System and method for approximating a 5-angle chromatic aberration model

Abstract

A system and method for approximating a 5-angle color difference model is provided, wherein the 5-angle color difference model utilizes a 5-angle equation. In an exemplary embodiment, an apparatus includes: a storage device for storing instructions; and one or more processors configured to execute the instructions. The processor is configured to receive 3-angle standard color measurements and 3-angle test color measurements, and input the 3-angle standard measurements into a neural network empirical model. The neural network empirical model includes a plurality of input nodes, a plurality of hidden nodes connected to the input nodes, and a plurality of output nodes connected to the hidden nodes. The neural network empirical model is configured to output a 3-angle tolerance value, and calculates a 3-angle color difference value for at least one of the 3 color measurement angles using the 5-angle equation, using the 3-angle standard color measurements and the 3-angle test color measurements and the 3-angle tolerance value.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of U.S. Provisional Application No. 62 / 903,072, filed on September 20, 2019, which is hereby incorporated by reference in its entirety. Technical Field

[0003] The technical field relates to coating technology, and more particularly to systems and methods for approximating a 5-angle color difference model based on 3-angle color measurements. Background Art

[0004] Automobiles, vehicles and other items are often painted to provide corrosion protection, as well as to provide an attractive appearance. However, different batches of coatings may have slightly different colorings. Changing batches during a coating operation may result in mismatched areas on the substrate. However, it is wasteful to discard a portion of a batch of coatings due to mismatch considerations. Moreover, different production equipment may produce products with slightly different colorings. Therefore, techniques for determining differences in similar coatings or colors provide benefits to both producers and consumers.

[0005] Quantification of the differences between different coatings can help OEM manufacturers or refinishing operations provide accurate color matching operations. In one embodiment, a 5-angle color difference model has been developed that is generally accepted as providing a reasonable and consistent quantification of the color difference between two coatings at the measured angles. This 5-angle color difference model may be referred to as a " The color difference between two coatings is often dependent on viewing angle, so a coating that may be substantially consistent at one viewing angle may be significantly different at a different viewing angle. This color difference is especially noticeable if the coating has effect pigments or "depth". The 5-angle color difference model uses 5 different angles to capture the apparent color difference at 5 different angles. Some aspects of the 5-angle color difference model utilize color properties measured at different angles, so the results are dependent on measurements from other angles. However, even though the 5-angle color difference model is not a perfect predictor of color difference at all angles, it does provide a consistent and repeatable measure of color difference that can be accepted and utilized by interested entities.

[0006] Some coating manufacturers provide color measurement equipment that utilizes 3 angles, so the 5-angle color difference model cannot be properly implemented. Even with the same viewing angles, the three-angle color difference calculation may provide different results than the results from the 5-angle color difference calculation because certain aspects of the 5-angle color difference model use other angles that may not be included in the 3-angle model. For example, for a single standard sample (referred to herein as the "standard coating" or "standard color") coating and a test sample (referred to herein as the "test coating" or "test color"), the three-angle color difference calculation may provide different results than the results from the 5-angle color difference calculation, even with the same viewing angles, because certain aspects of the 5-angle color difference model use other angles that may not be included in the 3-angle model. The color difference value of the color difference 5 angle equation will be different from the 3 angle difference calculation for the same standard coating and test coating at 15° (where the 3 angles are 15°, 45°, and 110°). This lack of consistent results for the same standard coating, the same test coating, and the same measurement angles makes it difficult to compare coatings from different manufacturers that utilize different numbers of color measurement angles.

[0007] Therefore, it is desirable to provide systems and methods for approximating a 5-angle color difference model using a 3-angle color measurement system. The defects in the 5-angle color difference model should be repeatable within the new model using 3-angle color measurement, so the use of both the 3-angle color measurement tool and the 5-angle color measurement tool can be used with consistent color difference value estimates for the same standard color, test color, and measurement angle. In addition, other desirable features and characteristics will become apparent from the following summary and detailed description of the invention and the appended claims, taken in conjunction with the drawings and this background technology. Summary of the invention

[0008] An apparatus and method for approximating a 5-angle color difference model is provided, wherein the 5-angle color difference model utilizes a 5-angle equation. In an exemplary embodiment, an apparatus includes: a storage device for storing instructions; and one or more processors configured to execute the instructions. The processor is configured to receive a 3-angle standard color measurement and a test color measurement, and input one of the following into a neural network empirical model: (i) a 3-angle standard measurement or (ii) a geometric mean of brightness and chromaticity of the standard color measurement and the test color measurement. The neural network empirical model includes a plurality of input nodes, a plurality of hidden nodes connected to the input nodes, and a plurality of output nodes connected to the hidden nodes. The neural network empirical model is configured to output a 3-angle tolerance value, and calculate a 3-angle color difference value for at least one of the 3 color measurement angles using the 5-angle equation, using the 3-angle standard color measurement and the 3-angle test color measurement and the 3-angle tolerance value.

