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] Aspects described herein generally relate to methods and systems for adjusting the color of a sample coating to the color of a reference coating such that a sufficient color match is obtained. 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 adapted optical data for each color component present in the sample coating formulation and using the adapted optical data to determine a modified sample coating formulation. Using the adapted optical data for each color component present in the sample coating formulation in the color adjustment process can compensate for colorant strength characteristics variations in paint manufacturing. The optical data adjustment can improve the quality and / or accuracy of the adjusted sample coating formulation, thus reducing the number of adjustment steps required to obtain a desired color of the sample coating relative to the reference coating. [Background technology]

[0002] The paint manufacturing process for a given color standard usually starts with an initial coating formulation, such as a formulation loaded from a database. The color of the initial coating formulation is obtained by adding at least one pigment paste (hereinafter also called colorant) to a base varnish containing binders, solvents, and optionally additives. The pigment paste is an intermediate product that contains color-imparting components (such as pigments) in a matrix (typically binders, solvents, and optionally additives). Typically, the color of said intermediate product varies from batch to batch due to variations in the quality of raw materials such as pigments. To avoid adjustments of 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. Usually, the initial coating formulation contains a reduced amount of pigment paste (compared to the final paint formulation) to avoid the produced coating batch being too dark due to an overshoot of the color intensity properties of one or more colorants present in the coating formulation. An initial coating batch is produced according to this initial coating formulation, and the corresponding color of this coating batch is measured and compared to a reference color. Since the amount of colorant is reduced, the initial coating batch usually has a significant residual color difference compared to the reference coating. Therefore, a color adjustment process needs to be applied by modifying the formula of the initial coating to minimize the residual color difference between the color of the coating batch and the color of the reference coating. Then, a modified coating is prepared from the modified initial coating formula, and the color of the modified coating is determined and compared with the color of the reference coating. If there is no sufficient match, the color adjustment process needs to be repeated with the adjusted initial coating formula.

[0003] Most computer-aided color adjustment methods (also called color matching methods) are based on physical models that describe the interaction of light with scattering or absorbing media, such as colorants in a coating layer. Each coating layer has specific light reflectance properties that are due to the colorants present in the coating layer. Each of these colorants has specific optical properties that are represented by respective optical constants or optical data. These optical constants describe the absorption and scattering properties of these colorants in the context of the physical model, such as the K / S values ​​in the well-known "Kubelka / Munk" model. A physical model such as the "Kubelka / Munk" model can predict the light reflectance properties (color) of a coating layer based on information about the colorants present in the coating layer (e.g., based on information about the formula used to prepare the coating layer) along with the corresponding optical properties or respective optical constants of the colorants.

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

[0005] A suitable formula (or suitable color adjustment) for a given reference color can be predicted using a numerical optimization algorithm based on a physical model having existing optical constants of colorants and reflectance data of a reference coating as input parameters. However, the color prediction accuracy of the physical model is limited by the presence of systematic and statistical errors. Statistical errors can be caused by differences in the instrument used to determine the color, or the measurement process, e.g., the position of the instrument on the sample. A systematic error (hereinafter also referred to as model bias) is defined as the difference between the measured color of a sample coating and the color of the sample coating predicted by a physical model. By taking into account the model bias during the color adjustment process, the accuracy of the process can be improved. For example, European Patent EP 2149038 B1 discloses a color adjustment algorithm based on a physical model combined with a numerical optimization algorithm. The color adjustment algorithm minimizes the residual color difference between the coating batch and the reference color while taking into account the determined model bias of the physical model as a constant offset for color adjustment. Thus, the adjusted sample coating formula is a function of the reference color and the offset between the predicted and measured reflectance data of the sample coating. This color adjustment algorithm is based on the fundamental assumption that the model bias remains constant when the formula is changed on a "small scale" basis; that is, as long as the adjusted coating formula is "similar" to the original coating formula, the model bias is expected to be similar.

[0006] A limitation of this approach is that the optical properties (e.g., color intensity properties) of the colorant are not constant over time, but typically vary from manufacturing batch to manufacturing batch within a certain range due to variations in raw materials, e.g., pigments. Color intensity is defined as the ability of a colorant to modify the color of a coating layer and can be used as an indicator of the efficiency of a colorant, since it measures the degree of color change per amount of colorant. Color intensity is calculated according to the following formula: TIFF2025504811000002.tif9150 It can be defined according to:

[0007] Examples of color intensity include, for example, the color strength of a colorant used to color, or the color reducing power of a white colorant.

[0008] The greater the color intensity of a colorant, the greater its impact on the color of the coating layer. Thus, the color intensity characteristic of each colorant correlates with the "K" and "S" scales of the absorption and scattering properties of the colorant.

[0009] In conclusion, the color intensity properties of colorants such as pigment pastes present in the colorant batches used to prepare the sample coating formulation may differ from the color intensity properties of colorants present in the reference colorant batches used to prepare the reference coating. Depending on the scale of the difference in color intensity properties and the scale of the color difference between the sample coating and the reference coating, the color adjustment results may be significantly inaccurate, despite taking into account model biases as described in EP 2149038 B1. Summary of the Invention [Problem to be solved by the invention]

[0010] It would therefore be desirable to provide a method and system for generating an adjusted coating formula that adequately matches the color of a reference coating without the aforementioned drawbacks. More specifically, a computer-implemented method and system for determining an adjusted sample coating formula that matches the color of a reference coating should provide more accurate color adjustment results, particularly by taking into account variations in the color intensity of colorants present in the coating formula. [Means for solving the problem]

[0011] definition The term "reference coating" may refer to a coating having defined characteristics, such as defined colorimetric properties. The reference coating may be prepared by applying at least one defined coating material to a surface and curing the applied coating material, with the proviso 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 with the reference coating with respect to at least some of the defined characteristics, such as colorimetric properties. The sample coating may be prepared, as described for the reference coating, preferably by using the same number and types of coating formulations used to prepare the reference coating. The term "sample coating formulation" refers to the coating materials used to prepare the sample coating, whereas 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 has been modified with respect to the sample formulation (i.e., the unmodified sample formulation), for example by modifying the amount of said component. The terms "formulation", "color formulation" and "paint formulation" are used interchangeably herein.

[0012] "Display device" refers to an output device for presenting information in visual or tactile form (the latter may be used for tactile electronic displays for the visually impaired). "Display device screen" refers equally to 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 *The data may include color space data such as color value, gloss data, texture parameters such as shine characteristics and / or roughness characteristics, or a combination thereof.

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

[0015] "Individual color components" refers to separate components present within a coating formulation, such as the sample coating formulation and the reference coating formulation. Examples of individual color components include pigments, such as color 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 color pigments and effect pigments.

