Color adjustment method and system

Abstract

Aspects described herein generally relate to methods and systems for matching the color of a sample coating to the color of a reference coating. More specifically, aspects described herein relate to methods and systems for determining an adapted modified sample coating formulation that adequately matches the color of a reference coating when applied onto a substrate by determining adjusted optical data for each color component present in the sample coating formulation and using the adjusted optical data to determine a modified sample coating formulation. The color adjustment process can compensate for colorant strength characteristics variations in paint manufacturing by using the adjusted optical data for each color component present in the sample coating formulation. Adjustment of the optical data can improve the quality and / or accuracy of the modified sample coating formulation, thus reducing the number of correction steps required to obtain a desired color of the sample coating relative to the reference coating.

Description

[Technical Field]

[0001] Embodiments described herein generally relate to methods and systems for adjusting the color of a sample coating to the color of a reference coating so that a good color match can be obtained. More specifically, embodiments described herein relate to methods and systems for determining a modified sample coating formulation that closely matches the color of a reference coating by determining fitted optical data for the individual color components present in the sample coating formulation when applied to a substrate, and using the fitted optical data to determine the modified sample coating formulation. By using fitted optical data for the individual color components present in the sample coating formulation in the color adjustment process, variations in the colorant strength characteristics of colorants in paint manufacturing can be compensated for. The fitting of the optical data can improve the quality and / or accuracy of the adjusted sample coating formulation, and thus reduce the number of adjustment steps required to obtain the desired color of the sample coating relative to the reference coating. [Background technology]

[0002] The paint manufacturing process for a given color standard typically begins with an initial coating formulation, such as a formula read from a database. The color of the initial coating formulation is obtained by adding at least one pigment paste (hereinafter also referred to as a colorant) to a base varnish containing a binder, solvent, and optionally additives. The pigment paste is an intermediate product containing coloring components (such as pigments) in a matrix (typically a binder, solvent, and optionally additives). Typically, the color of the intermediate product varies from batch to batch due to variations in the quality of raw materials such as pigments. To avoid adjusting the color of each pigment paste produced, the pigment paste is used "as is" for the preparation of the initial coating formulation so that only the initial coating formulation needs to be adjusted. Typically, the initial coating formulation contains a reduced amount of pigment paste (compared to the final paint formulation) to avoid the manufactured coating batch becoming too dark due to an overshoot in the color intensity characteristics of one or more colorants present in the coating formulation. The initial coating batch is manufactured according to this initial coating formulation, and the corresponding color of this coating batch is measured and compared to the reference color. Because the amount of colorant is reduced, the first coating batch typically exhibits a significant residual color difference compared to the reference coating. Therefore, to minimize the residual color difference between the color of the coating batch and the color of the reference coating, a color adjustment process must be applied by modifying the initial coating formulation. Next, the modified coating is prepared from the modified initial coating formulation, the color of the modified coating is determined, and it is compared to the color of the reference coating. If the match is not sufficient, the color adjustment process must be repeated with the modified initial coating formulation.

[0003] Most computer-aided color matching methods are based on physical models that describe the interaction between light and a scattering or absorbing medium, such as a colorant in a coating layer. Each coating layer has specific light reflectivity characteristics due to the colorants present in that layer. Each of these colorants has specific optical properties represented by its respective optical constant or optical data. These optical constants describe the absorption and scattering properties of these colorants in the environment of the physical model, such as the K / S values ​​in the well-known Kubelka / Munk model. Physical models like the Kubelka / Munk model can predict the light reflectivity characteristics (color) of a coating layer based on information about the colorants present in the coating layer (for example, information about the formulation used to prepare the coating layer), along with the corresponding optical properties or respective optical constants of the colorants.

[0004] The optical properties of a colorant can be determined based on the color data of an existing reference coating prepared from a known coating formulation with known reflectance data. Therefore, the color prediction and matching process of the physical model always uses the optical properties of the colorant present in the batch used to prepare the reference coating (hereinafter also referred to as the "reference colorant batch").

[0005] A suitable formulation (or appropriate color adjustment) for a given reference color can be predicted using a numerical optimization algorithm based on a physical model that has existing optical constants of the colorant and reflectance data of the reference coating as input parameters. However, the accuracy of the color prediction by the physical model is limited by the presence of systematic and statistical errors. Statistical errors can be caused by differences in the equipment or measurement process used to determine the color, such as the position of the equipment on the sample. Systematic error (hereinafter also referred to as model bias) is defined as the difference between the measured color of the sample coating and the color of the sample coating predicted by the physical model. The accuracy of the process can be improved by considering the model bias during the color adjustment process. For example, European Patent EP 2149038 B1 discloses a color adjustment algorithm based on a physical model combined with a numerical optimization algorithm. This color adjustment algorithm minimizes the residual color difference between the coating batch and the reference color while considering the determined model bias of the physical model as a constant offset for color adjustment. Thus, the formulation of the adjusted sample coating is a function of the reference color and the offset between the predicted reflectance data and the measured reflectance data of the sample coating. This color adjustment algorithm is based on the fundamental assumption that the model's bias will remain constant if the formulation changes on a "small scale"; in other words, as long as the adjusted coating formulation is "similar" to the original coating formulation, the model's bias is expected to be similar as well.

[0006] A limitation of this approach is that the optical properties of the colorant (e.g., color intensity properties) are not constant over time, but typically vary within a certain range from batch to batch due to deviations in raw materials, such as pigments. Color intensity is defined as the ability of a colorant to correct the color of a coating layer and can be used as an indicator of the efficiency of the colorant, as it measures the degree of color change per unit amount of colorant. Color intensity is given by the following formula: TIFF0007855074000001.tif9150 It can be defined according to the following.

[0007] Examples of color intensity include, for instance, the coloring power of the coloring agent used for coloring, or the color-reducing power of the white coloring agent.

[0008] The greater the color intensity of a colorant, the greater its influence on the color of the coating layer. Therefore, the color intensity characteristics of each colorant correlate with the absorption and scattering characteristics "K" and "S" scales of the colorant.

[0009] In conclusion, the color intensity characteristics of colorants, such as pigment pastes, present in the colorant batch used to prepare the sample coating formulation may differ from those of the colorants present in the reference colorant batch used to prepare the reference coating. Depending on the scale of the difference in color intensity characteristics and the scale of the color difference between the sample coating and the reference coating, the color adjustment results may be significantly inaccurate, even after considering model bias as described in EP 2149038 B1. [Overview of the Initiative] [Problems that the invention aims to solve]

[0010] Therefore, it is desirable to provide a method and system for producing a modified coating formulation that is free from the aforementioned drawbacks and adequately matches the color of a reference coating. More specifically, a computer-implemented method and system for determining a modified sample coating formulation that matches the color of a reference coating needs to provide more accurate color matching results, in particular by taking into account variations in the color intensity of the colorants present in the coating formulation. [Means for solving the problem]

[0011] definition The term "reference coating" may refer to a coating having defined properties, such as defined colorimetric properties. A reference coating can be prepared by applying at least one defined coating material to a surface and curing the applied coating material, provided that at least one of the defined coating materials includes at least one colorant. In contrast, the term "sample coating" may refer to a coating that is evaluated in comparison to a reference coating with respect to at least some of the defined properties, such as colorimetric properties. A sample coating can be prepared, preferably using the same number and types of coating formulations used to prepare the reference coating, as described for the reference coating. The term "sample coating formulation" refers to the coating materials used to prepare the sample coating, while the term "reference coating formulation" refers to the coating materials used to prepare the reference coating. The term "modified sample coating formulation" refers to a sample coating formulation in which at least one component present in the sample coating formulation is modified with respect to the sample formulation (i.e., the unmodified sample formulation), for example, by modifying the amount of the component. The terms "formulation," "color formulation," and "paint formulation" are used synonymously herein.

[0012] "Display device" refers to an output device for presenting information in a visual or tactile format (the latter may be used in tactile electronic displays for the visually impaired). "Screen of display device" refers similarly to both the physical screen of a display device and the projection area of ​​a projected display device.

[0013] "Color data" includes reflectance data, CIEL * a * b * Value or CIEL * C * h *This includes color space data such as values, gloss data, texture parameters such as shine and / or roughness characteristics, or combinations thereof.

[0014] "Digital representation" may refer to a computer-readable representation of a sample coating, a reference coating, and individual color components. In particular, the digital representation of a sample coating includes at least the color data and sample coating formulation of the sample coating, in particular the color data and sample coating formulation obtained by determining the color data using a measuring device such as a multi-angle spectrophotometer. The digital representation of a sample coating may further include data indicating the sample coating, such as a color number / color code / barcode / unique database ID associated with the sample coating, the layer structure of the sample coating, the wet or dry film thickness of the sample coating, instructions for preparing the sample coating material associated with the sample coating, price, predefined criteria relating to the optical data of the individual components to be adapted, or a combination thereof. The digital representation of a reference coating includes at least the color data of the reference coating, in particular the color data of the reference coating obtained by determining the color data using a measuring device such as a multi-angle spectrophotometer. The digital representation of a reference coating may further include data indicating the reference coating, such as the color number / color code / barcode / unique database ID associated with the reference coating, the reference coating formulation, the layer structure of the reference coating, the wet or dry film thickness of the reference coating (hereinafter also referred to as the target wet or dry film thickness), instructions for preparing the reference coating formulation related to the reference coating, price, data indicating a method for determining the color difference, such as a color tolerance equation or other methods including similarity of spectral curve shapes, predefined criteria for the optical data of the individual components to be fitted, or a combination thereof. The digital representation of individual color components includes at least the optical data of the individual color components. The digital representation of individual color components may further include data indicating the individual color components, such as the material code / number or trademark name associated with the individual color component, predefined criteria for the optical data of the individual components to be fitted, or a combination thereof.