[0009] In another embodiment, a method for approximating a 5-angle color difference model using 3-angle measurement data is provided. The method includes receiving 3-angle standard color measurements and test color measurements at each of the 3 color measurement angles, and inputting one of the following into a neural network empirical model: (i) 3-angle standard color measurements or (ii) geometric mean values ​​of brightness and chromaticity of standard color measurements and test color measurements. The neural network empirical model includes multiple input nodes, multiple hidden nodes connected to the multiple input nodes, and multiple output nodes connected to the hidden nodes. The neural network empirical model outputs 3-angle tolerance values ​​for each of the 3 color measurement angles, and calculates 3-angle color difference values ​​for at least one of the 3 color measurement angles. The neural network empirical model uses the same 5-angle equations as those used by the 5-angle color difference model, except that the 3-angle tolerance values ​​are used instead of the 5-angle tolerance values ​​commonly used by the 5-angle equations.

[0010] In yet another embodiment, a method for generating a 3-angle color difference model that approximates a 5-angle color difference model is provided. The method includes receiving 5-angle standard color measurements of a standard color at each of 5 color measurement angles and calculating a plurality of 5-angle tolerance values. The 3-angle standard color measurements of the standard color are received at each of 3 color measurement angles, wherein the 3 color measurement angles are a subset of the 5 color measurement angles. A neural network empirical model is generated, which includes a plurality of input nodes, a plurality of hidden nodes connected to the plurality of input nodes, and a plurality of output nodes connected to the plurality of hidden nodes, wherein the neural network empirical model is configured to output the 3-angle tolerance value at each of the 3 color measurement angles. The neural network empirical model is trained using (1) the 5-angle standard color measurements, (2) the 3-angle standard color measurements, and (3) the 5-angle tolerance values, so that the 3-angle tolerance value output by the neural network empirical model is approximately the same as the 5-angle tolerance value at each of the 3 color measurement angles. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Other advantages of the disclosed subject matter will be readily appreciated as they become better understood by reference to the following detailed description when considered in conjunction with the accompanying drawings, in which:

[0012] Figure 1 is a box plot of training data and validation data for an exemplary neural network empirical model using color measurement angles of 15°, 45°, and 110°;

[0013] Figure 2 are histograms of training data and validation data for an exemplary neural network empirical model using color measurement angles of 15°, 45°, and 110°;

[0014] Figure 3 is a table summarizing training data and validation data for an exemplary neural network empirical model using color measurement angles of 15°, 45°, and 110°;

[0015] Figure 4 is a box plot of training data and validation data for an exemplary neural network empirical model using color measurement angles of 25°, 45°, and 110°;

[0016] Figure 5 are histograms of training data and validation data for an exemplary neural network empirical model using color measurement angles of 25°, 45°, and 110°; and

[0017] Figure 6 is a table summarizing the training data and validation data for an exemplary neural network empirical model using color measurement angles of 25°, 45°, and 110°. DETAILED DESCRIPTION

[0018] The following detailed description is not intended to limit the present description or its application and use. In addition, it is not intended to be limited by any theory presented in the previous background technology or the following detailed description. It should be understood that throughout the drawings, corresponding reference numerals indicate the same or corresponding parts and features.

[0019] By reading the following detailed description, it will be easier for those skilled in the art to understand the features and advantages identified in the present disclosure. It should be appreciated that certain features described above and below in the context of different embodiments for clarity may also be provided in combination in a single embodiment. Conversely, the various features described in the context of a single embodiment for brevity may also be provided separately or in the form of any sub-combination. In addition, unless the context clearly indicates otherwise, references in the singular may also include the plural (e.g., "one" and "an" may refer to one, or one or more).

[0020] It will be appreciated by those skilled in the art that bias nodes may be present in any layer except the output layer. Therefore, if bias nodes are not explicitly stated or shown, it should be understood that they may be present in any or all layers except the output layer.

[0021] In this article, technology and technology can be described from the perspective of functions and / or logic block components and with reference to the symbolic representation of operations and functions that can be performed by various computing components or devices. In fact, one or more data processors can perform the described operations, tasks and functions by manipulating electrical signals and other signal processing representing the data bits at the memory locations in the system memory. It should be appreciated that the various block components shown in the figure can be implemented by any number of hardware, software and / or firmware components configured to perform the specified functions. For example, the implementation of the system or component can adopt various integrated circuit components that can perform various functions under the control of one or more microprocessors or other control devices, such as storage elements, digital signal processing elements, logic elements, lookup tables, etc.

[0022] The following description will relate to elements or nodes or features that are "coupled" together or "connected". As used herein, unless otherwise expressly stated, "coupling" and / or "connection" means that an element / node / feature is directly or indirectly engaged to another element / node / feature (or directly or indirectly communicates with another element / node / feature), and need not be mechanically engaged. Therefore, although an example of the arrangement of elements may be described, additional intermediary elements, devices, features or parts may be present in the embodiment of the depicted theme. In addition, specific terms may also be used in the following description only for reference purposes, and are therefore not intended to be restrictive.