[0016] "Optical data of individual color components" refers to the optical properties and / or specific optical constants of the individual color components. The optical constants of the individual color components are parameters of a physical model, which can be determined by preparing a reference coating with a reference batch of pigment paste as described above and determining the optical properties, for example by measuring the reflectance spectrum of the prepared reference coating with a spectrophotometer. From the reflectance spectrum and the 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 models used according to the present invention are based on physical laws that describe the light absorption and light scattering properties of pigment systems.

[0018] The term "model bias" (hereinafter also referred to as physical model bias) refers to the systematic error of the physical model while predicting color data based on the optical data of the coating formulation and the individual color components. The systematic error includes the limitations of the physical model and the bias present in the optical data of the individual color components present in the sample coating formulation. The bias present in the optical data of the 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, since the color intensity characteristics of the pigment paste vary from batch to batch due to the deviations of the raw materials (e.g. 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 the 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 the individual color components allows the different color intensity characteristics of the pigment pastes to be taken into account during the color adjustment process.

[0019] A "communication interface" may refer to a software and / or hardware interface for establishing communication, such as the transfer or exchange of signals or data. A software interface may be, for example, a function call, an API. A communication interface may comprise a transceiver and / or a receiver. The 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, e.g., a short-range communication protocol, such as Bluetooth or WiFi, or a long-range communication protocol, e.g., 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 proprietary short-range or long-range protocol. A communication interface may support any one or more standard and / or proprietary protocols.

[0020] A "computer processor" refers to any logic circuitry configured to perform basic operations of a computer or system, and / or generally a device configured to perform calculations or logical operations. In particular, the processing means or computer processor may be configured to process basic instructions that run the computer or system. By way of example, the processing means or computer processor may comprise at least one arithmetic logic computing device ("ALU"), at least one floating point unit ("FPU"), such as a mathematical coprocessor or numeric coprocessor, a number of registers, in particular registers configured to supply operands to the ALU and to store the results of the operations, and memories, such as an L1 cache memory and an L2 cache memory. In particular, the processing means or computer processor may be a multi-core processor. In particular, the processing means or computer processor may be or comprise a central processing unit ("CPU"). 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 other instruction sets, 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 complex programmable logic device ("CPLD"), a digital signal processor ("DSP"), a network processor, or the like. 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.It should be understood that the term processing means or processor may refer to one or more processing devices, such as a distributed system of processing devices located across multiple computer systems (e.g., cloud computing), and is not limited to a single device unless otherwise specified. The terms "processor" and "computer processor" are used interchangeably herein.

[0021] A "data storage medium" may refer to physical media and other computer-readable media for carrying or storing computer-executable instructions and / or data structures. Such computer-readable media may be any available media accessible by a general-purpose or special-purpose computer system. Computer-readable media may 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 ("SSD"), flash memory, phase-change memory ("PCM"), optical disk storage, magnetic disk storage or other magnetic storage devices, or any other hardware storage device that may 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] A "database" may refer to a collection of related information that can be searched and retrieved. A database may be a searchable electronic numeric, alphanumeric, or text document; a searchable PDF document; a Microsoft Excel® spreadsheet; or any database commonly known in the state of the art. A database may be a set of electronic documents, photographs, images, diagrams, data, or drawings that reside on a computer readable storage medium that can be searched and retrieved. A database may be a single database, a set of related databases, or a collection of unrelated databases. "Related databases" means there is at least one common information element in related databases that can be used to relate such databases.

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

[0024] overview In order to solve the above problems from a high level, the following is proposed: 1. A computer-implemented method for determining a recipe for a sample coating adjusted to match a color of a reference coating, the method comprising: (i) to a computer processor via a communications interface; A digital representation of the sample coating, including color data of the sample coating and the sample coating formula; a digital representation of the reference coating, including color data of the reference coating; A digital representation of the individual color components, including the optical data of the individual color components; a physical model configured to predict the color of a sample coating by using optical data of the sample coating's formulation and individual color components as input parameters; providing a (ii) determining with a computer processor a color difference between the color data of the provided sample coating and the color data of the provided reference coating; (iii) calculating, by a computer processor, the model bias of the provided physical model; predicting color data of the sample coating based on the digital representation of the sample coating, the digital representations of the individual color components, and the physical model provided in step (i); determining a color difference between the provided color data of the sample coating and the predicted color data of the sample coating; determining the (iv) minimizing with a computer processor the model bias determined in step (iii) by fitting the provided individual color component optical data for at least a portion of the individual color components present in the sample coating formulation; (v) determining with the computer processor a residual model bias by determining a color difference between the provided color data and the predicted color data of the sample coating using the fitted optical data from step (iv); (vi) calculating with a computer processor an adjusted sample coating formula 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) providing said calculated adjusted sample coating formulation via a communications interface; Includes.

[0025] An essential advantage of the method according to the invention is that the part of the model bias of the physical model caused by the variation of the color intensity properties of the pigment pastes used for the production of the reference coating material and the sample coating material (variation of the color intensity of the individual color components) is minimized. In order to minimize this part of the model bias caused by the variation of the color intensity properties, the model bias of the sample coating is correlated with the variation of the color intensity properties of the individual color components contained in the physical model. This is done by adapting the provided optical data of the individual color components contained in the sample coating recipe in such a way that the model bias of the physical model is minimized. This results in adapted optical data that more accurately describes the actual optical properties of the individual color components used in the sample coating recipe. Subsequent adjustment of the sample coating recipe using the adapted optical data of the individual color components results in a more robust and more accurate color adjustment, and a sufficient color match can be obtained with fewer adjustment steps compared to the methods known in the prior art. This significantly increases the efficiency of the color adjustment method of the invention.

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

[0027] In an embodiment of step (i), providing a digital representation of the sample coating and / or a digital representation of the reference coating comprises determining color data of the sample coating and / or the reference coating using a measurement device and inputting the determined color data, optionally in combination with further data and / or metadata and / or user input, into a computer processor via a communications interface.

[0028] The color data can be measured using a commercially available multi-angle spectrophotometer, such as a spectrometer of the Byk-Mac® I or XRite MA®-T family. For this purpose, the reflectance of the respective sample and / or reference coating is measured for several geometries. In the case of effect coatings, texture images (grayscale or color images) are preferably acquired in several geometries. The multi-angle spectrophotometer is preferably connected to a computer processor, which can be programmed to process the measured reflectance data and the texture images, for example by calculating color data for each measurement geometry from the measured reflectance and / or texture characteristics for the defined measurement geometries. The determined color data can be stored in a data storage medium, such as an internal memory or a database, before providing the determined color data to the computer processor via a communication interface. This can include, if necessary, correlating the determined color data with further data and / or metadata and / or user inputs, before storing the determined color data, so that the stored color data can be retrieved using further data and / or metadata and / or user inputs. Storing the determined color data may be preferable if the data is needed several times, since the data does not have to be retrieved each time the appearance of each effect coating is displayed on the screen of a display device.