[0015] "Individual color components" refer to separate components present within a coating formulation, such as a sample coating formulation and a reference coating formulation. Examples of individual color components include pigments such as coloring pigments and effect pigments, binders, solvents, and additives such as matte pastes. Preferably, the term "individual color components" refers to pigment pastes or pigments such as coloring pigments and effect pigments.

[0016] "Optical data of individual color components" refers to the optical properties and / or specific optical constants of individual color components. These optical constants are parameters of a physical model, which can be determined by preparing a reference coating using a reference batch of pigment paste and determining its optical properties, for example, by measuring the reflectance spectrum of the prepared reference coating using a spectrophotometer, as described above. 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 "optical data of individual color components," "optical data of the individual color components," or "optical data of the colorants" are used synonymously.

[0017] The term "physical model" refers to a deterministic color prediction model based on physical laws. Particularly preferably, the physical model used in accordance with the present invention is based on physical laws that describe the light absorption and light scattering properties of the pigment system.

[0018] The term "model bias" (hereinafter also referred to as "physical model bias") refers to the systematic error of the physical model in predicting color data based on the optical data of coating formulations and individual color components. This systematic error includes the limitations of the physical model and the bias present in the optical data of individual color components present in the sample coating formulation. The bias present in the optical data of individual color components arises from the difference between the color intensity characteristics of the pigment paste used to prepare the reference coating and the color intensity characteristics of the pigment paste used to prepare the sample coating, because the color intensity characteristics of the pigment paste vary from batch to batch due to variations in the raw materials (such as pigments) used to prepare the pigment paste. The term "residual model bias" refers to the model bias that remains after adjusting the optical data of individual color components, such that the predicted color data using the adjusted optical data matches the measured color better than the predicted color data using the optical data determined for the reference colorant batch. Adjusting the optical data of individual color components allows for the consideration of different color intensity characteristics of pigment pastes during the color adjustment process.

[0019] "Communication interface" may refer to a software and / or hardware interface for establishing communication, such as the transfer or exchange of signals or data. A software interface may be, for example, a function call or an API. A communication interface may include transceivers and / or receivers. Communication may be wired or wireless. A communication interface may be based on or support one or more communication protocols. A communication protocol may be a wireless protocol, such as a short-range communication protocol such as Bluetooth® or WiFi, or a long-range communication protocol such as a cellular or mobile network such as a second-generation cellular network ("2G"), 3G, 4G, Long-Term Evolution ("LTE"), or 5G. Alternatively or additionally, a communication interface may be based on a dedicated short-range or long-range protocol. A communication interface may support any one or more standard protocols and / or dedicated protocols.

[0020] "Computer processor" refers to any logic circuit and / or, generally, a device configured to perform calculations or logical operations, configured to perform basic operations of a computer or system. In particular, a processing unit or computer processor may be configured to process basic instructions that drive a computer or system. As an example, a processing unit or computer processor may include at least one arithmetic logic computing device ("ALU"), at least one floating-point unit ("FPU") such as a mathematical coprocessor or a numerical coprocessor, a number of registers, in particular registers configured to supply operands to the ALU and store the results of calculations, and memory such as L1 cache memory and L2 cache memory. In particular, a processing unit or computer processor may be a multi-core processor. Specifically, a processing unit or computer processor may be a central processing unit ("CPU") or may include a central processing unit. The processing means or computer processor may be a graphics processing unit ("GPU"), a tensor processing unit ("TPU"), a complex instruction set computer microprocessor ("CISC"), a reduced instruction set computer ("RISC") microprocessor, a very long instruction word ("VLIW") microprocessor, or a processor implementing another instruction set, or a processor implementing 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 composite programmable logic device ("CPLD"), a digital signal processor ("DSP"), a network processor, or similar. The methods, systems, and apparatus described herein may be implemented as software in a DSP, microcontroller, or other side processor, or as hardware circuitry in an ASIC, CPLD, or FPGA.The term "processing means" or "processor" can refer to one or more processing devices, such as a distributed system of processing devices arranged across multiple computer systems (e.g., cloud computing), and should be understood not to be limited to a single device unless otherwise specified. The terms "processor" and "computer processor" are used synonymously herein.

[0021] The term "data storage medium" can refer to a physical medium and other computer-readable media for carrying or storing computer-executable instructions and / or data structures. Such computer-readable media can be any available media accessible by a general-purpose or special-purpose computer system. Computer-readable media can include physical storage media for storing computer-executable instructions and / or data structures. Physical storage media include computer hardware such as RAM, ROM, EEPROM, solid-state drives ("SSDs"), flash memory, phase change memory ("PCM"), optical disk storage, magnetic disk storage, or other magnetic storage devices, or any other hardware storage device that can be used to store program code in the form of computer-executable instructions or data structures, which can be accessed and executed by a general-purpose or special-purpose computer system to implement the disclosed functions of the present invention.

[0022] "Database" may refer to a collection of related information that can be searched and retrieved. The database can be a searchable electronic numerical, alphanumeric, or text document; a searchable PDF document; a Microsoft Excel (registered trademark) spreadsheet; or a database commonly known in the art. The database can be a set of electronic documents, photos, images, diagrams, data, or drawings existing on a computer-readable storage medium that can be searched and retrieved. The database can be a single database, a set of related databases, or a collection of unrelated databases. "Related databases" means that there is at least one common information element in the related databases that can be used to associate such databases.

[0023] "Client device" may refer to a computer or program that depends on sending requests to another program as part of its operation, or the hardware or software of a computer that accesses services provided by a server.

[0024] Overview To solve the above problems from an overall perspective, the following is proposed: A computer-implemented method for determining the formulation of an adjusted sample coating to match the color of a reference coating, the method comprising: (i) to a computer processor via a communication interface · a digital representation of the sample coating including the color data of the sample coating and the formulation of the sample coating, and · a digital representation of the reference coating including the color data of the reference coating, and · a digital representation of each individual color component including the optical data of each individual color component, and · a physical model configured to predict the color of the sample coating by using the formulation of the sample coating and the optical data of each individual color component as input parameters, and providing; (ii) A step of determining the color difference between the provided sample coating color data and the provided reference coating color data using a computer processor, (iii) The model bias of the provided physical model is processed by a computer processor. Based on the digital representation of the sample coating, the digital representation of individual color components, and the physical model provided in step (i), predict the color data of the sample coating. • Determine the color difference between the provided sample coating color data and the predicted sample coating color data, The steps to be determined by, (iv) A step in which the model bias determined in step (iii) is minimized by a computer processor by fitting the provided optical data of the individual color components to at least some of the individual color components present in the sample coating formulation, (v) Using the optical data fitted in step (iv), the computer processor determines the residual model bias by determining the color difference between the provided color data and the predicted color data of the sample coating, (vi) A step in which a computer processor calculates the adjusted sample coating formulation based on the color difference determined in step (ii), the fitted optical data of the individual color components obtained in step (iv), the residual model bias determined in step (v), and the provided physical model, (vii) The step of providing the calculated adjusted sample coating formulation via a communication interface, Includes.

[0025] An essential advantage of the method according to the present invention is that the portion of the model bias in the physical model caused by variations in the color intensity characteristics (variations in the color intensity of individual color components) of the pigment paste used in the manufacture of the reference coating material and the sample coating material is minimized. To minimize this portion of the model bias caused by variations in color intensity characteristics, the model bias of the sample coating is correlated with the variations in the color intensity characteristics of the individual color components included in the physical model. This is done by fitting the provided optical data of the individual color components included in the sample coating formulation so as to minimize the model bias in the physical model. As a result, fitted optical data is obtained that more accurately describes the actual optical properties of the individual color components used in the sample coating formulation. Subsequent adjustments of the sample coating formulation using the fitted optical data of the individual color components result in a more robust and accurate color matching, and sufficient color matching can be obtained with fewer adjustment steps compared to methods known in the prior art. This significantly improves the efficiency of the color matching method of the present invention.

[0026] In step (i) of the method of the present invention, digital representations of a sample coating and a reference coating, digital representations of individual color components, and a physical model (i.e., a physical color prediction model) are provided to a computer processor via a communication interface.

[0027] In an embodiment of step (i), providing a digital representation of a sample coating and / or a reference coating includes determining color data of the sample coating and / or reference coating using a measuring device, and inputting the determined color data, optionally combined with further data and / or metadata and / or user input, to a computer processor via a communication interface.

[0028] Color data can be measured using a commercially available multi-angle spectrometer, such as a Byk-Mac® I or XRite MA®-T family spectrometer. For this purpose, the reflectance of each sample and / or reference coating is measured for several geometries. In the case of effect coatings, texture images (grayscale or color images) are preferably obtained for several geometries. The multi-angle spectrophotometer is preferably connected to a computer processor that can be programmed to process the measured reflectance data and texture images by, for example, calculating the color data for each measurement geometry from the measured reflectance and / or texture properties for defined measurement geometries. The determined color data can be stored in a data storage medium such as internal memory or a database before being provided to the computer processor via a communication interface. This may include, if necessary, correlating the determined color data with further data and / or metadata and / or user input before saving the determined color data, so that the saved color data can be retrieved using further data and / or metadata and / or user input. Storing the determined color data may be preferable if the data is needed multiple times, as it eliminates the need to acquire the data each time the appearance of each effect coating is displayed on the screen of a display device.

[0029] Further data and / or metadata and / or user input may include the aforementioned listed color numbers / color codes / barcodes / unique database IDs associated with each coating, the layer structure of each coating, the wet or dry film thickness of each coating, preparation instructions for each coating material associated with each coating, price, or a combination thereof.