[0023] For the sake of brevity, conventional techniques related to graphics and image processing, touch screen display, and other functional aspects of certain systems and subsystems (and their independent operating components) may not be described in detail herein. In addition, connecting lines are intended to represent examples of functional relationships and / or physical couplings between various elements. It should be noted that many alternative or additional functional relationships or physical connections may exist in the embodiments of this theme.

[0024] As used herein, the terms "module" and / or "node" refer to any hardware, software, firmware, electronic control component, processing logic and / or data processor, alone or in any combination, including but not limited to: application specific integrated circuits (ASICs), electronic circuits, (shared, dedicated or grouped) data processors and memories that execute one or more software or firmware programs, combinational logic circuits and / or other suitable components that provide the described functionality.

[0025] The term "color data" or "color characteristics" of a coating may include measured color data, including spectral reflectance values; X, Y, Z values; L*, a*, b* values, where L* represents lightness, a* represents colors from green (-) to red (+), and b* represents colors from blue (-) to yellow (+); L*, C*, h* values, where L* represents lightness, C* represents chromaticity, and h* represents hue; dynamic color index; or a combination thereof. The color data may also include a color code, a color name or description, or a combination thereof for the vehicle. The color data may even further include visual aspects, chromaticity, hue, brightness or darkness of the color of the coating. The color data may be obtained by visual inspection or by using a color measuring device such as a colorimeter, a spectrophotometer, or a goniospectrophotometer. In particular, a spectrophotometer obtains color data by determining the amount of light reflected by the coating at each wavelength. Color data may also include: descriptive data, such as the name of a color, a vehicle's color code; a binary, text, or encrypted data file containing descriptive data for one or more colors; a measurement data file, such as a measurement data file generated by a color measurement device; or an export / import data file generated by a computing device or a color measurement device. Color data may also be generated by a color appearance dual measurement device.

[0026] A processor-implemented system for approximating a 5-angle color difference model is provided. The 5-angle color difference model includes 5-angle equations, wherein the 5-angle equations are:

[0027] (A)dE γi =((dL * γi k L ·S 5L，γi ) 2 +(dC * γi k c ·S 5c，γi ) 2 +(dH * γi k H ·S 5H，γi ) 2 )

[0028] Where: dE γi is the 5-angle color difference value at a given angle γ; dL* is the difference in color brightness between the standard color-test color pair; γ is the color measurement angle or the angle at which color measurement is performed, wherein, in an exemplary embodiment, γ includes 5 angles; i is the iteration of the measurement angle, such as the first color measurement angle, the second color measurement angle, etc.; dC* is the difference in color chromaticity between the standard color-test color pair; dH* is the difference in hue between the standard color-test color pair; K L , Kc and K H is the acceptance limit, which in an exemplary embodiment may be a constant such as 1 for each value of K; and S 5L , S 5c and S 5H are the five angle tolerance values ​​of color brightness, color chromaticity, and color hue, respectively, at a specific color measurement angle (i.e., a specific γ). In an exemplary embodiment, the five angle equations are 2000 color difference 5 angle equation, but in alternative embodiments, other 5 angle equations can be approximated. The 5 angle equation can be solved for any number of angles, i.e., the value of "i" can be iterated from 1 to any desired integer, but 5 discrete angles are generally used. Similarly, the 5 angle equation can be solved for 3 angles, where the value of "i" is iterated from 1 to 2, and then to a final value of 3. The result of the 5 angle equation when only 3 angles are used is referred to herein as the 3-angle color difference value. As the number of angles used in the equation changes, the result according to the equation generally changes as well.

[0029] Calculate the 5-angle tolerance value for use in the 5-angle equation. In an exemplary embodiment, 2000 Color Difference 5 Angle Equation Use the following equation to calculate the 5 angle tolerance value.

[0030] (B)S 5Lγi =1.000·((|L * γi -L * γi+1 |) / (γ i+1 -γ i )) 2 / 3 +0.002·C* 45 +0.33

[0031] (C)S 5Cγi =1.478·((|C * γi -C * γi+1 |) / (γ i+1 -γ i ))+0.014·C * 45 +0.27

[0032] (D)S 5Hγi =0.800·((|C * γi -C * γi+1 |) / (γ i+1 -γ i ))+0.004·C *45 +0.30

[0033] wherein the previously described symbols have the meanings listed above, wherein L* and C* are the lightness and chromaticity of the standard color, and wherein C * 45 is the chromaticity of the standard color measured at 45°. Typically, the standard color is the color used as a reference. If neither color can be identified as a standard color, an average value is used in the above equations (B), (C), and (D). In particular, if a standard color can be identified as a reference color, the values ​​used for L* and C* in equations (B), (C), and (D) are the geometric mean of the lightness and chromaticity of the two colors at the selected measurement angle, and C * 45 is the geometric mean of the chromaticity of the two colors at a 45° angle. In this specification, in all cases, two colors are referred to as the "standard" and "test" colors, so if both colors are obviously not the reference color, one of the colors is randomly called the "standard" color and the other is called the "test" color, but the geometric mean of the L* and C* values ​​of the two colors at the selected measurement angle is used in equations (B), (C) and (D). 5 Angle 2000k in the color difference equation L , k C and k H The value of each of k is 1. L , k C and k H The above item is allowed L *、d C * and d H * Values ​​are weighted independently of the parameter factors.