[0029] The additional data and / or metadata and / or user input may include the above listed color number / color code / barcode / unique database ID 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 combinations thereof.

[0030] In alternative aspects, providing a digital representation of the reference coating includes providing a digital representation of a sample coating and / or providing data indicative of 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 indicative of the reference coating, and providing the obtained digital representation of the reference coating.

[0031] The data indicative of the reference coating may include a color name, color number, color code, bar code, ID, etc. associated with the reference coating. The data indicative of the reference coating may be entered by a user via a GUI displayed on the screen of the display device, may be retrieved from a database based on a scanned code, such as a QR code, or may be associated with a predefined user action. A predefined user action may include, for example, selecting a desired action on a GUI displayed on the screen of the display device, such as displaying a list of saved measurements with associated images, or displaying a list of available reference coatings according to search criteria, a user profile, etc.

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

[0033] The digital representation of the sample coating includes color data of the sample coating and the formula of the sample coating, i.e., the types and amounts of components included in the formula of the sample coating. The color data of the sample coating is preferably color data determined using a measurement device, and therefore does not include simulated color data, i.e., color data that is not generated from measurement data, such as reflectance values ​​or texture images. In one embodiment, the digital representation of the sample coating further includes data indicative of the sample coating, the layer structure of the sample coating, instructions for preparing the formula of the sample coating, prices, predefined criteria regarding the optical data of the individual components to be matched, or combinations thereof. The data indicative of the sample coating may include, for example, a color number, a color code, a unique database ID, a bar code, or combinations thereof.

[0034] The digital representation of the reference coating includes color data of the reference coating. The color data of the reference coating is preferably color data determined with a measurement device, and therefore does not include simulated color data, i.e., color data that is not generated from measurement data, such as reflectance values ​​or texture images. In one embodiment, the digital representation of the reference coating further includes data indicative of the reference coating, the layer structure of the reference coating, a formulation associated with the reference coating, instructions for preparing the reference coating formulation, a price, data indicative of a method for determining color differences, such as a color tolerance equation or other methods including shape similarity of the spectral curves, predefined criteria for the optical data of the individual components to be matched, or a combination thereof. The data indicative of the reference coating can include, for example, a color number, a color code, a unique database ID, a bar code, or a combination thereof.

[0035] In one aspect, the color data includes reflectance data, color space data, particularly CIEL * a * b * Value or CIEL * C * h * The color data may include color values, gloss data, texture parameters, in particular shine and / or roughness characteristics, or a combination thereof. The color data may be determined using a multi-angle spectrophotometer, as described above. The color data may be modified by using color and / or texture offsets, for example by lightening or darkening colors.

[0036] The digital representation of the individual color components includes optical data for the individual color components. In one embodiment, the digital representation further includes data indicative of the individual color components. The data indicative of the individual color components may be a name, a trade name, a unique ID (i.e., a material code or number) associated with the component, or a combination thereof.

[0037] In one aspect, the optical data for the individual color components includes the optical constants of the individual color components, in particular the wavelength dependent scattering and absorption properties of the individual color components. The optical constants may further include the orientation of the individual color components, such as effect pigments within a coating.

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

[0039] In one aspect, the color difference in steps (ii) and / or (iii) and / or (v) is determined using a color tolerance equation, in particular the Delta E (CIE 1994) color tolerance equation, the Delta E (CIE 2000) color tolerance equation, the Delta E (DIN 99) color tolerance equation, the Delta E (CIE 1976) color tolerance equation, the Delta E (CMC) color tolerance equation, the Delta E (Audi 95) color tolerance equation, the Delta E (Audi 2000) color tolerance equation or other color tolerance equations.

[0040] In an alternative embodiment, the color difference in steps (ii) and / or (iii) and / or (v) is determined using shape similarity of the spectral curves. The use of shape similarity of the spectral curves is preferred as it avoids modifying the characteristics or "fingerprints" of the individual color components, which would make the color tuning process more complicated.

[0041] The determined color difference can be stored in a data storage medium, such as an internal data storage medium or 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 the acquisition of the data in any one of the subsequent method steps.

[0042] In one aspect, steps (ii) to (vii) are performed simultaneously. "Simultaneously" refers to the time during which a computer processor performs steps (ii) to (vii). Preferably, this time is small enough so that an adjusted sample recipe can be generated ad-hoc, i.e., within a few milliseconds of starting step (ii).

[0043] In step (iii), a model bias of the provided physical model is determined by a computer processor. As described above, the model bias of the provided physical model is mainly caused by biased specific optical constants due to the variation in color intensity of the individual color components between the reference color components 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 color data of the sample coating based on the digital representation of the provided sample coating and the digital representation of the provided individual color components. Then, a color difference between the color data of the sample coating included 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 described above 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, in particular the optical constants, of the sample coating formulation and the individual color components present in the sample coating formulation as input parameters of the 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 a data storage medium, such as an internal data storage medium or a database. The predicted color data can be correlated with further data, such as data contained in a digital representation of the provided sample coating formulation, to enable data retrieval in any one 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 color intensity variations 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 thus the adjusted sample coating formulation in step (vi) of the method of the present invention can be more accurately calculated.

[0046] In one aspect, minimizing the model bias determined in step (iii) comprises: - providing a numerical method configured to fit the optical data of at least a portion of the individual color components present in the sample coating formulation by minimizing a predetermined cost function, starting from the optical data provided in step (i); - fitting the optical data of at least a part 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 color data of the provided sample coating until a cost function falls below a predefined threshold or the number of iterations reaches a predefined limit; Includes.

[0047] Thus, 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 of the individual color components is fitted. In another example, the optical data of only some of the individual color components is fitted as described below, thus leaving the optical data of the remaining portions of the individual color components unchanged.

[0048] Suitable numerical methods include the COBYLA (Constrained Optimization by Linear Approximation) method described in "A direct search optimization method that models the objective and constraint functions by linear interpolation" by MJD Powell, 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-free optimization method that supports arbitrary nonlinear inequality and equality constraints.

[0049] The numerical method may be stored in a data storage medium, such as an internal memory of a computing device comprising the computer processor, or in a database connected to the computer processor via a communication interface. When performing step (iv), 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 an internal data storage or a database. In one example, the adapted color data and / or all the recursively predicted color data are stored. This may be preferred when data storage limitations are not important. In another example, only a portion of the adapted color data and / or the recursively predicted color data, for example predicted color data related to the adapted optical constants where the cost function is below a predefined threshold or obtained at a maximum limit of the iterations, is stored in the data storage medium. This may be preferred when data storage capacity is limited. The stored adapted optical data and / or predicted color data may be correlated with data included in the digital representation of the sample coating to allow 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 color data of the sample coating and the predicted color data of the sample coating. Said 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.