[0030] In an alternative embodiment, providing a digital representation of a reference coating includes providing a digital representation of a sample coating and / or providing data indicating the reference coating, obtaining a digital representation of the reference coating based on the provided representation of the sample coating and / or the provided data indicating the reference coating, and providing the obtained digital representation of the reference coating.

[0031] Data indicating a reference coating may include the color name, color number, color code, barcode, ID, etc., associated with the reference coating. This data may be entered by the user via a GUI displayed on the display device screen, retrieved from a database based on scanned codes such as QR codes, or associated with predefined user actions. Predefined user actions may include selecting a desired action on the GUI displayed on the display device screen, such as displaying a list of stored measurements including related images, or displaying a list of available reference coatings according to search criteria, user profiles, etc.

[0032] In one embodiment, obtaining a digital representation of a reference coating based on a digital representation of a provided sample coating includes accessing a database containing a digital representation of a reference coating that is interrelated with data contained in the digital representation of the sample coating, such as the color name, color code, and barcode of the sample coating, and obtaining a digital representation of the reference coating from the database based on the data contained in the digital representation of the sample coating. The database is preferably connected to a computer processor via a communication interface, and the digital representation of the sample coating may be provided to the computer processor, for example, by selecting a digital representation stored in a data storage medium via a GUI displayed on the screen of a display device, or by inputting data indicating the sample coating, such as the color name and color code, and obtaining a digital representation of the sample coating based on the input data.

[0033] The digital representation of a sample coating includes the color data of the sample coating and the formulation of the sample coating, i.e., the types and amounts of components contained in the formulation of the sample coating. The color data of the sample coating is preferably color data determined using a measuring device and therefore does not include simulated color data, i.e., color data not generated from measured data such as reflectance values ​​or texture images. In one embodiment, the digital representation of a sample coating further includes data indicating the sample coating, the layer structure of the sample coating, instructions for preparing the formulation of the sample coating, price, predefined criteria relating to the optical data of the individual components to be adapted, or a combination thereof. The data indicating the sample coating may include, for example, a color number, color code, a unique database ID, a barcode, or a combination thereof.

[0034] The digital representation of the reference coating includes the color data of the reference coating. The color data of the reference coating is preferably the color data determined by a measuring device, and thus does not include simulated color data, that is, color data not generated from measurement data such as reflectance values or texture images. In one aspect, the digital representation of the reference coating further includes data indicating the reference coating, the layer structure of the reference coating, the formulation related to the reference coating, instructions for preparing the reference coating formulation, price, a method for determining color differences such as a color tolerance equation or other methods including the shape similarity of the spectral curve, predefined criteria regarding the optical data of the individual components to be matched, or combinations thereof. The data indicating the reference coating can include, for example, a color number, a color code, a unique database ID, a barcode, or combinations thereof.

[0035] In one aspect, the color data includes reflectance data, color space data, particularly CIEL * a * b * values or CIEL * C * h * values, gloss data, texture parameters, particularly brilliance characteristics and / or roughness characteristics, or combinations thereof. As described above, the color data can be determined using a multi-angle spectrophotometer. The color data can be changed, for example, by making the color lighter or darker, by using color and / or texture offsets.

[0036] The digital representation of the individual color components includes the optical data of the individual color components. In one aspect, the digital representation further includes data indicating the individual color components. The data indicating the individual color components can be a name, a trade name, a unique ID related to the component (i.e., a material code or number), or combinations thereof.

[0037] In one embodiment, the optical data for individual color components includes the optical constants of each color component, particularly the wavelength-dependent scattering and absorption characteristics of each color component. The optical constants may further include the orientation of each color component, such as effect pigments in a coating.

[0038] In step (ii), a computer processor determines the color difference between the provided sample coating color data and the provided reference coating color data. Step (ii) can also be performed after step (iii). Therefore, the order of steps (ii) and (iii) can be reversed, i.e., step (iii) can be performed before step (ii).

[0039] In one embodiment, the color difference in steps (ii) and / or (iii) and / or (v) is determined using a color tolerance equation, particularly the Delta E (CIE1994) color tolerance equation, the Delta E (CIE2000) color tolerance equation, the Delta E (DIN99) color tolerance equation, the Delta E (CIE1976) color tolerance equation, the Delta E (CMC) color tolerance equation, the Delta E (Audi95) color tolerance equation, the Delta E (Audi2000) color tolerance equation, or other color tolerance equations.

[0040] In an alternative embodiment, the color difference in steps (ii) and / or (iii) and / or (v) is determined using spectral curve shape similarity. The use of spectral curve shape similarity is preferred because it avoids altering the characteristics or "fingerprints" of individual color components, which would complicate the color adjustment process.

[0041] The determined color difference can be stored on an internal data storage medium or a data storage medium such as a database. The determined color difference may be correlated with further data, such as data contained in a digital representation of the provided sample coating formulation, to enable data acquisition in any of the subsequent method steps.

[0042] In one embodiment, steps (ii) through (vii) are performed concurrently. "Concurrently" refers to the time it takes for the computer processor to perform steps (ii) through (vii). Preferably, this time is small enough so that the prepared sample formulation can be produced ad hoc, i.e., within a few milliseconds from the start of step (ii).

[0043] In step (iii), the model bias of the provided physical model is determined by a computer processor. As previously mentioned, the model bias of the provided physical model is caused primarily by biased specific optical constants resulting from variations in the color intensity of individual color components between the reference color component and the color components used to prepare the sample coating formulation, and by the limitations of the physical model. To determine the model bias, the physical model is used to predict the color data of the sample coating based on the digital representation of the provided sample coating and the digital representation of the individual color components provided. Subsequently, the color difference between the color data of the sample coating contained in the digital representation of the provided sample coating and the predicted color data of the sample coating is determined. The color difference can be determined as previously mentioned in relation to step (ii).

[0044] In one embodiment, the color data of the sample coating is predicted in step (iii) using the optical data, particularly optical constants, of the sample coating formulation and the individual color components present within it as input parameters to a provided physical model. The provided physical model then predicts color data, such as reflectance data, of the sample coating formulation based on the input parameters. The predicted color data can be stored in an internal data storage medium or a data storage medium such as a database. The predicted color data may be correlated with further data, such as data contained in a digital representation of the provided sample coating formulation, to enable data acquisition in any of the subsequent method steps.

[0045] In step (iv) of the method of the present invention, the determined model bias is minimized using a computer processor by fitting the provided optical data of at least some of the individual color components present in the sample coating formulation. By correlating the model bias of the sample coating with the variation in the color intensity of the individual color components included in the provided physical model, the actual optical properties of the individual color components used to produce the sample coating formulation can be better described, and as a result, the sample coating formulation adjusted in step (vi) of the method of the present invention can be calculated more accurately.

[0046] In one embodiment, minimizing the model bias determined in step (iii) is: - A step of providing a numerical method configured to match the optical data of at least some of the individual color components present in a sample coating formulation by starting with the optical data provided in step (i) and minimizing a predetermined cost function, - The steps of fitting optical data of at least some of the individual color components present in the sample coating formulation using the provided numerical method and the provided physical model, by comparing the recursively predicted color data of the sample coating obtained using the provided physical model with the provided color data of the sample coating until the cost function falls below a predetermined threshold or the number of iterations reaches a predetermined limit, Includes.

[0047] Therefore, minimizing model bias involves fitting the optical data of at least some of the individual color components present in the sample coating formulation using the provided numerical methods and physical models. In one example, the optical data of all individual color components is fitted. In another example, the optical data of only some of the individual color components is fitted as described below, and therefore the optical data of the remaining individual color components remains unchanged.

[0048] Appropriate numerical methods include the COBYLA (Constrained Optimization by Linear Approximation) method described by MJD Powell in "Advances in Optimization and Numerical Analysis," edited by S. Gomez and J.-P. Hennart (Kluwer Academic: Dordrecht, 1994), pp. 51-67. The COBYLA method is a local derivative-less optimization method that supports arbitrary nonlinear inequalities and equality constraints.

[0049] The numerical method may be stored in a data storage medium such as the internal memory of a computing device equipped with a computer processor, or in a database connected to the computer processor via a communication interface. When step (iv) is executed, the computer processor retrieves the numerical method from the data storage medium such as the computer processor.

[0050] The adapted optical data and / or the recursively predicted color data of the sample coating may be stored in a data storage medium such as internal data storage or a database. In one example, the adapted color data and / or all recursively predicted color data are stored. This may be preferable when data storage limitations are not significant. In another example, only the adapted color data and / or a portion of the recursively predicted color data, for example, predicted color data related to the adapted optical constants obtained when the cost function falls below a predetermined threshold or at the maximum limit of iterations, are stored in the data storage medium. This may be preferable when data storage capacity is limited. The stored adapted optical data and / or predicted color data may be correlated with data contained in the digital representation of the sample coating so as to enable retrieval of the stored data in any of the subsequent steps of the method of the present invention.

[0051] In one example, the cost function is the color difference between the provided sample coating color data and the predicted sample coating color data. The color difference can be calculated as described in relation to step (ii) above. If the cost function is the color difference, the predetermined threshold is preferably a predetermined color difference.

[0052] In one example, the cost function includes a penalty function that assigns a penalty term to a greater fit of at least some of the optical data for individual color components. The term "greater fit" refers to a greater fit of at least 10% of the optical data for at least some of the individual color components. In one example, the penalty term is assigned to a 10% optical data fit. In another example, the penalty term is assigned to a 20% optical data fit. In yet another example, the penalty term is assigned to a 50% optical data fit. This allows us to provide adjusted optical data that is as similar as possible to the original optical data (i.e., the optical data contained in the digital representation of the individual color components provided), and prevents the color of individual color components from being excessively shifted to compensate for small color differences between the color data of the provided sample coating and the predicted color data of the sample coating, or to compensate for some of the model bias or residual model bias. Such excessive color shifts are undesirable because they result in impossible adjusted sample coating formulations that cannot be prepared using the available individual color components.

