Method and system for quantifying spectral similarity between a sample color and a target color

Abstract

The present invention relates to a computer-implemented method and system (500) for providing a match metric for quantifying spectral similarity between a target coating and at least one sample coating, the system comprising a computing device (510) and a computer program product comprising computer executable code stored on a computer-readable storage medium (560) functionally coupled to the computing device (510) and causing the computing device (510) to perform a computational process when executed, the computational process comprising the steps of: receiving reflectance values ​​for a target coating and a sample coating for a plurality of wavelength values; normalizing each of the reflectance values ​​of the target coating and the sample coating by using a nonlinear scaling function; generating a normalized reflectance curve for the target coating and the sample coating for each wavelength value; generating a derivative value of the normalized reflectance curve of the target coating with respect to wavelength and a derivative value of the normalized reflectance curve of the sample coating with respect to wavelength for the plurality of wavelength values; generating a difference between the derivative value of the target coating and the derivative value of the sample coating for each wavelength value of the plurality of wavelength values; and generating a match metric for similarity between the normalized reflectance curves of the target coating and the sample coating based on at least the differences across all of the plurality of wavelength values.

Description

Technical Field

[0001] The present disclosure relates to a method and system for providing a matching metric for quantifying spectral similarity between at least one sample coating and a target coating. Background Art

[0002] Typically, the specification of a color base is determined by using a reference color defined / expressed in the CIELab* color space (also known as the CIE L*a*b* color space). The CIELab* color space is a color space defined by the International Commission on Illumination (CIE) in 1976 that represents colors as three values, L*, a*, and b*. In practice, the space is typically mapped to a three-dimensional integer space for digital representation, and therefore the L*, a*, and b* values ​​are typically absolute, with a predefined range. L* represents lightness, where the L* axis represents black when L*=0 and white when L*=100, the a* axis ranges from green (negative axis) to red (positive axis), and the b* axis ranges from blue (negative axis) to yellow (positive axis).

[0003] To compare and / or adjust the sample color to the target color, the color difference dE* in the CIELab* color space may be used, where the color difference dE* is defined by the following formula:

[0004]

[0005] However, the formula for a smaller color difference dE* (see formula (1)) does not guarantee that the pigmentation used in the target color, i.e. the pigment combination, can be accurately adjusted. In order to reproduce the pigmentation of the target color, it is necessary to characterize the coloring base in detail with the help of spectral analysis. Therefore, the spectral curve is determined based on the reflectance values ​​measured at different wavelength values ​​(e.g. in the range of 400nm to 700nm). In addition, the spectral curve is captured for different measurement geometries (i.e. at different viewing angles and / or different illumination angles). However, simply visually observing such a spectral curve is not sufficient to identify the similarities and differences between the target color and the sample color. So far, identifying the pigmentation of the target color is both time-consuming and expensive, so that the process is usually simplified to an approximation of the color coordinates in the CIELab* color space.

[0006] Therefore, it is an object of the present disclosure to provide a possibility to quantify the spectral similarity between a sample color (hereinafter also referred to as sample coating) and a target color (hereinafter also referred to as target coating). Summary of the Invention

[0007] The present disclosure provides systems and methods having the features of the independent claims. Embodiments are subject matter of the dependent claims as well as the description and drawings.

[0008] Today, the color matching and adjustment process is based on the use of multi-angle spectrometers (such as Byk- I or XRite -T Series spectrometer). The reflectance of color coatings is measured from several geometries (illumination and viewing directions / angles). The typical measurement geometry is a fixed illumination angle of 45° measured relative to the normal of the coating surface and viewing angles of -15°, 15°, 25°, 45°, 75°, and 110°. Each angle is measured relative to the specular angle (i.e., the specular direction), which is defined as the outgoing direction at the same angle to the normal of the color coating surface as the incident direction of the corresponding light. It is also possible to keep the viewing angle constant and change the illumination angle.

[0009] The basic structure of a known color matching and adjustment process includes the following steps:

[0010] 1. Measure the spectral (reflectance) curve of the target color, i.e. the target coating (spectral curve).

[0011] 2. Measure the spectrum (reflectance) curve of the sample color, that is, the sample coating (spectral curve).

[0012] 3. Calculate the color values ​​of the target color and the sample color (ie, the target coating and the sample coating), wherein the corresponding coating is described in the CIELab* color space (Lab* or LCh* values).

[0013] 4. Determine a metric for the “cost function”, such as a cumulative color difference metric between the target color and the sample color (ie, the target coating and the sample coating for all geometries), such as CIE dE*, see equation (1).

[0014] 5. Modify the recipe of the sample coating so that the color difference metric ("cost function") is minimized (usually done through a color matching algorithm).