[0052] In one example, the cost function includes a penalty function that assigns a penalty term to a greater match of the optical data of at least some of the individual color components. The term "greater match" refers to a match of the optical data of at least some of the individual color components by at least 10%. In one example, the penalty term is assigned to a match of the optical data by 10%. In another example, the penalty term is assigned to a match of the optical data by 20%. In yet another example, the penalty term is assigned to a match of the optical data by 50%. This allows the adjustment optical data to be provided that is as similar as possible to the original optical data (i.e., the optical data included in the digital representation of the provided individual color components) and prevents the color of the individual color components from being excessively shifted to correct for small color differences between the color data of the provided sample coating and the predicted color data of the sample coating, or to correct for some of the model bias or residual model bias. Such excessive shifting of color is undesirable because it results in an unlikely adjusted sample coating formulation that cannot be prepared using the available individual color components.

[0053] The fitting of at least some of the optical data of the individual color components present in the sample coating formulation 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 color data of the provided sample coating. Examples of predefined criteria may include the amount of the individual color components present in the sample coating formulation, and / or the type of the individual color components. The predefined criteria may be included in the digital representation of the sample coating, the reference coating or the individual color components provided in step (i). This allows fitting the optical data of only a defined number of individual color components, e.g. individual color components present in greater numbers, or individual color components that are not white pigments, and thus reduces the total number of variables used by the numerical method. Reducing the total number of variables makes the optimization method more robust, e.g. 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 the sample coating formulation includes applying a scaling function to the optical data.

[0055] Suitable scaling functions include the linear scaling function in Eq. (1), TIFF2025504811000003.tif7150 Here TIFF2025504811000004.tif6150In particular, it refers to the optical constants, TIFF2025504811000005.tif6150 TIFF2025504811000006.tif7150 Refers to fitted optical data, especially fitted optical constants, TIFF2025504811000007.tif6150 refers to index, ranges from 1 to n, TIFF2025504811000008.tif61501 to m in range.

[0056] TIFF2025504811000009.tif6150 is preferably used for all wavelength-dependent optical data of the individual color components, in particular for all wavelength-dependent optical constants of the individual color components. Using the same scaling factor for all wavelength-dependent optical data, such as all optical constants K and S of the individual color components, allows the characteristics or "fingerprints" of the individual color components to be preserved during the fitting. In contrast, arbitrarily fitting the optical data may result in significant changes in the characteristics or "fingerprints" of the individual color components, 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 adjusted optical data in step (iv). The predicted color data obtained using the adjusted optical data 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 connection with step (ii).

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

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

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

[0061] The residual model bias is taken into account during the adjustment of the concentration of at least one individual color component as a constant, which allows to take into account the remaining model bias when the model bias could not be minimized to zero in step (iv) and thus improves the calculation accuracy of the adjusted sample coating recipe.

[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. Said color difference can be calculated as described in relation to step (ii) above. If the cost function is the color difference, the predefined threshold is preferably a predefined color difference.

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

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

[0065] In one aspect, the display device comprises a housing that houses a computer processor and a screen for performing 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 performing steps (ii) to (vii) are configured as separate components. According to this embodiment, the display device comprises a housing that houses a screen but not a computer processor performing steps (ii) to (vii) of the method of the present invention. The computer processor performing steps (ii) to (vii) of the method of the present invention is therefore present 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 allow data exchange. The use of a further computer processor present outside the display device allows the use of higher computing power than is provided by the processor of the display device, thus reducing the computation time required to perform these steps and therefore reducing the overall time until the calculated adjusted sample coating recipe is displayed on the screen of the display device. This allows the calculated adjusted sample coating recipe to be displayed ad-hoc without the need for a display device with high computing power. The further computer processor can be located on a server such that steps (ii) to (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 a server via a network, as described below.

[0067] The display device may be a mobile display device or a fixed display device, 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 display device screen can be constructed according to any emissive or reflective display technology to have a suitable resolution and color gamut. Suitable resolutions are, for example, 72 dots per inch (dpi) or higher, such as 300 dpi, 600 dpi, 1200 dpi, 2400 dpi or higher. This ensures that the generated appearance data can be displayed with high quality. A suitable wide color gamut is the standard red-green-blue (sRGB) color gamut or higher. In various embodiments, the screen can be selected to have a color gamut close to the color gamut perceptible by human vision. In one aspect, the display device screen is constructed according to liquid crystal display (LCD) technology, in particular according to liquid crystal display (LCD) technology further including a touch screen panel. The LCD may be backlit by any suitable illumination 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 aspect, the display device screen is constructed according to light emitting polymer or organic light emitting diode (OLED) technology. In yet another aspect, the screen of the display device can be constructed according to reflective display technology such as electronic paper or ink. Known manufacturers of electronic ink / paper displays include E INK and XEROX. Preferably, the screen of the display device also has a reasonably wide field of view that can produce an image that does not become blurred or change significantly when a user views the screen from different angles. Because LCD screens operate with polarized light, some models exhibit high viewing angle dependency. However, various LCD structures have relatively wide fields of view and may be preferred for this reason. For example, LCD screens constructed according to thin film transistor (TFT) technology 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 selected for this reason.

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

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

[0071] In one embodiment, the method of the present invention further comprises initiating at least one action related to adjusting the 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 a user input indicating to initiate the action. The user input may be detected, for example, via an interaction element of a display device.

[0072] Initiating the at least one action may include providing the adjusted sample coating formula to a printing device and / or a data storage medium and / or a mixing device. The mixing device may be an automatic mixing device configured to add an adjusted amount of each color component to an already prepared sample coating formula. In one embodiment, the processor determines whether the calculated adjustment exceeds a predefined threshold before providing the adjusted sample formula to the printing device and / or the data storage medium and / or the mixing device. The predefined threshold may be a deviation, e.g. a percentage deviation, of the adjusted concentration of each color component compared to the concentration of each color component included in the provided digital representation of the sample coating. This ensures that unnecessary data transfers are not performed in case the adjusted sample coating formula calculated in step (vii) is substantially identical to the sample coating formula.

[0073] The method of the present invention allows for a more accurate and reliable color adjustment of the sample coating formulation required to adequately match the color of the reference coating by taking into account the variation in color intensity properties between the colorant batches used to prepare the sample coating and the reference coating, thereby allowing for the determination of adjusted optical data for the colorants present in the sample coating formulation that more accurately describes the actual color intensity properties of the colorants, thus allowing for a more accurate and reliable color adjustment process and reducing the number of steps required to obtain an adequate color match, thus significantly improving the efficiency of the method of the present invention.