[0053] The fitting of optical data for at least some of the individual color components present in the sample coating formulation may involve determining the optical data of the individual color components to be fitted, particularly based on at least one predefined criterion, before comparing the recursively predicted color data of the sample coating obtained using the provided physical model with the color data of the provided sample coating. Examples of predefined criteria may include the amount of individual color components present in the sample coating formulation and / or the type of individual color components. The predefined criteria may be included in the digital representation of the sample coating, reference coating, or individual color components provided in step (i). This allows for fitting the optical data of only a defined number of individual color components, such as, for example, the more numerous individual color components or individual color components that are not white pigments, thereby reducing the total number of variables used by the numerical method. Reducing the total number of variables makes the optimization method more robust, for example, when colorants with similar optical behavior are present in the sample coating formulation.

[0054] In one example, fitting the optical data of at least some of the individual color components present in a sample coating formulation includes applying a scaling function to the optical data.

[0055] A suitable scaling function includes the linear scaling function of equation (1), TIFF0007855074000002.tif7150 here TIFF0007855074000003.tif6150 In particular, it refers to optical constants. TIFF0007855074000004.tif6150 TIFF0007855074000005.tif7150 refers to adapted optical data, in particular adapted optical constants. TIFF0007855074000006.tif6150 points to an index ranging from 1 to n. The range is from TIFF0007855074000007.tif61501 to m.

[0056] Preferably, the same scaling factor is used for all wavelength-dependent optical data of each color component, in particular for all wavelength-dependent optical constants of each color component. Using the same scaling factor for all wavelength-dependent optical data, such as all optical constants K and S of each color component, allows for the preservation of the characteristics or "fingerprint" of each color component during fitting. In contrast, arbitrarily fitting the optical data can result in significant changes to the characteristics or "fingerprint" of each color component, complicating the color adjustment process as described above.

[0057] In step (v) of the method of the present invention, the residual model bias is determined using a computer processor by determining the color difference between the color data contained in the digital representation of the provided sample coating and the predicted color data obtained using the optical data adjusted in step (iv). The predicted color data obtained using the optical data adjusted in step (iv) refers to the predicted color data determined when minimizing the model bias in step (iv), as described above. The color difference can be determined as described above in relation to step (ii).

[0058] In step (vi) of the method of the present invention, the adjusted sample coating formulation is calculated by a computer processor based on the color difference determined in step (ii), the fitted optical data of the individual color components obtained in step (iv), the residual model bias determined in step (v), and the provided physical model.

[0059] In one embodiment, calculating the adjusted sample coating formulation is: - A numerical method is provided which is configured to adjust the concentration of at least one individual color component present in a sample coating formulation by starting from the concentrations of individual color components contained in a digital representation of a provided sample coating and minimizing a predetermined cost function. - A step of adjusting the concentration of at least one individual color component present in the sample coating formulation by comparing the recursively predicted color data of the recursively adjusted formulation of the sample coating with the color data of the provided reference coating, using the provided numerical method, the adapted optical data obtained in step (iv), the residual model bias, and the provided physical model, until the color difference falls below a predetermined threshold or the number of iterations reaches a predetermined limit. Includes.

[0060] A suitable numerical method includes the Levenberg-Marquardt algorithm (referred to as LMA or LM), also known as the damped least squares method (DLS). The numerical method can be stored in a data storage medium, such as the internal memory of a computing device including a computer processor, or in a database connected to the computer processor via a communication interface. When step (vi) is performed, the computer processor retrieves the numerical method from the data storage medium, such as the computer processor itself.

[0061] The residual model bias is considered as a constant during the adjustment of the concentration of at least one individual color component. This allows for the consideration of any residual model bias if it could not be minimized to zero in step (iv), thus improving the calculation accuracy of the adjusted sample coating formulation.

[0062] In one example, the cost function is the color difference between the predicted color data of the sample coating and the color data of the reference coating. The color difference can be calculated as described in relation to step (ii) above. When the cost function is the color difference, the predetermined threshold is preferably a predetermined color difference.

[0063] The sample coating formulation is adjusted in step (vi) using the fitted optical data obtained in step (iv) and the recursively adjusted sample coating formulation as input parameters to the provided physical model. The provided physical model then predicts color data, such as reflectance data, for the adjusted sample coating formulation based on the input parameters. This prediction is performed for each adjustment of the sample coating formulation until the cost function falls below a predetermined threshold or the maximum limit of iterations is reached.

[0064] In step (vii) of the method of the present invention, the adjusted sample coating formulation calculated in step (vi) is provided via a communication interface. In one embodiment, providing the calculated adjusted sample coating formulation includes providing the adjusted sample coating formulation, optionally combined with further data, to a display device having a screen for displaying it on a screen via the communication interface. The display device then displays the provided adjusted sample coating formulation and further data on the screen, for example, in a GUI.

[0065] In one embodiment, the display device comprises a housing that houses a computer processor and a screen that perform steps (ii) to (vii). Thus, the display device comprises a computer processor and a screen. The housing may be made of plastic, metal, glass, or a combination thereof.

[0066] In another embodiment, the display device and the computer processor that performs steps (ii) through (vii) are configured as separate components. According to this embodiment, the display device comprises a housing that accommodates a screen but does not accommodate the computer processor that performs steps (ii) through (vii) of the method of the present invention. Thus, the computer processor that performs steps (ii) through (vii) of the method of the present invention resides separately from the display device, for example, in a further computing device. The computer processor of the display device and the further computer processor are connected via a communication interface to enable data exchange. The use of a further computer processor located outside the display device allows the use of higher computing power than that provided by the processor of the display device, thus reducing the computation time required to perform these steps, and thus reducing the overall time until the calculated adjusted sample coating formulation is displayed on the screen of the display device. This allows the calculated adjusted sample coating formulation to be displayed ad hoc without requiring a display device with high computing power. The further computer processor can be located on a server so that steps (ii) through (vii) of the method of the present invention are performed in a cloud computing environment. In this case, the display device can be used to provide the digital representation described in relation to step (i), and therefore functions as a client device connected to the server via a network, as will be described later.

[0067] The display device may be a mobile display device or a fixed display device, and is preferably a mobile display device. Fixed display devices include computer monitors, television screens, projectors, etc. Mobile display devices include laptops, or handheld devices such as smartphones and tablets.

[0068] The screen of a display device can be constructed according to any radiative or reflective display technology to have an appropriate resolution and color gamut. An appropriate resolution is, for example, a resolution of 72 dots per inch (dpi) or higher, e.g., 300 dpi, 600 dpi, 1200 dpi, 2400 dpi or higher. This ensures that the generated visual data can be displayed in high quality. An appropriate wide color gamut is a color gamut of standard red-green-blue (sRGB) or higher. In various embodiments, the screen can be configured to have a color gamut close to the color gamut perceptible to human vision. In one embodiment, the screen of a display device is constructed according to liquid crystal display (LCD) technology, particularly liquid crystal display (LCD) technology further including a touch screen panel. The LCD may be backlit by any appropriate light source. However, the color gamut of the LCD screen can be widened or otherwise improved by selecting a light-emitting diode (LED) backlight or multiple backlights. In another embodiment, the screen of a display device is constructed according to light-emitting polymer or organic light-emitting diode (OLED) technology. In yet another embodiment, the screen of the display device can be constructed according to reflective display technology such as electronic paper or ink. Known manufacturers of electronic ink / paper displays include E INK and XEROX. Preferably, the screen of the display device also has a reasonably wide field of view, capable of producing an image that does not become blurry or change significantly when the user views the screen from different angles. Because LCD screens operate by polarization, some models exhibit high viewing angle dependence. However, various LCD structures have a relatively wide field of view, which may be preferable. For example, an LCD screen constructed according to thin-film transistor (TFT) technology can have a reasonably wide field of view. Also, screens constructed according to electronic paper / ink technology and OLED technology can have a wider field of view than many LCD screens and may be chosen for this reason.

[0069] The display device may include interaction elements to facilitate user interaction with the display device. In one example, the interaction elements may be physical interaction elements such as input devices or input / output devices, particularly a mouse, keyboard, trackball, touch screen, or a combination thereof. The interaction elements may be used to provide a digital representation to a computer processor in step (i) of the method of the present invention, or to simulate further actions, as described below.

[0070] Examples of further data displayed with the calculated modified sample coating formulation may include data contained in the digital representation of the sample coating and / or the reference coating, determined fitted color data for individual color components, residual model bias, or a combination thereof.

[0071] In one embodiment, the method of the present invention further includes initiating at least one action related to the preparation of a sample coating formulation. The action may be a predefined action. In one example, the action may be initiated by a computer processor based on its programming. In another example, the action may be initiated after detecting user input indicating that the action should be initiated. User input may be detected, for example, through an interaction element of a display device.

[0072] Initiating at least one action may include providing the adjusted sample coating formulation to a printing apparatus and / or a data storage medium and / or a mixing apparatus. The mixing apparatus may be an automated mixing apparatus configured to add adjusted amounts of individual color components to an already prepared sample coating formulation. In one embodiment, the processor determines whether the calculated adjustments exceed a predetermined threshold before providing the adjusted sample formulation to the printing apparatus and / or a data storage medium and / or a mixing apparatus. The predetermined threshold may be a deviation, e.g., a percentage deviation, of the adjusted concentration of individual color components compared to the concentration of individual color components contained in the digital representation of the provided sample coating. This ensures that no unnecessary data transfer is performed if the adjusted sample coating formulation calculated in step (vii) is substantially identical to the sample coating formulation.