[0034] As an example, for a 5-angle system using 15°, 25°, 45°, 75°, and 110°, the 5-angle tolerance value for chromaticity at 15° would be:

[0035] S C15 =1.478·((|C * 15 -C * 25 |) / (25-15))+0.014·C 45 +0.27

[0036] It can be seen that the 5-angle tolerance value depends on the color measurement angle (γ), as well as the next iteration of the color measurement angle (γ+1). Therefore, the three-angle system using 15°, 45°, and 110° has no chromaticity value at 25°. Likewise, the exemplary 3-angle system produces a 3-angle tolerance value for chromaticity at 15° that is different from the 5-angle tolerance value for chromaticity at 15°. This means that the same color measurement value of the same standard color-test color pair at 15° produces different results for the 3-angle color difference value and the 5-angle color difference value. However, a technique is described herein for generating a 3-angle tolerance value that is approximately the same as the 5-angle tolerance value calculated above, wherein the technique is The 2000 5-angle color difference model produces consistent results for 3-angle and 5-angle color data.

[0037] The processor-implemented system includes a storage device for storing instructions for approximating a 5-angle color difference model and for storing instructions for approximating a result of the 5-angle color difference model using 3-angle color measurement values. The system also includes one or more data processors, which are configured to execute the following instructions: (1) receiving 3-angle standard color measurements of a standard color at each of the 3 color measurement angles; (2) receiving 3-angle test color measurements of a test color at each of the 3 color measurement angles; (3) inputting the 3-angle standard color measurements into a neural network empirical model including a plurality of input nodes, a plurality of hidden nodes, and a plurality of output nodes, wherein the neural network empirical model is configured to output a 3-angle tolerance value S at each of the 3-angle measurement points. 3L , S 3c and S 3H ; and (4) using equation (A) to calculate 3-angle color difference values ​​using 3-angle standard color measurement, and wherein the 3-angle tolerance value is used instead of the 5-angle tolerance value.

[0038] The system may include an input device for receiving 3-angle color measurements, and optionally for receiving 5-angle color measurements and / or 5-angle color difference values ​​and / or 5-angle tolerance values. Other data or information may also be entered using the input device. The input device may be selected from the following devices: a digital input device, such as a wired keyboard, a wireless keyboard, a digital writing tablet, a touch screen, an input port that can be connected to an electrical device or another computer, or any other digital device that can input data into a computing device; an optical input device, such as a barcode reader, a scanner, a digital camera, a digital video camera, or any other optical device that can input data into a computing device; an electromagnetic input device, such as a radio receiver, an RFID (radio frequency identification) receiver, an infrared data receiver, or any other device that can receive data over a wide range of electromagnetic wavelengths; or a combination thereof. Each of the one or more input devices may also require the necessary adapters or couplers to input data into the data processor, wherein these adapters or couplers can be easily determined by a person skilled in the art. These adapters or couplers may also be wired or wireless.

[0039] The system may optionally include a display. The display may be selected from the following devices: a digital display device, such as a computer monitor, a PDA, a computer, a cellular phone, a smart phone, a tablet computer, or a television; an optical display device, such as a projector; a print display, such as a printer; other display devices, or a combination thereof. The display may also be a dual function display / data input device. An example of such a dual function device is a touch screen of a computer, a smart phone, a tablet computer, or a PDA.

[0040] Use the neural network empirical model to calculate the 3 angle tolerance values, namely S 3L , S 3C and S 3H , where the above 5 angle tolerance values ​​S are replaced by 5L , S 5c and S 5H Set the 3 angle tolerance value S 3L , S 3C and S 3HSubstitute into the 5-angle equation. Then use the 3-angle tolerance value instead of the 5-angle tolerance value to apply the 5-angle equation. The neural network empirical model is configured so that the 3-angle tolerance value of each standard color at each of the 3 color measurement angles is approximately the same as the 5-angle tolerance value of the same standard color at each of the 3 color measurement angles. The difference between the 3-angle color difference value and the 5-angle color difference value for a given standard color-test color pair is caused by the use of different color measurement angles in the above equations (B), (C) and (D) for the tolerance values, rather than by the difference in the 5-angle equation (A). Therefore, if the 3-angle tolerance value generated by the neural network empirical model is approximately the same as the 5-angle tolerance value, the 3-angle color difference value will be approximately the same as the 5-angle color difference value.