[0074] Further disclosure includes: 1. A computing device for determining a recipe for a sample coating adjusted to match a color of a reference coating, the system comprising: a communications interface, A digital representation of the sample coating, including the color data of the sample coating and the sample coating recipe; a digital representation of the reference coating, including color data of the reference coating; a digital representation of the individual color components including their optical data; a physical model configured to predict the color of the sample coating by using the sample coating's formulation and optical data of the individual color components as input parameters; a communication interface for providing - a processing module in communication with the communication interface, said processing module comprising at least one computer processor; - a memory storing instructions configured, when executed by a processing module, to cause a computing device to perform the steps of a computer-implemented method of the present invention; Equipped with.

[0075] The computing device of the present invention can more accurately and reliably determine the color adjustments required to obtain sufficient color matching of the sample and reference coatings because variations in color intensity characteristics between colorant batches used to prepare the sample and reference coating formulations are taken into account during the color adjustment process.

[0076] In one aspect, the apparatus further comprises a display device having a screen, where the display device is separate from the processing module and the memory.

[0077] In an alternative embodiment, the processing module and memory reside in a display device further including a screen for displaying the calculated adjusted sample coating recipe received from the processing module on a screen of the display device.

[0078] In one embodiment, the device further comprises at least one database containing the digital representation and / or the physical model. The digital representation and the physical model may be stored in one database, or in multiple databases. The databases are connected to a processing module of the device of the invention via a communication interface, allowing the processor of the processing module to retrieve the data stored in the database.

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

[0080] Further disclosure includes: A non-transitory computer-readable storage medium comprising instructions that, when executed by a computing device as disclosed herein, cause the computing device to perform steps in accordance with a computer-implemented method as described herein.

[0081] The present disclosure applies equally to the method, system and non-transitory computer-readable storage medium disclosed herein. Therefore, no distinction is made between the method, the system and the non-transitory computer-readable storage medium. All features disclosed in relation to the method of the present invention are also valid for the system and the non-transitory computer-readable storage medium disclosed herein.

[0082] Further disclosed is the use of the method disclosed herein or the computing device disclosed herein in a color tuning process. The term "color tuning process" refers to a process in which the color of an existing sample coating recipe, e.g. a sample coating recipe obtained from a database or a computer-calculated sample recipe, is adjusted in at least one step to sufficiently match the color of a reference coating. Particularly preferably, the color tuning process starts with a sample coating recipe obtained from a database and used to manufacture a coating batch, and matches the color of the manufactured coating batch to the color of the reference coating so as to meet customer requirements regarding the appearance of the coating resulting from the manufactured coating batch.

[0083] Further disclosed is a client device for determining a formulation of a sample coating adjusted to match the color of a reference coating on a server device, the client device being configured to provide 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 each color component including optical data of the each color component to the server device, the server device being a computing device of the present invention.

[0084] The server may be an HTTP server and may be accessed by conventional Internet web-based technology. The use of a client device is particularly useful where the service of determining tailored sample coating formulations is provided to a customer(s) or in a larger corporate setup. [Brief description of the drawings]

[0085] These and other features of the present invention will be more fully described in the following description of exemplary embodiments of the invention. To easily identify the discussion of any particular element or act, the most significant digit or digits of a reference number refer to the figure number in which that element is first introduced. This description is provided with reference to the accompanying drawings, in which: [Figure 1] 1 shows a schematic diagram of a color adjustment method known in the prior art; [Diagram 2] 1 shows a schematic diagram of a color adjustment method of the present invention. [Diagram 3] FIG. 1 shows a block diagram of one embodiment of a method of the present invention for determining a recipe for a sample coating adjusted to match the color of a reference coating. [Figure 4] FIG. 1 illustrates one embodiment of a system of the present invention for determining a recipe for a sample coating adjusted to match the color of a reference coating. [Diagram 5] FIG. 2 illustrates a client-server setup of the method of the present invention. [Figure 6] FIG. 1 shows a graph containing reflectance spectra of a reference coating (top) and a reference coating formulation (bottom). [Figure 7] FIG. 1 shows a graph including measured and predicted reflectance spectra of a reference coating and an adjusted sample coating (top); color data of the reference coating, the adjusted sample coating and the predicted sample coating determined using the method described in EP 2149038 B1 (middle); and the adjusted sample colorant formulation (bottom). [Figure 8] FIG. 1 shows a graph including the measured reflectance spectrum of a reference coating (top), color data for the reference coating, adjusted sample coatings and predicted sample coatings determined using the method of the present invention (middle), and adjusted sample colorant formulations (bottom). DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0086] Detailed Description of the Drawings The detailed description set forth below is intended as a description of various aspects of the present subject matter and is not intended to represent the only configurations in which the present subject matter may be practiced. The accompanying drawings are incorporated herein and constitute a part of the detailed description. The detailed description includes specific details for the purpose of providing a thorough understanding of the present subject matter. However, it will be apparent to one skilled in the art that the subject matter may be practiced without these specific details.

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

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

[0089] The reference coating 110 data includes color data, such as reflectance data, of a reference coating prepared from the reference coating formulation, and optical constants, such as K and S values, of the individual color components (shown as "colorants" in FIG. 1) present in the reference coating formulation. The individual color components have associated therewith 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 as a constant while adjusting the sample coating recipe using the numerical method 106.

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

[0092] 2 is a schematic diagram of a color tuning method 200 according to the present invention. The color tuning method of the present invention also uses a physical model 204, e.g., a physical model describing the interaction of light with a scattering or absorbing medium, e.g., 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 of the sample coating 108 and the data of the reference coating 110 are provided to the processor 202 as described above in relation to Fig. 1. In contrast to the color adjustment method described in Fig. 1, the physical model 204 uses the fitted optical constants 212 (labeled "Adj. constants" in Fig. 2) to predict the color of the adjusted sample coating formula. The fitted optical constants 212 of the individual color components (labeled "colorants" in Fig. 2) are obtained by minimizing the model biases described in relation to Fig. 1 using a numerical optimization algorithm 206 and the physical model 204 as described in relation to the method of the present invention. Instead of the model biases, the residual model biases (i.e. the model biases remaining after fitting the optical constants) are taken into account. The use of fitted optical constants allows a more accurate adjusted sample coating formula to be calculated, since the adjustment of the optical constants can take into account the color intensity variations of the individual color components used to prepare the sample coating formula and the individual color components used to prepare the reference coating formula, as described above.

[0094] After determining the fitted optical constants of 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 fitted 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 predefined threshold or until a predefined maximum limit of iterations is reached. The adjusted sample formulation 214 associated with the color difference reaching the predefined threshold or the adjusted sample formulation 214 associated with the maximum number of iterations is then displayed on a screen by the processor, for example via a communication interface.