[0073] The method of the present invention makes it possible to obtain more accurate and reliable color tuning of the sample coating formulation necessary to adequately match the color of the reference coating by taking into account the variability in color intensity characteristics between batches of colorants used to prepare the sample coating and the reference coating. This makes it possible to determine adjusted optical data that more accurately describes the actual color intensity characteristics of the colorants present in the sample coating formulation, thus enabling a more accurate and reliable color tuning process, reducing the number of steps required to obtain sufficient color matching, and thus significantly improving the efficiency of the method of the present invention.

[0074] Further disclosures include: A computing device for determining the formulation of a sample coating adjusted to match the color of a reference coating, wherein the system: - A communication interface, 〇 Digital representation of the sample coating, including the color data and formulation of the sample coating, ○ Digital representation of the reference coating, including the color data of the reference coating, ○ Digital representation of individual color components, including optical data for each color component, A physical model configured to predict the color of a sample coating by using the formulation of the sample coating and the optical data of individual color components as input parameters, A communication interface to provide, - A processing module that communicates with a communication interface, wherein the processing module comprises at least one computer processor, - A memory that stores instructions configured to cause a computing device to perform steps of the computer implementation method of the present invention when executed by a processing module, It is equipped with.

[0075] The computing device of the present invention takes into account variations in color intensity characteristics between batches of colorants used to prepare the sample coating formulation and the reference coating formulation during the color adjustment process, thereby enabling more accurate and reliable determination of the color adjustments necessary to obtain sufficient color matching between the sample coating and the reference coating.

[0076] In one embodiment, the apparatus further comprises a display device having a screen. In this case, the display device exists separately from the processing module and the memory.

[0077] In an alternative embodiment, the processing module and memory are located within a display device that further includes a screen for displaying the calculated adjusted sample coating formulation received from the processing module on the screen of the display device.

[0078] In one embodiment, the apparatus further comprises at least one database containing digital representations and / or physical models. The digital representations and physical models may be stored in one or more databases. The database is connected to a processing module of the apparatus of the present invention via a communication interface, enabling the processor of the processing module to retrieve the data stored in the database.

[0079] In one embodiment, the apparatus further comprises a measuring device for measuring color data of a sample coating and / or a reference coating. The measuring device may be a spectrophotometer, such as the multi-angle spectrophotometer described above. Reflectance data and texture images and / or texture properties determined using such a spectrophotometer at multiple measurement geometries may be provided to a processing module via a communication interface and processed by the computer processor of the processing module, or processed by the processor of the measuring device as described above in relation to the method of the present invention. The measuring device may be connected to the processing module via a communication interface.

[0080] Further disclosures include: A non-transient computer-readable storage medium, the computer-readable storage medium, when executed by a computing device disclosed herein, includes instructions causing the computing device to perform steps according to the computer implementation method described herein.

[0081] This disclosure applies equally to the methods, systems, and non-transient computer-readable storage media disclosed herein. Therefore, there is no distinction between the methods, systems, and non-transient computer-readable storage media. All features disclosed in connection with the methods of the present invention are also valid for the systems and non-transient computer-readable storage media disclosed herein.

[0082] Further disclosure is the use of methods or computing devices disclosed herein in a color adjustment process. The term “color adjustment process” refers to a process in which the color of an existing sample coating formulation, e.g., a sample coating formulation obtained from a database or a sample formulation calculated by a computer, is adjusted in at least one step so that it adequately matches the color of a reference coating. Particularly preferably, the color adjustment process begins with a sample coating formulation obtained from a database and used in the manufacture of a coating batch, and matches the color of the manufactured coating batch to the color of the reference coating so that it meets customer requirements regarding the appearance of the coating obtained from the manufactured coating batch.

[0083] Further disclosed is a client device for determining the formulation of a sample coating adjusted to match the color of a reference coating on a server device, wherein the client device is configured to provide the server device with a digital representation of the sample coating including color data of the sample coating and the sample coating formulation, a digital representation of the reference coating including color data of the reference coating, and a digital representation of individual color components including optical data of the individual color components, the server device being the computing device of the present invention.

[0084] The server may be an HTTP server and can be accessed using conventional internet web-based technologies. The use of client devices is particularly useful when a service is provided to a customer(s) to determine a prepared sample coating formulation, or in larger company configurations. [Brief explanation of the drawing]

[0085] These and other features of the present invention are described more fully in the following description relating to exemplary embodiments of the present invention. To facilitate the identification of any particular element or action, the most significant digit or number of the reference number refers to the figure number in which that element is first introduced. This description is presented with reference to the accompanying drawings: [Figure 1] A schematic diagram of a color adjustment method known from prior art is shown. [Figure 2] A schematic diagram of the color adjustment method of the present invention is shown. [Figure 3] A block diagram of one embodiment of the present invention's method for determining the formulation of a sample coating adjusted to match the color of a reference coating is shown. [Figure 4] This figure shows one embodiment of the system of the present invention for determining the formulation of a sample coating adjusted to match the color of a reference coating. [Figure 5] This figure shows the client-server setup for the method of the present invention. [Figure 6] This figure shows a graph (top) containing the reflectance spectrum of the reference coating and the reference coating formulation (bottom). [Figure 7] The figure shows a graph (top) containing the measured and predicted reflectance spectra of the reference coating and the adjusted sample coating, a graph (middle) containing the color data of the reference coating, the adjusted sample coating and the predicted sample coating determined using the method described in EP 2149038 B1, and a graph (bottom) containing the adjusted sample colorant formulation. [Figure 8] The figure shows a graph (top) containing the measured reflectance spectrum of the reference coating, color data for the reference coating, the adjusted sample coating, and the predicted sample coating determined using the method of the present invention (middle), and the adjusted sample colorant formulation (bottom). [Modes for carrying out the invention]

[0086] Detailed description of the drawing The detailed description below is intended to illustrate various aspects of the subject matter and not to represent the only possible configurations in which the subject matter can be implemented. The accompanying drawings are incorporated herein and constitute part of the detailed description. The detailed description includes specific details for the purpose of fully understanding the subject matter. However, it will be apparent to those skilled in the art that the subject matter can be implemented without these specific details.

[0087] Figure 1 shows a schematic diagram of a color adjustment method 100 known in the prior art, such as the one disclosed in EP 2149038 B1. This color adjustment method uses a physical model 104, for example, a physical model that describes the interaction of light with a scattering or absorbing medium, such as a colorant in a coating layer, and a numerical optimization algorithm 106, both of which are implemented and executed on at least one processor 102. The processor receives data on a sample coating and a reference coating.

[0088] The data for sample coating 108 includes the color data of the sample coating prepared from the sample coating formulation, such as reflectance data. The color data of the sample coating can be determined using a multi-angle spectrophotometer, as described above.

[0089] The data for the reference coating 110 includes color data such as reflectance data of the reference coating prepared from the reference coating formulation, and optical constants such as K and S values ​​for the individual color components (shown as "colorants" in Figure 1) present in the reference coating formulation. Each individual color component is associated with a set of constants such as wavelength-dependent K and S values. The provided optical constants, and the sample coating formulation or adjusted sample coating formulation, are used as input parameters for the physical model 104 to predict the color data of the sample coating, as described above.

[0090] The predicted sample coating color data is used to determine the model bias as described above by determining the color difference between the provided sample coating color data and the sample coating color data predicted by the physical model 104. The determined model bias is then considered a constant while adjusting the sample coating formulation using the numerical method 106.

[0091] After determining the model bias, numerical method 106 adjusts the concentration of at least one colorant present in the sample coating formulation by minimizing the color difference between the color data of the reference coating and the color data of the sample coating predicted by the physical model 104. During each adjustment of the sample coating formulation by numerical method 106, the physical model 104 is used to predict color data based on optical constants and the adjusted sample coating formulation. The adjustment is repeated by numerical method 106 until the color difference between the color data of the reference coating and the predicted color data of the adjusted sample coating reaches a predetermined threshold, or until a predefined maximum limit of iterations is reached. The adjusted sample formulation 112 associated with the color difference that reached the predetermined threshold, or the adjusted formulation 112 associated with the maximum number of iterations, is then provided for display on a screen by a processor, for example, via a communication interface.

[0092] Figure 2 is a schematic diagram of the color adjustment method 200 according to the present invention. The color adjustment method of the present invention also uses a physical model 204, for example, a physical model that describes the interaction of light with a scattering or absorbing medium, such as a colorant in a coating layer, and a numerical optimization algorithm 206, both of which are implemented and executed on at least one processor 202.

[0093] The data for sample coating 108 and the data for reference coating 110 are provided to the processor 202, as previously described in relation to Figure 1. In contrast to the color adjustment method described in Figure 1, the physical model 204 uses adapted optical constants 212 (labeled "Adj.constants" in Figure 2) to predict the color of the adjusted sample coating formulation. The adapted optical constants 212 for the individual color components (labeled "colorants" in Figure 2) are obtained by minimizing the model bias described in relation to Figure 1 using the numerical optimization algorithm 206 and the physical model 204, as described in relation to the method of the present invention. Instead of the model bias, residual model bias (i.e., the model bias remaining after the optical constants have been adapted) is considered. The use of adapted optical constants allows for the calculation of a more accurate adjusted sample coating formulation because the adjustment of the optical constants can take into account the variation in color intensity between the individual color components used to prepare the sample coating formulation and the individual color components used to prepare the reference coating formulation, as previously described.