[0041] As mentioned above, the neural network empirical model approximates the 3-angle tolerance value. This design makes it possible to use the above 5-angle tolerance value S when (a) 5L , S 5c and S 5H Using 5-angle color measurement for standard color-test color pairs or (b) using 3-angle tolerance values ​​S calculated by the neural network empirical model 3L , S 3C and S 3H When the 5-angle equation is applied using the 3-angle color measurements for the same standard color-test color pair, the 5-angle equation produces approximately the same 3-angle color difference values ​​as the 5-angle color difference values.

[0042] The accuracy of the neural network empirical model can be determined by the tolerance value difference, where the tolerance value difference is the difference between the 3-angle tolerance value and the 5-angle tolerance value for each 3-angle measurement angle for each standard color. Ideally, the tolerance value difference is zero, but experimental data typically includes some variation. Likewise, the standard deviation of the tolerance value differences provides a good measure of the accuracy of the approximation produced by the neural network empirical model. In an exemplary embodiment, the standard deviation of the tolerance value differences for multiple standard colors is about 0.1 or less, but in an alternative embodiment, the standard deviation of the tolerance value differences is about 0.07 or less. The standard deviation of the tolerance values ​​can use a statistically significant number of sample data points, such as about 30 data points or more.

[0043] The term "approximately the same" as used herein with respect to results from the neural network empirical model or the 5-angle equation means that the difference in tolerance values ​​for a plurality of standard colors (ie, approximately 30 or more different standard colors) is approximately 0.1 or less.

[0044] A neural network empirical model with multiple input nodes, multiple hidden nodes, and multiple output nodes is established. Each of the input nodes is connected to one or more hidden nodes, and each of the hidden nodes is connected to one or more output nodes. In an exemplary embodiment, each input node is connected to each hidden node, and each hidden node is connected to each output node. The input nodes accept 3-angle color measurements, and the output nodes generate 3-angle tolerance values ​​S 3L , S 3C and S 3H . Multiple input nodes may be referred to as "input layers", multiple output nodes may be referred to as "output layers", and multiple hidden nodes may be referred to as "hidden layers". In some embodiments, multiple hidden nodes in one hidden layer may be connected to multiple hidden nodes in different hidden layers, and thus there may be one, two, or more hidden layers. Unless otherwise specified, the description generally refers to a model with one hidden layer. The input layer and hidden layer of the neural network empirical model may also include one or more bias nodes. The bias node is connected to each node in the subsequent layer without being connected to any node in the previous layer. The bias node of the hidden layer is also not connected to any hidden node within the hidden layer. In an exemplary embodiment, the input data and output data are scaled before the model is trained or the model is used for prediction. Typical scaling implementations involve scaling the data to a minimum value of 0 and a maximum value of 1, or a minimum value of 0.1 and a maximum value of 0.9, or a mean value of 0 and a standard deviation of 1.

[0045] As an example, the scaling equation (E) for scaling the data to arbitrary minimum and maximum values, such as 0.1 and 0.9 respectively, may be:

[0046] (E) Output scaling value (X) = (scaling maximum value - scaling minimum value) · (measured value - measured minimum value) / (measured maximum value - measured minimum value) + scaling minimum value

[0047] So for an input H* color measurement of 5, scaled to a range of 0.1 to 0.9 where the maximum H* color measurement is 10 and the minimum H* color measurement is 3, the calculation is:

[0048] Output scaling value = ((0.9-0.1)·(5-3)) / (10-3)+0.1

[0049] Output scaling value = (0.8·2) / 7+0.1

[0050] Output scaling value ~ 0.33

[0051] In an exemplary embodiment, the neural network empirical model initially generates 3-angle tolerance values ​​S within a scaled range such as a minimum value of 0 and a maximum value of 1, or a mean value of 0 and a standard deviation of 1.3L , S 3C and S 3H . These values ​​can be "de-scaled" to a physically meaningful range in a manner similar to the scaling process described above. The minimum 5-angle tolerance value and the maximum 5-angle tolerance value are the minimum 5-angle tolerance value and the maximum 5-angle tolerance value from the standard colors used to train the neural network empirical model, as described below. Likewise, the 3-angle tolerance value output by the neural network empirical model will typically be within a range of approximately the minimum 5-angle tolerance value and the maximum 5-angle tolerance value, which are determined based on the set of standard colors used to train the neural network empirical model.

[0052] The functional form of a single-layer neural network (one hidden layer with nodes) can be expressed as: (F)Y = f i+1 (f i (X.W i +b i )·W i+1 +bi+1), where W and b are the weight and bias for the model, respectively, “i” indicates the hidden layer of the network, and “i+1” indicates the output layer of the network. i ” and “f i +1" is an activation function that applies a linear or nonlinear transformation to each element of the network. Alternative equations representing different network structures may be utilized in alternative embodiments.

[0053] Then, the weights and biases (W and b in the above example) can be determined by inputting training data into the neural network empirical model in the training phase. The training data includes at least: 3-angle standard color measurement data of the standard color; and 5-angle tolerance values ​​(i.e., S) according to the above equations (B), (C) and (D). 5L , S 5c and S 5H ), where the 5-angle tolerance values ​​are calculated using the 5-angle measurement data of the same standard color. This training can be applied multiple times for multiple different standard colors, so that weights and biases (W and b in the above example, but other constants can be determined in alternative embodiments) can be determined and set for the neural network empirical model.