[0095] FIG. 3 shows a non-limiting embodiment of a method 300 for determining a recipe for a sample coating to match the color of a reference coating according to an embodiment of the present invention. In this example, the sample coating is a solid shade, i.e., a sample coating that does not contain an effect pigment. In another example, the sample coating is an effect coating that includes at least one effect pigment. The method of the present invention can be used during the production of a sample coating recipe to adjust the color of the produced sample coating recipe 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 a part thereof. In this example, the method of the present invention is performed on a mobile or stationary display device that includes a housing that houses a screen and computer processor(s) that execute blocks 302 to 334 of FIG. 3 as described in relation to FIG. 4. In another example, the processor(s) that execute blocks 302 to 336 of FIG. 3 are separate from the display device having a screen on which the adjusted sample coating recipe is displayed, as described in relation to the client-server configuration of FIG. 5.

[0096] In block 302 of the method 300, the routine 301 obtains a digital representation of the reference coating, including color data of the reference coating. The color data, such as reflectance data and / or texture characteristics, can be determined using a multi-angle spectrophotometer, as described in connection with step (i) of the method of the present invention. In this example, the digital representation of the reference coating (DRR) is obtained based on data included in the digital representation of the sample coating (DRS) provided to the processor(s) performing the routine 301. To this end, the routine 301 can access a database including digital representations of the reference coatings that correlate with data included in the digital representation of the sample coating, such as the color name, color code, barcode, etc. of the sample coating, and obtain the corresponding digital representation (DRR) from the database based on data included in the provided digital representation of the sample coating. In another example, the digital representation of the reference coating is obtained based on data indicative of the reference coating, such as the color name, color number, color code, etc. The data may be entered by a user via a GUI and may be used by the processor(s) performing routine 301 to obtain the respective digital representations (DRRs) from a database that contains the digital representations (DRRs) that correlate with the data entered by the user from a data storage medium, such as a database. In another example, the digital representation of the reference coating is obtained by obtaining color data determined using a multi-angle spectrophotometer from the device, e.g., by connecting the device to the processor(s) performing routine 301 and determining color data of the reference coating using the device.

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

[0098] In block 306, the routine 301 obtains a digital representation (DRS) of the sample coating, including color data of the sample coating and a formula of the sample coating, although this block is generally optional. Color data, such as reflectance data and / or texture characteristics, can be determined as described above using a multi-angle spectrophotometer. In one example, the digital representation of the sample coating is obtained from a database based on the data included in the digital representation (DRR) obtained in block 304. In another example, the digital representation (DRS) is obtained by obtaining color data determined using a multi-angle spectrophotometer from said device, for example by connecting the device to the processor(s) performing the routine 301 and using said device to determine color data of the sample coating. In yet another example, the digital representation (DRS) is obtained based on data indicative of the sample coating, such as a color name, color number, color code, etc. The data may be input by a user via a GUI and may be used by the processor(s) performing the routine 301 to obtain the respective digital representation (DRR) from a database that includes the digital representation (DRS) correlated with the data input by the user from a data storage medium, such as a database.

[0099] In block 308, the routine 301 obtains digital representations (DRCs) of the individual color components including optical data of the individual color components, in particular optical constants such as scattering and absorption characteristics. The digital representations (DRCs) may further include data indicative of the individual color components, such as names, trademark names, unique IDs, or combinations thereof. In one example, the obtaining may be performed based on data included in the digital representations (DRR) provided in block 304 and / or data included in the digital representations (DRS) provided in block 306.

[0100] In block 310, the routine 301 obtains a physical model configured to predict the color of the sample coating by using the sample coating's formulation 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 models disclosed in EP 2149038 B1) and include physical models that describe the interaction of light with scattering or absorbing media, such as colorants in a coating layer, such as the Kubelka / Munk model. In this example, a "Kubelka / Munk" model is obtained in block 310.

[0101] In block 312, the 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, the routine 301 proceeds to block 320, described below. Otherwise, the routine 301 proceeds to block 314, described below.

[0102] In block 314, the routine 301 executes a so-called "matching from scratch" method to determine 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 applies, for example, when there is no formulation database. In practice, the "matching from scratch" method often starts with a pre-selection step of ingredients expected to be included in the reference coating formulation. The pre-selection step is not mandatory. The "matching from scratch" method / algorithm calculates one or more preliminary matching formulations to the reference coating as a first solution.

[0103] At block 316, the routine 301 provides for displaying the calculated matching formula. In one example, the formula is provided to a display device with a screen such that the formula can be displayed on the display device screen, e.g., within a GUI. This allows a user to prepare a sample coating material based on the displayed formula. In one example, preparing the displayed sample coating material can include transmitting the displayed sample coating formula to an automated dosing device and automatically preparing the respective sample coating material based on the transmitted data. In another example, the sample coating material can be prepared by manually dosing the respective components based on the displayed data.

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

[0105] In block 320, the routine 301 determines the color difference between the color data of the provided sample coating and the color data of the provided reference coating. In this example, block 320 is performed before block 322. In another example, block 320 is performed after block 324 and before block 326. In this example, the shape similarity of the spectral curves is used to determine the color difference. The use of the shape similarity of the spectral curves is preferred because it avoids changing the characteristics or "fingerprints" of the individual color components, which makes the color adjustment process more complicated. In another example, the color difference is determined using color tolerance equations such as the Delta E (CIE 1994) color tolerance equation, the Delta E (CIE 2000) color tolerance equation, the Delta E (DIN 99) color tolerance equation, the Delta E (CIE 1976) color tolerance equation, the Delta E (CMC) color tolerance equation, the Delta E (Audi 95) color tolerance equation, or the Delta E (Audi 2000) color tolerance equation. These equations may be included in the digital representation (DRR) or (DRS). In this example, the determined color differences are correlated with data indicative of the sample coating and stored on a data storage medium.

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

[0107] In block 322, the routine 301 predicts color data of the sample coating based on the color data of the sample coating, the sample coating formula, 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 formula of the sample coating are included in the digital representation (DRS) provided in block 302 or 306. In another example, i.e., if the "match from scratch" method is performed, the formula of the sample coating is determined in block 314 and 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 optical data, in particular the optical constants, of the provided sample coating formula and the individual color components present in the sample coating formula as input parameters of the provided physical model. The predicted color data can be stored in a data storage medium, such as an internal data storage medium or 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 formula, to enable data acquisition in any one of the following blocks.

[0108] In block 324, the 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 connection with 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 color intensity variations of the included colorants 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, resulting in a more accurate calculation of the adjusted sample coating formulation in block 332 of the method of the present invention.