[0094] After determining the adapted optical constants for at least some of the individual color components present in the sample coating formulation, a numerical optimization algorithm 206 is used to adjust the concentration of at least one individual color component present in the sample coating formulation, and a physical model 204 is used to predict the color data of the adjusted sample coating formulation using the adapted optical constants. The adjustment is repeated by the numerical method 206 until the color difference between the color data of the reference coating and the predicted color data of the adjusted sample coating reaches a predetermined threshold, or until a predefined maximum limit of iterations is reached. Subsequently, the adjusted sample formulation 214 associated with the color difference that reached the predetermined threshold, or the adjusted sample formulation 214 associated with the maximum number of iterations, is displayed on a screen by the processor, for example, via a communication interface.

[0095] Figure 3 shows a non-limiting embodiment of Method 300 for determining a sample coating formulation adjusted to match the color of a reference coating, according to one embodiment of the present invention. In this example, the sample coating is a solid shade, i.e., a sample coating without effect pigments. In another example, the sample coating is an effect coating containing at least one effect pigment. The method of the present invention can be used during the production of a sample coating formulation to adjust the color of the produced sample coating formulation to match the color of a reference coating, for example, to meet specifications in terms of optical appearance when the sample coating material is applied to a substrate such as an automobile or its parts. In this example, the method of the present invention is performed in a mobile or fixed display device comprising a screen and a housing that accommodates a computer processor(s) running blocks 302 to 334 of Figure 3, as described in relation to Figure 4. In another embodiment, the processor(s) running blocks 302 to 336 of Figure 3 are located separately from a display device having a screen on which the adjusted sample coating formulation is displayed, as described in relation to a client-server configuration in Figure 5.

[0096] In block 302 of Method 300, routine 301 obtains a digital representation of a reference coating, including color data for the reference coating. Color data, such as reflectance data and / or texture properties, can be determined using a multi-angle spectrophotometer, as described in connection with step (i) of the Method of the Invention. In this example, the digital representation (DRR) of the reference coating is obtained based on data contained in the digital representation (DRS) of a sample coating provided to the processor(s) performing routine 301. For this purpose, routine 301 can access a database containing the digital representation of the reference coating, which is interrelated with the data contained in the digital representation of the sample coating, such as the color name, color code, and barcode of the sample coating, and obtain the corresponding digital representation (DRR) from the database based on the data contained in the provided digital representation of the sample coating. In another example, the digital representation of the reference coating is obtained based on data indicating the reference coating, such as the color name, color number, and color code. The aforementioned data may be entered by a user via a GUI and may be used by a processor(s) performing routine 301 to retrieve each digital representation (DRR) from a database containing digital representations (DRRs) that are interrelated with the data entered by the user from a data storage medium such as a database. In another example, the digital representation of a reference coating is obtained by acquiring color data determined using a multi-angle spectrophotometer from the device, for example, by connecting the device to a processor(s) performing routine 301 and determining the color data of the reference coating using the device.

[0097] In block 304, routine 301 determines whether the sample coating data, i.e., the color data and formulation of the sample coating, is available. This can be determined, for example, by whether the digital representation of the sample coating, including the color data, and the formulation of the sample coating were provided in block 302, or by displaying a menu prompting the user to select whether the data is available and detecting user input. If the digital representation (DRS) of the sample coating was already provided in step 302, routine 301 proceeds to block 308, described below. If routine 301 determines in block 304 that the sample coating data is available but not yet provided in block 302, routine 301 proceeds to block 306, described below. If routine 301 determines in block 304 that the sample coating data is not available, it proceeds to block 308, described below.

[0098] In block 306, routine 301 obtains a digital representation (DRS) of the sample coating, including the color data and formulation of the sample coating; however, this block is generally optional. Color data, such as reflectance data and / or texture characteristics, can be determined using a multi-angle spectrophotometer as described above. In one example, the digital representation of the sample coating is obtained from a database based on the data contained in the digital representation (DRR) obtained in block 304. In another example, the digital representation (DRS) is obtained by obtaining the color data determined using a multi-angle spectrophotometer from the device, for example, by connecting the device to a processor(s) performing routine 301 and determining the color data of the sample coating using the device. In yet another example, the digital representation (DRS) is obtained based on data indicating the sample coating, such as color name, color number, and color code. This data may be entered by a user via a GUI and may be used by a processor(s) performing routine 301 to obtain each digital representation (DRR) from a database containing digital representations (DRS) that are interrelated with the user-entered data from a data storage medium such as a database.

[0099] In block 308, routine 301 obtains a digital representation (DRC) of each color component, including optical data for each color component, particularly optical constants such as scattering and absorption properties. The digital representation (DRC) may further include data indicating the individual color component, such as a name, trademark, unique ID, or a combination thereof. In one example, the acquisition may be performed based on data contained in the digital representation (DRR) provided in block 304 and / or data contained in the digital representation (DRS) provided in block 306.

[0100] In block 310, routine 301 obtains a physical model configured to predict the color of a sample coating by using the formulation of the sample coating and optical data of the individual color components as input parameters. Suitable physical color prediction models are well known in the prior art (see, for example, the physical model disclosed in EP 2149038 B1) and include physical models that describe the interaction between light and a scattering or absorbing medium, such as the Kubelka / Munk model, for example, the colorant in the coating layer. In this example, the "Kubelka / Munk" model is obtained in block 310.

[0101] In block 312, routine 301 determines whether a digital representation (DRS) of the sample coating was obtained in block 306 or provided in block 302. If a digital representation (DRS) was obtained or provided, routine 301 proceeds to block 320, described below. Otherwise, routine 301 proceeds to block 314, described below.

[0102] In block 314, routine 301 performs a so-called "matching from scratch" method, determining a sample coating formulation using the digital representation (DRR) provided in block 302, the digital representation DCC provided in block 308, and the physical model provided in block 310. This method is applied, for example, when a formulation database is unavailable. In practice, the "matching from scratch" method often begins with a pre-selection step of components expected to be included in a reference coating formulation. The pre-selection step is not mandatory. The "matching from scratch" method / algorithm calculates one or more preliminary matching formulations for the reference coating as a first solution.

[0103] In block 316, routine 301 is provided for displaying the calculated matching formula. In one example, the formula is provided to a display device having a screen so that the formula can be displayed on the screen of the display device, for example, in a GUI. This allows the user to prepare a sample coating material based on the displayed formulation. In one example, preparing the displayed sample coating material may include sending the displayed sample coating formulation to an automated dosing device and automatically preparing each sample coating material based on the transmitted data. In another example, the sample coating material may be prepared by manually dosing each component based on the displayed data.

[0104] In block 318, routine 301 obtains color data for a sample coating prepared from the sample coating formulation provided in block 316. The acquisition of color data can be performed, for example, by determining the color data using a multi-angle spectrophotometer, as described in relation to block 302.

[0105] In block 320, routine 301 determines the color difference between the color data of a provided sample coating and the color data of a provided reference coating. In this example, block 320 is executed before block 322. In another example, block 320 is executed after block 324 and before block 326. In this example, spectral curve shape similarity is used to determine the color difference. The use of spectral curve shape similarity is preferred because it avoids altering the characteristics or "fingerprints" of individual color components, which would complicate the color adjustment process. In another example, the color difference is determined using a color tolerance equation such as the Delta E (CIE1994) color tolerance equation, the Delta E (CIE2000) color tolerance equation, the Delta E (DIN99) color tolerance equation, the Delta E (CIE1976) color tolerance equation, the Delta E (CMC) color tolerance equation, the Delta E (Audi95) color tolerance equation, or the Delta E (Audi2000) color tolerance equation. These equations may be included in the Digital Representation (DRR) or (DRS). In this example, the determined color difference is correlated with data representing the sample coating and stored on a data storage medium.

[0106] In blocks 322 and 324, routine 301 determines the model bias of the provided physical model by predicting the color data of the sample coating layer in block 322 and determining the color difference between the provided sample coating color data and the predicted sample coating color data in block 324. As previously mentioned, the model bias of the provided physical model is caused primarily by biased specific optical constants resulting from variations in the color intensity of individual components between the reference color components and the components used to prepare the sample coating formulation, and by the limitations of the physical model.

[0107] In block 322, routine 301 predicts the color data of the sample coating based on the color data of the sample coating, the formulation of the sample coating, the digital representation DRC provided in block 308, and the physical model provided in block 310. In this example, the color data of the sample coating and the formulation of the sample coating are included in the digital representation (DRS) provided in block 302 or 306. In another example, i.e., when the “match from zero” method is performed, the formulation of the sample coating is determined in block 314 and the color data is obtained in block 318. In this example, the color data of the sample coating is predicted in block 322 using the provided sample coating formulation and the provided optical data, particularly optical constants, of the individual color components present in the sample coating formulation as input parameters for the provided physical model. The predicted color data can be stored in an internal data storage medium or a data storage medium such as a database. The predicted color data may be correlated with further data, such as data included in the digital representation of the provided sample coating formulation, to enable data retrieval in any of the following blocks.

[0108] In block 324, routine 301 determines the color difference between the provided sample coating color data and the sample coating color data predicted in block 322. The color difference can be determined as described above in relation to block 320.

[0109] In blocks 326 and 328, the model bias determined in blocks 322 and 324 is minimized by routine 301 by fitting the provided optical data, particularly the optical constants, of at least some of the individual color components. By correlating the model bias of the sample coating with the variation in color intensity of the colorants included in the provided physical model, the actual optical properties of the individual color components used to produce the sample coating formulation can be better described, and as a result, the sample coating formulation adjusted in block 332 of the method of the present invention can be calculated more accurately.

