coating present under the second physical conditions using the color prediction model and the data provided in step (a); and providing, via a communications interface, determined color data of the adjusted sample coating present under said second physical conditions. A method comprising:

11. 1. A computer-implemented method for determining a formula for a second adjusted sample coating to match the color of a reference coating present under second physical conditions based on color data of a first adjusted sample coating present under first physical conditions, the method comprising the steps of: receiving, by at least one processor, via a communications interface, a request to provide: a color difference between the measured color data of the sample coating present under the second physical conditions and the predicted color data of the sample coating present under the second physical conditions, the sample coating being relative to the first adjusted sample coating; optical data for individual color components associated with the first physical condition; reference coating data, including color data of the reference coating present under said second physical conditions; first adjusted sample coating data including a first adjusted sample coating recipe; a condition adaptation parameter related to the difference between the first physical condition and the second physical condition of the first conditioned sample coating; a correction term for a color prediction model determined according to the method of claim 1; and and a color prediction model configured to predict the color of the second adjusted sample coating present under said second physical conditions 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 terms as input data. determining, by the at least one processor in response to the request, a second adjusted sample coating formula using the color prediction model and the provided data; and Providing the determined second adjusted sample coating formula via the communication interface. A method comprising:

12. 3. An apparatus including one or more computing nodes and one or more computer-readable media having computer-executable instructions thereon that, when executed by the one or more computing nodes, cause the apparatus to perform the method of claim 1 or 2.

13. 10. The use of a correction term determined according to the method of claim 1 to improve the accuracy of color data of an adjusted sample coating present under a second physical condition, wherein the color data is predicted by a color prediction model based on color data of an 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 computing systems, instruct the computing nodes or computing systems to perform the steps of the method according to any one of claims 1, 10 and 11.

15. A computer program element comprising instructions which, when executed by an apparatus according to claim 13, direct the apparatus to perform the steps of the method according to claim 1.

Images