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

[0111] In block 328, the routine 301 converts the provided optical data, particularly the provided optical constants, of at least some of the individual color components present in the sample coating formulation into - a numerical optimization algorithm configured to fit the optical data of at least a portion of the individual color components present in the sample coating formulation by minimizing a predetermined cost function starting from the obtained optical data; - the obtained physical model; Use to fit.

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

[0113] The adapted optical data and / or recursively predicted color data of the sample coating generated in block 328 may be stored, completely or at least partially, in a data storage medium, such as an internal data store or a database, as previously described. The stored adapted optical data and / or predicted color data may be correlated with data contained in a digital representation of the sample coating to enable 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 of at least some of the individual color components, thereby providing adapted 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 provided individual color components) and preventing the colors of the individual color components from being shifted excessively.

[0115] If the optical data of only a portion of the individual color components present in the sample coating formulation are fitted in block 328, 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 color data of the provided sample coating. The predefined criterion may be included in the obtained 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 amounts 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 may reduce the computation time required to minimize the bias of the model or reduce the computation 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) above. The same scaling function is used for all the wavelength-dependent optical data of the individual color components, in particular all the wavelength-dependent optical constants of the individual color components. This is because it allows the characteristics or “fingerprints” of the individual color components to be preserved during the blending process, thus avoiding significant changes in the characteristics or “fingerprints” of the individual color component(s), which, as discussed above, would make the color adjustment process more complicated.

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

[0118] At block 332, the routine 301 the color differences determined in blocks 320 and 330, - the matched optical data obtained in block 328; and - a numerical optimization algorithm obtained in block 326, configured to adjust the concentration of at least one individual color component present in the sample coating formulation by minimizing a predetermined cost function starting from the obtained concentrations of the individual color components included in the sample coating formulation; the physical model obtained in block 310; Determine the adjusted sample coating formula based on:

[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, the predetermined threshold can be the predetermined color difference.

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

[0121] In block 334, the routine 301 provides the adjusted sample coating formulation to a display device for display on a screen of the display device. Further data in addition to the adjusted sample coating formulation, such as data contained in the acquired representations of the sample coating and / or reference coating, determined matched color data for individual color components, residual model biases, or combinations thereof, may be provided for display in block 334. Suitable display devices may include mobile display devices or fixed display devices as previously described.

[0122] At block 336, the routine 301 initiates at least one action related to adjusting the sample coating formulation determined at block 332, which block is generally optional. The action is preferably a predefined action. In one example, the action may be initiated by the routine 301 based on its programming. In another example, the action may be initiated after detecting a user input indicating that the action should be initiated by the routine 301. The user input may be detected, for example, via an interaction element of a display device. Initiating the 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 completing block 336 , the routine 301 either ends the method 300 or returns to block 302 .

[0124] 4 illustrates an example of a system 400 for determining an adjusted sample coating formula to match the color of a reference coating that can be used to implement blocks 302 to 336 of the method 300 described in connection with FIG. 3. The system 400 includes a computing device 402 that houses a computer processor 404 and a memory 406. The processor 404 executes instructions, e.g., retrieved from the memory 406, to perform operations associated with the computer system 400, i.e., - Through the communication interface A digital representation of the sample coating, including the 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; A digital representation of the individual color components, including the optical data of the individual color components; a physical model configured to predict the color of a sample coating by using optical data of the sample coating's formulation and individual color components as input parameters; and receiving; - determining a color difference between color data of a provided sample coating and color data of a provided reference coating; - The model bias of the obtained physical model, predicting color data for the sample coating based on the digital representation of the sample coating, the digital representations of the individual color components, and the obtained physical model; determining a color difference between the obtained sample coating color data and the predicted sample coating color data; and to determine by; - minimizing the determined model bias by fitting the individual color component optical data obtained for at least some of the individual color components present in the sample coating formulation; - determining a residual model bias by determining a color difference between the acquired color data of the sample coating and the predicted color data using the fitted optical data; - calculating an adjusted sample coating formula based on the determined color difference, the optical data of the fitted individual color components, the determined residual model bias, and the obtained physical model; - providing a calculated adjusted sample coating recipe via a communication interface; is configured to run

[0125] The processor 404 may be a single chip processor or may be implemented with multiple components. In most cases, the processor 404, together with an operating system, operates to execute computer code and generate and use data. In this example, the computer code and data reside in a memory 406 operatively coupled to the processor 404. The memory 406 generally provides a place to hold data used by the computer system 400. As an example, the memory 406 may include a read-only memory (ROM), a random access memory (RAM), a hard disk drive, and / or the like. In another example, the computer code and data may reside on a removable storage medium and may 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 in a local computing device or in a cloud environment (see, for example, FIG. 5). In the latter case, the display device 424 may function as a client device and access a server (i.e., the computing device 402) via a network (i.e., the communication interface 426).

[0126] The computing device 402 is connected to databases 408, 410, 412, 414 via communication interfaces 416, 418, 420, 422. The databases 408, 410, 412, 414 store digital representations of sample coatings, reference coatings, individual color components, and physical models that can be retrieved by the processor 404 via the communication interfaces 416, 418, 420, 422. The digital representations of the sample coatings stored in said databases include color data and formulations of the sample coatings. The digital representations of the reference coatings include color data of the reference coatings. The digital representations of the individual color components include optical data of the individual color components, in particular optical constants. In one example, each digital representation can include further data as mentioned above. In one example, the respective digital representations of the sample coating and reference coating are retrieved from the respective databases by the processor 404 based on data indicative of the sample coating and / or reference coating input by a user via the display device 424, or data indicative of 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 a 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, etc.).

[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 the calculated adjusted sample coating formulation from the processor 404 and displays the received adjusted sample coating formulation on a screen, in particular via a graphical user interface (GUI), to a user. For this purpose, the display device 424 is operatively 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 equipped with 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 allow user input to obtain a digital representation as described above. In another example, the screen of the display device 424 may be a separate component (peripheral device, not shown). By way of example, the screen of display device 424 may be a monochrome display, a color graphics adapter (CGA) display, an enhanced 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 measurement device 428, such as a multi-angle spectrophotometer, such that color data of the reference coating and / or the sample coating may be determined using said device 428. The measurement device is coupled to the processor 404 via a communication interface 430 such that the determined data may be acquired by the processor 404. The determined data may be measured data or color data already processed by the processor of the measurement device.

[0129] Turning now to FIG. 5, an internet-based system 500 for determining adjusted sample coating formulas to match the color of a reference coating that can be used to implement the method 300 described in relation to FIG. 3 is shown. The system 500 comprises a server 502 accessible by one or more clients 506.1-506.n via a network 504, such as the internet. In one example, the server corresponds to the computing device 402 described in relation to FIG. 4. Preferably, the server is an HTTP server and is accessed via conventional internet web-based technology. The client 306 is a computer terminal accessible by a 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 of FIG. 4. The client comprises 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 where services are provided to customers or in a larger corporate set-up. The client 506 can be used to provide 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 digital representations of the individual color components, including optical data of the individual color components, to the server's computer processor.