[0110] In block 326, routine 301 obtains at least one numerical optimization algorithm (also called a numerical method). The obtained numerical optimization algorithm is configured to fit the provided optical data by minimizing a predetermined cost function and to adjust the concentration of at least one individual color component present in the obtained sample coating formulation. In this example, a numerical optimization algorithm configured to fit the provided optical data by minimizing a predetermined cost function, and a numerical optimization algorithm configured to fit to adjust the concentration of at least one individual color component present in the obtained sample coating formulation by minimizing a predetermined cost function are obtained in block 326. In another example, block 326 is repeated before executing block 332 if only a numerical optimization algorithm configured to fit the provided optical data is obtained in block 326. The algorithms may be obtained from the data storage medium as described above, based on the stored algorithms and their related data.

[0111] In block 328, routine 301 takes the provided optical data, in particular the provided optical constants, of at least some of the individual color components present in the sample coating formulation. - An acquired numerical optimization algorithm configured to adapt the optical data of at least some of the individual color components present in the sample coating formulation by starting from acquired optical data and minimizing a predetermined cost function, - The acquired physical model, Use to adapt.

[0112] Fitting is performed by comparing the recursively predicted color data of the sample coating obtained using the acquired physical model with the acquired sample coating color data, until the cost function falls below a predetermined threshold or the number of iterations reaches a predetermined limit. In this example, the cost function is the color difference between the acquired sample coating color data and the predicted, in particular, recursively predicted, sample coating color data. The color difference can be calculated as described above in relation to block 320. In this example, the predetermined threshold is the predetermined color difference.

[0113] The adapted optical data and / or recursively predicted color data of the sample coating generated in block 328 may be stored, fully or at least partially, in a data storage medium such as an internal data storage device or a database, as described above. The stored adapted optical data and / or predicted color data may be correlated with data contained in the digital representation of the sample coating in order to enable the retrieval of the stored data in any of the blocks of method 300 below.

[0114] In one example, the cost function used in block 328 includes a penalty function that assigns a penalty term to a greater fit of the optical data for at least some of the individual color components. This makes it possible to provide fitted optical data that is as similar as possible to the original optical data (i.e., the optical data contained in the digital representation of the individual color components provided) and prevents the colors of the individual color components from being excessively shifted.

[0115] If block 328 is to fit the optical data of only some of the individual color components present in the sample coating formulation, block 328 may include determining the optical data of the individual color components to be fitted, in particular based on at least one predefined criterion, before comparing the recursively predicted color data of the sample coating obtained using the provided physical model with the provided sample coating color data. The predefined criterion may be included in the acquired digital representation (DRS) and / or (DRR) and / or (DRC). This allows fitting the optical data of only a defined number of individual color components, for example, individual color components present in large quantities, or individual color components that are not white pigments, and as a result, the total number of variables used by the numerical method can be reduced. Reducing the total number of variables can shorten the computation time required to minimize the bias of the model, or reduce the computational resources used to determine the bias of the model.

[0116] In this example, the optical data of at least some of the individual color components present in the sample coating formulation are fitted in block 328 by a numerical optimization algorithm using a scaling function, in particular the linear scaling function of equation (1) described above. The same applies to all wavelength-dependent optical data of the individual color components, in particular to all wavelength-dependent optical constants of the individual color components. TIFF0007855074000009.tif13150 This is because it is possible to retain the characteristics or "fingerprints" of individual color components during the process, and therefore, as mentioned above, it is possible to avoid significant changes in the characteristics or "fingerprints" of individual color components (multiple may be present) which would complicate the color adjustment process.

[0117] In block 330, the residual model bias is determined by routine 301 by determining the color difference between the acquired sample coating color data and the predicted sample coating color data obtained during the minimization of the model bias in block 328. The color difference can be determined as described above in relation to block 320.

[0118] In block 332, routine 301 is: - The color difference determined in blocks 320 and 330, - The adapted optical data obtained in block 328, - A numerical optimization algorithm configured to adjust the concentration of at least one individual color component present in the sample coating formulation by starting from the concentrations of individual color components obtained in block 326 and contained in the obtained sample coating formulation, and minimizing a predetermined cost function, - The physical model obtained in block 310, The sample coating formulation is determined based on the adjustments made.

[0119] In this example, the cost function is the color difference between the color data of the sample coating predicted in block 332 and the color data of the provided reference coating. The color difference can be calculated as described in relation to block 320 above. In this example, a predetermined threshold may be a predetermined color difference.

[0120] The sample coating formulation is adjusted in block 332 using the adapted optical data obtained in block 328 and the recursively adjusted sample coating formulation as input parameters for the acquired physical model. The acquired physical model then predicts color data, such as reflectance data, for the adjusted sample coating formulation based on the input parameters. This prediction is performed for each adjustment of the sample coating formulation until the cost function falls below a predetermined threshold or the maximum limit of iterations is reached.

[0121] In block 334, routine 301 provides the display device with a prepared sample coating formulation for display on the display device's screen. In addition to the prepared sample coating formulation, further data, such as data included in the acquired representation of the sample coating and / or reference coating, determined fitted color data for individual color components, residual model bias, or a combination thereof, may be provided in block 334 for display. Suitable display devices may include the mobile display devices or fixed display devices described above.

[0122] In block 336, routine 301 initiates at least one action related to the adjustment of the sample coating formulation determined in block 332, and this block is usually optional. The action is preferably a predefined action. In one example, the action may be initiated by routine 301 based on its programming. In another example, the action may be initiated after routine 301 detects user input indicating that it is initiating an action. User input may be detected, for example, through an interaction element of a display device. Initiating at least one action may include providing the adjusted sample coating formulation to a printing device and / or a data storage medium and / or a mixing device.

[0123] After block 336 finishes, routine 301 either terminates method 300 or returns to block 302.

[0124] Figure 4 shows an example of a system 400 for determining a sample coating formulation adjusted to match the color of a reference coating, which can be used to carry out blocks 302 to 336 of method 300 described in relation to Figure 3. The system 400 comprises a computing device 402 housing a computer processor 404 and memory 406. The processor 404 executes instructions obtained, for example, from memory 406, and performs operations related to the computer system 400, i.e. - Via communication interface • Digital representation of the sample coating, including the color data and formulation of the sample coating, • Digital representation of the reference coating, including color data of the reference coating, • Digital representation of individual color components, including optical data for each color component, A physical model configured to predict the color of a sample coating by using the formulation of the sample coating and the optical data of the individual color components as input parameters, Receiving; - To determine the color difference between the provided sample coating color data and the provided reference coating color data; - The model bias of the acquired physical model, • Predicting the color data of a sample coating based on a digital representation of the sample coating, a digital representation of individual color components, and an acquired physical model. • To determine the color difference between the acquired sample coating color data and the predicted sample coating color data, It will be determined by; - Minimizing the determined model bias by fitting the optical data of individual color components obtained for at least some of the individual color components present in the sample coating formulation; - Determining residual model bias by determining the color difference between the acquired sample coating color data and the predicted color data using fitted optical data; - Calculate the adjusted sample coating formulation based on the determined color difference, the optical data of the fitted individual color components, the determined residual model bias, and the acquired physical model; - To provide the calculated and adjusted sample coating formulation via the communication interface, It is configured to perform the following:

[0125] The processor 404 may be a single-chip processor or it may be implemented as multiple components. In most cases, the processor 404 works with the operating system to execute computer code and generate and use data. In this example, the computer code and data reside in memory 406 operably coupled to the processor 404. Memory 406 generally provides a place to hold data used by the computer system 400. As an example, memory 406 may include read-only memory (ROM), random access memory (RAM), a hard disk drive and / or similar. In another example, the computer code and data may reside on removable storage media and be loaded or installed into the computer system when needed. Removable storage media include, for example, CD-ROMs, PC-CARDs, floppy disks, magnetic tapes, and network components. The processor 404 may be located on a local computing device or in a cloud environment (see, for example, Figure 5). In the latter case, the display device 424 functions as a client device and can access a server (i.e., computing device 402) via a network (i.e., communication interface 426).

[0126] The computing device 402 is connected to databases 408, 410, 412, and 414 via communication interfaces 416, 418, 420, and 422. Databases 408, 410, 412, and 414 store digital representations of sample coatings, reference coatings, individual color components, and physical models that can be retrieved by processor 404 via communication interfaces 416, 418, 420, and 422. The digital representation of the sample coating stored in the database includes the color data and formulation of the sample coating. The digital representation of the reference coating includes the color data of the reference coating. The digital representation of individual color components includes the optical data of the individual color components, in particular, the optical constants. In one example, each digital representation may include the further data described above. In one example, the digital representations of the sample coating and the reference coating are retrieved by the processor 404 from their respective databases based on data indicating the sample coating and / or reference coating entered by the user via the display device 424, or data indicating the sample coating and / or reference coating associated with a predefined user action performed on the display device 424, such as selecting a desired action on the GUI of the display device 424 (e.g., displaying a list of saved and measured color data, displaying a list of available sample / reference coatings).

[0127] The system 400 may further include a display device 424 coupled to the computing device 404 via a communication interface 426. The display device 424 receives a prepared sample coating formulation calculated from the processor 404 and displays the received prepared sample coating formulation on a screen, in particular to the user via a graphical user interface (GUI). For this purpose, the display device 424 is operably coupled to the processor 404 of the computing device 402 via the communication interface 426. In this example, the display device 424 is an input / output device comprising a screen and integrated with a processor and memory (not shown) to form a desktop computer (all-in-one machine), laptop, handheld or tablet, etc., and is used to enable user input for obtaining a digital representation as described above. In another example, the screen of the display device 424 may be a separate component (a peripheral device, not shown). For example, the screen of the display device 424 may be a monochrome display, a color graphics adapter (CGA) display, an extended graphics adapter (EGA) display, a variable graphics array (VGA) display, a super VGA display, a liquid crystal display (e.g., active matrix, passive matrix, etc.), a cathode ray tube (CRT), a plasma display, etc.