[0054] The neural network empirical model can then be applied with 3-angle color measurement data of multiple verification standard colors that are different from the multiple standard colors used to train the neural network empirical model. The neural network empirical model is applied with 3-color standard color measurement data from multiple verification standard colors to verify that the 3-angle tolerance value results for the same multiple verification standard colors closely approximate the 5-angle tolerance values.

[0055] The neural network empirical model can be established and utilized in various ways. For example, the 3-angle input data includes 3-angle color measurement data, but there are several different possible variations. For example, in one embodiment, the 3 angles used for color measurement are fifteen degrees (15°), 45°, and 110°. However, in an alternative embodiment, the 3 angles used for color measurement are 25°, 45°, and 110°. Other angles can be utilized in other embodiments, and 2, 4, 6, 7 or more angles can be used in other embodiments. In an exemplary embodiment, at least two different neural network empirical models are generated, including a neural network empirical model for 15°, 45°, and 110° color measurement, and a neural network empirical model for 25°, 45°, and 110° color measurement. The five angles used in the 2000 color difference five-angle equation are 15°, 25°, 45°, 75° and 110°, so the angles used in the two different three-angle neural network empirical models mentioned above are 2000 Chromatic Aberration 5 A subset of the angles used in the angle equation.

[0056] In an exemplary embodiment, the 3-angle input data includes: (1) luminance (L*) from black (0) to white (+) at each of the 3 angles, (2) a* from green (-) to red (+) at each of the 3 angles; (3) b* from blue (-) to yellow (+) at each of the 3 angles; (4) chroma (C*) at each of the 3 angles; and (5) a single flop index for all angles, for a total of 13 input nodes. However, in alternative embodiments, the 3-angle input data may not include a flop index, and may not include a chroma (C*) value at any angle. Alternative color values ​​may also be used, including but not limited to L*, C*, h* color spaces instead of L*, a*, b* color spaces. Other possible color space measurement techniques are also possible.

[0057] In an exemplary embodiment, the 3-angle neural network empirical model includes 25 hidden nodes and bias nodes in a single layer, wherein each hidden node is connected to each input node, including an input bias node, and each hidden node is connected to each output node. Using 25 hidden nodes in a single hidden layer produces accurate test results. However, in alternative embodiments, more or less than 25 hidden nodes may be used. In other embodiments, the 3-angle neural network empirical model may include 2 or more hidden node layers. Accuracy may be improved by using additional hidden nodes or additional hidden layers, but the training process of the 3-angle neural network empirical model may be more complicated, making it more difficult to obtain accurate results.

[0058] Example

[0059] Two different 3-angle neural network empirical models were developed, one for measuring angles of 15°, 45° and 110°, and the other for measuring angles of 25°, 45° and 110°. As described above, each of the 3-angle neural network empirical models includes 13 input nodes, 25 hidden nodes and 9 output nodes. Using the above techniques, each of the 3-angle neural network empirical models was trained with data from 2200 known standard colors. The performance of the two 3-angle neural network empirical models was verified using known data from 2470 validation standard colors, which are different from the standard colors used to train the neural network empirical models. Figures 1 to 6 The letters TRN in refers to the training data and are Figures 1 to 6 The letters VAL in the table refer to the validation data. Figures 1 to 6 , 3 angle tolerance value is S 3L , S 3C and S 3H The output results are expressed with the measured angles indicated in subscript brackets, with the number "3" removed from the subscript for simplicity. The data is marked with a "d" in the subscript to indicate that the result is the difference between (1) the 3-angle tolerance value at a specific angle and (2) the 5-angle tolerance value at the same specific angle for the same standard color. Therefore, a value of "0" means that the calculated 3-angle tolerance value is exactly the same as the calculated 5-angle tolerance value, and therefore, the closer the value is to zero, the more accurate the 3-angle neural network empirical model. It can be seen that the difference between the TRN value and the VAL value is relatively small, indicating that the results from the 3-angle neural network empirical model will closely approximate the results from the 5-angle 2000 The result of the color difference equation.

[0060] Although at least one embodiment has been presented in the foregoing detailed description, it should be appreciated that there are a large number of variations. It should also be appreciated that one or more embodiments are merely examples and are not intended to limit the scope, applicability, or configuration in any way. Rather, the foregoing detailed description will provide those skilled in the art with a convenient way to implement the embodiments, and it should be understood that various changes may be made to the functions and arrangements of the elements described in the embodiments without departing from the scope set forth in the attached claims and their legal equivalents.