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

[0131] FIG. 7 shows a graph 702 (top) including the measured and predicted reflectance spectra of the reference coating and the adjusted sample coating, color data (middle) of the reference coating 706', the adjusted sample coating 710' and the predicted sample coating 708' determined using the method described in EP2149038 B1, and the adjusted sample coating formula 714 (bottom). A portion of the graph 702 is expanded at 704 to show the variation 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 variation in the reflectance spectrum between the reference coating 706 and the adjusted sample coating 710 is also reflected in the color data 712. This variation is due to the fact that the color intensity of the black color paste was not adjusted during the determination of the adjusted sample coating formula, but was assumed to be 100%. The adjusted sample coating formula is too thin, so the color intensity of the black color paste used to prepare the sample coating formula should be less than 100%. A limitation of this state-of-the-art method is that the optical properties of colorants are not constant over time. Real colorants are subject to a systematic bias caused by changes in the optical properties of the colorants compared to the "reference" colorants (especially changes in the color intensity properties), which propagates to the adjusted recipe. Depending on the scale of this bias and the scale of the residual color difference, the color adjustment results can be significantly inaccurate, as shown in Figure 7.

[0132] FIG. 8 shows a graph 802 (top) including the measured reflectance spectrum of the reference coating, color data (middle) of the reference coating 806', adjusted sample coating 810', and predicted sample coating 808' determined using a method of the present invention, such as the method 300 described in connection with FIG. 3, and an adjusted sample coating formula 814 (bottom). A portion of the graph 802 is expanded at 804 to show the variation 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 high accuracy of the method of the present invention compared to the results shown in FIG. 7 is due to the consideration of the color intensity of the black color paste used to formulate the sample coating formula, which is less than 100% compared to the color intensity of the black color paste used to formulate the reference coating formula. In summary, the color adjustment method of the present invention can achieve an accurately adjusted sample formula regardless of the color intensity of the individual color components used to prepare the reference coating formula and the sample coating formula, and therefore can reduce the number of color adjustments required to achieve a desired color match.

Claims

1. 1. A computer-implemented method for determining a recipe for a sample coating adjusted to match a color of a reference coating, the method comprising: (i) to a computer processor via a communications interface; 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, the digital representation including color data of the reference coating; - a digital representation of each color component including optical data of each color component; a physical model configured to predict the color of a sample coating by using the sample coating's formulation and optical data of the individual color components as input parameters; providing a (ii) determining with a computer processor a color difference between the color data of the provided sample coating and the color data of the provided reference coating; (iii) calculating, by a computer processor, a model bias for the provided physical model; - predicting color data for a sample coating based on the digital representation of the sample coating, the digital representations of the individual color components, and the physical model provided in step (i); determining a color difference between the provided color data of the sample coating and the predicted color data of the sample coating; determining the (iv) minimizing with a computer processor the model bias determined in step (iii) by fitting the provided optical data of at least some of the individual color components present in the sample coating formulation; (v) determining with a computer processor a residual model bias by determining a color difference between the provided color data and the predicted color data of the sample coating using the fitted optical data of step (iv); (vi) calculating with a computer processor an adjusted sample coating formulation based on the color differences determined in step (ii), the fitted optical data of the individual color components obtained in step (iv), the residual model biases determined in step (v), and the provided physical model; (vii) providing said calculated adjusted sample coating formulation via a communications interface; A method comprising:

2. 10. The method of claim 1, wherein the digital representation of the sample coating further comprises data indicative of the sample coating, a layer structure of the sample coating, instructions for preparing a sample coating formulation, a price, or a combination thereof.

3. 3. The method of claim 1 or 2, wherein the digital representation of the reference coating further comprises data indicative of the reference coating, a layer structure of the reference coating, a formulation associated with the reference coating, instructions for preparing the reference coating formulation, a price, or a combination thereof.

4. The color data may include reflectance data, color space data, in particular CIE ＊ a ＊ b ＊ Value or CIE L ＊ C ＊ h ＊ The method according to claim 1 or 2, further comprising determining the surface area of ​​the surface from which the surface is to be measured, the surface area being measured, the surface area including a surface area of ​​the surface, ...

5. 3. The method according to claim 1 or 2, wherein the optical data of the individual color components comprises the optical constants of the individual color components, in particular the wavelength-dependent scattering and absorption properties of the individual color components.

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

7. The minimization of the model bias determined in step (iii) is - providing a numerical method adapted to fit the optical data of at least a portion of the individual color components present in the sample coating formulation by minimizing a predefined cost function starting from the optical data provided in step (i); - fitting the 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 color data of the provided sample coating until the cost function falls below a predefined threshold or the number of iterations reaches a predefined limit.

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

9. The scaling function comprises a linear scaling function of equation (1): [0010] where 【number】 In particular, it refers to the optical constants. 【number】 【number】 , specifically refers to the optical constants that have been adapted. 【number】 refers to the index, ranging from 1 to n, 【number】 The method of claim 8, wherein m ranges from 1 to m.

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

11. Calculating the modified sample coating formula providing a numerical method adapted to adjust the concentration of at least one individual color component present in a sample coating formulation by minimizing a predetermined cost function, starting from the concentrations of the individual color components contained in a digital representation of a provided sample coating; - adjusting the concentration of at least one individual color component present in the sample coating formulation using the provided numerical method, the adapted optical data obtained in step (iv), the residual model biases and the provided physical model 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 until the color difference falls below a predefined threshold or the number of iterations reaches a predefined limit; The method of claim 1 or 2, comprising:

12. 1. A computing device for determining a recipe for a sample coating adjusted to match a color of a reference coating, the system comprising: a communications interface, A digital representation of the sample coating, including the color data of the sample coating and the sample coating recipe; a digital representation of the reference coating, including color data of the reference coating; a digital representation of the individual color components including their optical data; a physical model configured to predict the color of the sample coating by using the sample coating's formulation and optical data of the individual color components as input parameters; a communication interface for providing a processing module in communication with said communication interface, said processing module comprising at least one computer processor; a memory storing instructions configured, when executed by said processing module, to cause a computing device to perform the steps of the computer-implemented method of claim 1; A computing device comprising:

13. 13. A non-transitory computer-readable storage medium comprising instructions that, when executed by a computing device of claim 12, cause the computing device to perform steps according to the method of claim 1 or 2.

14. Use of the method of claim 1 or the computing device of claim 12 in a color adjustment process.

15. A client device for determining an adjusted sample coating formulation to match the color of a reference coating on a server device, the client device being configured to provide to the server device 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 digital representations 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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