[0128] The system may further include a measuring device 428, such as a multi-angle spectrophotometer, so that the color data of a reference coating and / or a sample coating can be determined using the device 428. The measuring device is coupled to the processor 404 via a communication interface 430 so that the determined data can be acquired by the processor 404. The determined data may be measured data or color data already processed by the processor of the measuring device.

[0129] Turning to Figure 5, an internet-based system 500 is shown for determining a sample coating formulation adjusted to match the color of a reference coating, which can be used to carry out the method 300 described in relation to Figure 3. The system 500 comprises a server 502 accessible by one or more clients 506.1 to 506.n via a network 504 such as the Internet. In one example, the server corresponds to the computing device 402 described in relation to Figure 4. Preferably, the server is an HTTP server and is accessed via conventional internet web-based technology. 5 06 is a computer terminal accessible by the user and may be a customized device such as a data entry kiosk, or a general-purpose device such as a personal computer. In one example, the client device corresponds to the display device 424 in Figure 4. The client has a screen and is used to display the generated appearance data. A printer 508 can be connected to the client terminal 506. The internet-based system 500 is particularly useful when the service is provided to customers or in larger company setups. The client 506 can be used to provide the server's computer processor with a digital representation of the sample coating, including the color data and formulation of the sample coating; a digital representation of the reference coating, including the color data of the reference coating; and a digital representation of individual color components, including the optical data of the individual color components.

[0130] Figure 6 shows graph 602 of the reflectance spectra 604 of the reference coating (top) and the associated reference coating formulation 608 (bottom). On the left side, color data 606 determined by a multi-angle spectrophotometer is shown. The reference coating contains a large amount of white pigment and is colored with a small amount of black pigment having a color intensity of 100%.

[0131] Figure 7 shows graph 702 (top) containing the measured and predicted reflectance spectra of the reference coating and the adjusted sample coating, color data for the reference coating 706', the adjusted sample coating 710', and the predicted sample coating 708' determined using the method described in EP2149038 B1 (middle), and the adjusted sample coating formulation 714 (bottom). Part of graph 702 is enlarged to 704 to show the variability between the measured reflectance spectrum of the reference coating 706, the measured reflectance spectrum of the adjusted sample coating 710, and the predicted reflectance spectrum of the adjusted sample coating 708. The variability in the reflectance spectra between the reference coating 706 and the adjusted sample coating 710 is also reflected in the color data 712. This variability is due to the assumption that the color intensity of the black coloring paste was not adjusted and was set to 100% during the determination of the adjusted sample coating formulation. The adjusted sample coating formulation is too dilute, so the color intensity of the black coloring paste used to prepare the sample coating formulation must be less than 100%. A limitation of this state-of-the-art method is that the optical properties of the colorant are not constant over time. Actual colorants are affected by a systematic bias caused by changes in the optical properties of the colorant compared to a "reference" colorant (particularly changes in color intensity properties), and this bias propagates to the adjusted formulation. Depending on the scale of this bias and the scale of residual color difference, the color adjustment results can be significantly inaccurate, as shown in Figure 7.

[0132] Figure 8 shows graph 802 (top) containing the measured reflectance spectrum of the reference coating, color data for the reference coating 806', the adjusted sample coating 810', and the predicted sample coating 808' determined using the methods of the present invention, such as method 300 described in relation to Figure 3 (middle), and the adjusted sample coating formulation 814 (bottom). Part of graph 802 is enlarged to 804 to show the variability between the measured reflectance spectrum of the reference coating 806, the measured reflectance spectrum of the adjusted sample coating 810, and the predicted reflectance spectrum of the adjusted sample coating 808. The higher accuracy of the methods of the present invention compared to the results shown in Figure 7 is due to the consideration of the color intensity of the black coloring paste used to formulate the sample coating formulation, which is less than 100% compared to the color intensity of the black coloring paste used to formulate the reference coating formulation. In summary, the color adjustment method of the present invention can achieve accurately adjusted sample formulations regardless of the color intensity of the individual color components used to prepare the reference coating formulation and the sample coating formulation, and thus can reduce the number of color adjustments required to achieve the desired color matching.

Claims

1. A computer-implemented method for determining the formulation of a sample coating adjusted to match the color of a reference coating, wherein the method is: (i) To the computer processor via a communication interface - Digital representation of the sample coating, including the color data and formulation of the sample coating, - Digital representation of the reference coating, including the color data of the reference coating, - Digital representation of individual color components, including optical data for each color component, A physical model configured to predict the color of a sample coating by using the formulation of the sample coating and the optical data of individual color components as input parameters, The steps to provide, (ii) A step in which a computer processor determines the color difference between the provided sample coating color data and the provided reference coating color data, (iii) The model bias of the provided physical model is processed by a computer processor. - Predicting the color data of the sample coating based on the digital representation of the sample coating, the digital representation of the individual color components, and the physical model provided in step (i), - To determine the color difference between the provided sample coating color data and the predicted sample coating color data, The steps to be determined by, (iv) A step in which the model bias determined in step (iii) is minimized by a computer processor by fitting the provided optical data of at least some of the individual color components present in the sample coating formulation, (v) A step in which the residual model bias is determined by a computer processor by determining the color difference between the provided color data and the predicted color data of the sample coating using the optical data fitted in step (iv), (vi) A step in which a computer processor calculates the adjusted sample coating formulation based on the color difference determined in step (ii), the fitted optical data of the individual color components obtained in step (iv), the residual model bias determined in step (v), and the provided physical model, (vii) The step of providing the calculated adjusted sample coating formulation via a communication interface, Methods that include...

2. The method according to claim 1, wherein the digital representation of the sample coating further includes data indicating the sample coating, the layer structure of the sample coating, instructions for preparing the sample coating formulation, a price, or a combination thereof.

3. The method according to claim 1 or 2, wherein the digital representation of the reference coating further includes data indicating the reference coating, the layer structure of the reference coating, the formulation related to the reference coating, instructions for preparing the reference coating formulation, a price, or a combination thereof.

4. The method according to claim 1 or 2, wherein the color data includes reflectance data, color space data, or a combination thereof.

5. The method according to claim 1 or 2, wherein the optical data for each color component includes the optical constants of each color component.

6. The method according to claim 1 or 2, wherein the color of the sample coating is predicted in step (iii) using the optical data of the sample coating formulation and the individual color components present within the sample coating formulation as input parameters of a provided physical model.

7. Minimizing the model bias determined in step (iii) is: - A numerical method is provided which is configured to match the optical data of at least some of the individual color components present in a sample coating formulation by starting from the optical data provided in step (i) and minimizing a predetermined cost function, The method according to claim 1 or 2, further comprising the step of fitting optical data of at least some of the individual color components present in the sample coating formulation using the provided numerical method and the provided physical model, by comparing the color data of the sample coating obtained using the provided physical model with the color data of the provided sample coating until the cost function falls below a predetermined threshold or the number of iterations reaches a predetermined limit.

8. The method according to claim 7, wherein fitting the optical data of at least some of the individual color components present in the sample coating formulation includes applying a scaling function to the optical data.

9. The scaling function includes the linear scaling function of equation (1), [Math 1] Here 【number】 【number】 【number】 Refers to the adapted optical data. 【number】 It refers to an index, ranging from 1 to n. 【number】 The method according to claim 8, wherein the range is from 1 to m.

10. The method according to claim 9, used for optical data of all wavelength-dependent individual color components.

11. Calculating the corrected sample coating formulation - A numerical method is provided which is configured to adjust the concentration of at least one individual color component present in a sample coating formulation by starting from the concentrations of individual color components contained in a digital representation of a provided sample coating and minimizing a predetermined cost function. - A step of adjusting the concentration of at least one individual color component present in the sample coating formulation by comparing the recursively predicted color data of the recursively adjusted formulation of the sample coating with the color data of a provided reference coating, using the provided numerical method, the adapted optical data obtained in step (iv), the residual model bias, and the provided physical model, until the color difference falls below a predetermined threshold or the number of iterations reaches a predetermined limit. The method according to claim 1 or 2, including the method described in claim 1 or 2.

12. A computing device for determining the formulation of a sample coating adjusted to match the color of a reference coating, wherein the computing device: - A communication interface, 〇 Digital representation of the sample coating, including the color data and formulation of the sample coating, ○ Digital representation of the reference coating, including the color data of the reference coating, ○ Digital representation of individual color components, including optical data for each color component, A physical model configured to predict the color of a sample coating by using the formulation of the sample coating and the optical data of individual color components as input parameters, A communication interface to provide, - A processing module that communicates with the aforementioned communication interface, wherein the processing module comprises at least one computer processor, - A memory that stores instructions configured to cause a computing device to perform the steps of the computer implementation method described in claim 1 when executed by the processing module, A computing device equipped with the following features.

13. A non-transient computer-readable storage medium, wherein the computer-readable storage medium includes an instruction that causes the computing device to perform a step according to the method of claim 1 or 2 when executed by the computing device of claim 12.

14. The use of the method according to claim 1 or the computing device according to claim 12 in a color adjustment process.

15. A system comprising a server device and a client device, wherein the client device is for determining a sample coating formulation adjusted to match the color of a reference coating in the server device, the client device is configured to provide the server device with a digital representation of the sample coating including color data of the sample coating and the sample coating formulation, a digital representation of the reference coating including color data of the reference coating, and a digital representation of individual color components including optical data of the individual color components, the server device being the computing device of claim 12.

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