Claims

1. A processor-implemented device for approximating a 5-angle color difference model, the device comprising: A storage device for storing instructions for approximating the 5-angle color difference model, wherein the 5-angle color difference model includes 5-angle equation (A), wherein the 5-angle equation (A) is: (A)dEY i =((dL*Y i / k L ·S 5L，Υi ) 2 +(dC*Y i / k c ·S 5c，γi ) 2 +(dH*γ i / k H ·S 5H，γi ) 2 ) of the square root, Among them, dE γi is the 5-angle color difference value, dL* is the brightness difference between the standard color and the test color pair, Υ is the measurement angle, i is the iteration of the measurement angle, dC* is the chromaticity difference between the standard color and the test color pair, dH* is the hue difference between the standard color and the test color pair, K L , Kc and K H is the acceptance limit, S 5L , S 5c and S 5H are the 5-angle tolerance values ​​for lightness, chroma, and hue at a specific color location; and one or more data processors configured to execute the instructions to: receiving a 3-angle standard color measurement of a standard color at each of three color measurement angles, wherein the three color measurement angles are a subset of the five color measurement angles; receiving a 3-angle test color measurement of a test color at each of the 3 color measurement angles; One of the following is input into a neural network empirical model: (i) the 3-angle standard color measurement; or (ii) the geometric mean of the lightness L* and chromaticity C* of the standard color measurement and the test color measurement; the neural network empirical model includes a plurality of input nodes, a plurality of hidden nodes connected to the plurality of input nodes, and a plurality of output nodes connected to the hidden nodes, wherein the neural network empirical model is configured to output a 3-angle tolerance value S for each of the 3 color measurement angles. 3L , S 3c , and S 3H , wherein the 3-angle tolerance values ​​output by the neural network empirical model are approximately the same as the 5-angle tolerance values ​​at each of the 3 color measurement angles; and The 3-angle color difference value for at least one of the 3 color measurement angles is calculated using the 3-angle standard color measurement, the 3-angle test color measurement and the 3-angle tolerance value using the 5-angle equation (A), wherein the 3-angle tolerance value is used to replace the 5-angle tolerance value in the 5-angle equation (A).

2. The device according to claim 1, wherein: The 5 angle tolerance values ​​S are calculated by equations (B), (C) and (D) 5L , S 5C and S 5H , (B)S 5LΥi =1,000·((|L * Υi -L * Υi+1 |) / (Y i+1 -Y i )) 2 / 3 +0.002°C * 45 +0.33; (C)S 5CΥi =1.478·((|C * Υi -C * Υi+1 |) / (Υ i+1 -Y i ))+0.014·C * 45 +0.27; (D)S 5HΥi =0.800·((|C * Υi -C * Υi+1 |) / (Y i+1 -Y i ))+0.004·C* 45 +0.30; Wherein, L*, C* and H* are the lightness, chromaticity and hue of the standard color, and C* 45 is the chromaticity of the standard color measured at 45 degrees.

3. The device according to claim 2, wherein: A standard deviation of tolerance value differences for a plurality of standard colors, which are differences between a 3-angle tolerance value and a 5-angle tolerance value for each 3-angle measurement angle for each standard color, is about 0.1 or less.

4. The device according to claim 1, wherein: The input nodes of the neural network empirical model include a brightness node L*, a red-green node a*, and a blue-yellow node b*.

5. The device according to claim 1, wherein: The neural network empirical model includes 13 input nodes, 25 hidden nodes and 9 output nodes.

6. The device according to claim 5, wherein: The 13 input nodes include: an input node L* for each of the three color measurement angles, an input node a* for each of the three color measurement angles, an input node b* for each of the three color measurement angles, a chromaticity input node (C*) for each of the three color measurement angles, and a dynamic color index.

7. The device according to claim 6, wherein: The function form of a single-layer neural network is Y = f i+1 (f i (X.W i +b i )·W i+1 +b i+1 ), where W and b are the weights and biases used for the model, respectively.

8. The device according to claim 7, wherein: Before applying the neural network empirical model, the 3-angle standard color measurement and the 3-angle test color measurement are scaled to a range from 0.1 to 0.9, so that the minimum value of each 3-angle test color measurement is scaled to 0.1 and the maximum value of each 3-angle test color measurement is scaled to 0.

9.

9. The device according to claim 1, wherein: The three color measurement angles are 15°, 45° and 110°.

10. The device according to claim 1, wherein: The three color measurement angles are 25°, 45° and 110°.

11. A method for approximating a 5-angle color difference model using 3-angle measurement data, the method comprising the following steps: receiving a 3-angle standard color measurement of a standard color at each of three color measurement angles, wherein the three color measurement angles are a subset of the five color measurement angles; receiving a 3-angle test color measurement of a test color at each of the 3 color measurement angles; Inputting one of the following into a neural network empirical model: (i) the 3-angle standard color measurement; or (ii) the geometric mean of the lightness L* and chromaticity C* of the standard color measurement and the test color measurement; the neural network empirical model comprising a plurality of input nodes, a plurality of hidden nodes connected to the plurality of input nodes, and a plurality of output nodes connected to the plurality of hidden nodes; Output the three-angle tolerance value S at each of the three color measurement angles from the neural network empirical model 3L , S 3c and S 3H , wherein the 3-angle tolerance values ​​output by the neural network empirical model are approximately the same as the 5-angle tolerance values ​​at each of the 3 color measurement angles; and Use the 5-angle equation (A) using the 3-angle standard color measurement, the 3-angle test color measurement, and the 3-angle tolerance value S 3L , S 3c and S 3H To calculate the 3-angle color difference value for at least one of the 3 color measurement angles, the 3-angle tolerance value S 3L , S 3c and S 3H Replace 5 angle tolerance values ​​S 5L , S 5c and S 5H , where the 5-angle equation (A) is: (A)dE Υi =((dL* Υi / k L ·S 5L，Υi ) 2 +(dC*Υ i / k c ·S 5c，Υi ) 2 +(dH*γ i / k H ·S 5HΥi ) 2 ), Among them, dE Υi is the 5-angle color difference value, dL* is the brightness difference between the standard color and the test color pair, γ is the measurement angle, i is the iteration of the measurement angle, dC* is the chromaticity difference between the standard color and the test color pair, dH* is the hue difference between the standard color and the test color pair, K L , Kc, K H is the acceptance limit, S 5L , S 5C , S 5H These are the 5 angle tolerance values ​​for brightness, chroma, and hue.

12. The method according to claim 11, further comprising: The 3-angle standard color measurement and the 3-angle test color measurement are scaled to a range from 0.1 to 0.

9.

13. The method according to claim 11, wherein: Receiving the 3-angle standard color measurement includes: receiving the 3-angle standard color measurement, wherein the 3-angle standard color measurement is measured at three color test angles of 15°, 45°, and 110°.

14. The method according to claim 13, wherein: Approximating the 5-angle color difference model includes: approximating the 5-angle color difference model, wherein the 5-angle color difference model uses 5 color measurement angles of 15°, 25°, 45°, 75°, and 110°.

15. A method for generating a 3-angle color difference model that approximates a 5-angle color difference model, the method comprising the following steps: receiving 5-angle standard color measurements of the standard color at each of the 5 color measurement angles; Calculate multiple 5-angle tolerance values ​​S using equations (B), (C), and (D) 5L , S 5C and S 5H , (B)S 5LΥi =1,000·((|L * Υi -L * Υi+1 |) / (Y i+1 -c i )) 2 / 3 +0.002°C * 45 +0.33; (C)S 5CΥi =1.478·((|C * Υi -C * Υi+1 |) / (Υ i+1 -Y i ))+0.014·C * 45 +0.27; (D)S 5HΥi =0.800·((|C * Υi -C * Υi+1 |) / (Y i+1 -Y i ))+0.004·C * 45 +0.30; Where L*, C* and H* are lightness, chromaticity and hue, γ is the measurement angle, i is the iteration of the measurement angle, and C* 45 is the chromaticity of the standard color measured at 45 degrees; receiving a 3-angle standard color measurement of the standard color at each of three color measurement angles, wherein the three color measurement angles are a subset of the five color measurement angles; generating a neural network empirical model, the neural network empirical model comprising a plurality of input nodes, a plurality of hidden nodes connected to the plurality of input nodes, and a plurality of output nodes connected to the plurality of hidden nodes, wherein the neural network empirical model is configured to output a three-angle tolerance value S at each of the three color measurement angles. 3L , S 3c and S 3H ; The neural network empirical model is trained using (1) the 5-angle standard color measurement, (2) the 3-angle standard color measurement, and (3) the 5-angle tolerance values, so that the 3-angle tolerance values ​​output by the neural network empirical model are approximately the same as the 5-angle tolerance values ​​at each of the 3 color measurement angles.

16. The method of claim 15, wherein: Training the neural network empirical model includes: training the neural network empirical model with multiple standard colors so that a standard deviation of tolerance value differences for the multiple standard colors is approximately 0.1 or less, wherein the tolerance value difference is a difference between a 3-angle tolerance value and a 5-angle tolerance value for each 3-angle measurement angle of each standard color.

17. The method according to claim 16, wherein: Training the neural network empirical model includes: A plurality of weights and biases of the neural network empirical model are calculated so that the weights and biases of the neural network empirical model produce a standard deviation of about 0.1 or less of the tolerance value difference for the plurality of standard colors.

18. The method of claim 15, wherein: Receiving a plurality of 5-angle color difference values ​​at each of the 5 color measurement angles includes: receiving a plurality of 5-angle color difference values ​​at each of the 5 color measurement angles, wherein the 5 color measurement angles are 15°, 25°, 45°, 75°, and 110°.

19. The method of claim 18, wherein: Receiving a plurality of 3-angle standard color measurements and a plurality of 3-angle test color measurements of standard color-test color pairs at each of the 3 color measurement angles includes using 3 color measurement angles of 15°, 45°, and 110°.

20. The method of claim 18, wherein: Receiving a plurality of 3-angle standard color measurements and a plurality of 3-angle test color measurements of standard color-test color pairs at each of the 3 color measurement angles includes using 3 color measurement angles of 25°, 45°, and 110°.

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