[0015] However, as mentioned previously, performing a matching process based solely on color difference (i.e., using a color difference metric) is generally insufficient, since the pigmentation of the sample coating may still deviate from the pigmentation of the target coating in an unacceptable manner. Therefore, in order to fully account for the pigmentation of the target coating, it is necessary to provide further metrics that complement the already existing metrics (such as the color difference metric).

[0016] According to claim 1, the present disclosure provides a computer-implemented method for providing a matching metric for quantifying the similarity of spectral profiles of a target coating and at least one sample coating, the method comprising at least the following steps:

[0017] a) obtaining, via a communication interface, reflectance values ​​of a target coating and reflectance values ​​of a sample coating for a plurality of wavelength values, wherein the reflectance values ​​of the target coating are determined at one or more measurement geometries, in particular measured at one or more measurement geometries, and the reflectance values ​​of the sample coating are determined at one or more measurement geometries, in particular measured at one or more measurement geometries;

[0018] and by at least one processor:

[0019] b) normalizing each of the reflectance values ​​of the target coating determined at the respective one or more measurement geometries, e.g. measured at the respective one or more measurement geometries, and the reflectance values ​​of the sample coating determined at the respective one or more measurement geometries, e.g. measured at the respective one or more measurement geometries, by using a scaling function, in particular a non-linear scaling function;

[0020] c) generating a normalized reflectivity curve of the target coating based on the normalized reflectivity value of the target coating for each wavelength value, and generating a normalized reflectivity curve of the sample coating based on the normalized reflectivity value of the sample coating for each wavelength value;

[0021] d) generating, for a plurality of wavelength values, a normalized first derivative value of a normalized reflectivity curve of the target coating with respect to wavelength and a normalized first derivative value of a normalized reflectivity curve of the sample coating with respect to wavelength;

[0022] e) generating, for each wavelength value of the plurality of wavelength values, a difference between a normalized first derivative value of the normalized reflectance curve of the target coating and a normalized first derivative value of the normalized reflectance curve of the sample coating;

[0023] f) generating a matching metric of similarity between the normalized reflectance curves of the target coating and the sample coating based on the differences across all of the multiple wavelength values, and

[0024] g) outputting the generated match metric to a user using an output device.

[0025] According to another aspect of the present disclosure, the method further comprises the following steps:

[0026] h) Modifying the initial recipe of the sample coating so as to minimize a matching metric of spectral profile similarity between the target coating and the sample coating as a constraint (in addition to the existing color difference metric).

[0027] According to another aspect, the initial formulation of the sample coating is retrieved as one of one or more preliminary matching formulations from a database comprising coating formulations and associated color properties, such as L*, a*, b* values, and optionally texture properties, such as sparkle or roughness values. This means that, starting with the target coating, the database is first searched for one or more preliminary matching formulations whose color and, optionally, texture data are identical or at least similar to the color and, optionally, texture data of the target coating, i.e., using a color and, optionally, texture matching algorithm, the color difference and, optionally, texture difference between the one or more preliminary matching formulations and the target coating are minimal.

[0028] This means that an initial formulation for a sample coating can be given in advance or can be selected from a formulation database comprising formulations of coating compositions and associated appearance data. As used herein, "appearance" refers to the visual experience / perception of viewing or recognizing a coating. Thus, appearance can include the color, shape, texture, shimmer, sparkle, gloss, transparency, opacity and other visual effects of the coating, or a combination thereof. "Modification" includes mixing one or more components into the initial formula and / or omitting one or more components from the initial formula and / or changing the respective concentrations / amounts of one or more components of the initial formula to obtain a modified formula that better matches the target color with respect to its appearance, which can be expressed by different metrics, such as color difference metrics and spectral similarity as expressed by the matching metrics disclosed herein.

[0029] The term "spectral similarity" between a sample coating and a target coating is to be understood as the similarity between the shape of the spectral (reflectivity) curve of the sample coating and the shape of the spectral (reflectivity) curve of the target coating.

[0030] The proposed method provides a matching metric to characterize the spectral similarity between two reflectance curves. The value of the matching metric is used as a means to quantify the similarity between the pigmentation of the target coating and the pigmentation of the sample coating. In addition, all possible values ​​of the matching metric are located in a scale range that corresponds to or is at least comparable to those scales used in other metrics used in the color matching process (such as the color difference metric dE* already mentioned defined in the CIELab* color space). Smaller values ​​of the matching metric indicate better spectral similarity, while higher values ​​of the matching metric indicate poorer spectral similarity between the two considered reflectance curves.

[0031] A low spectral similarity metric indicates that the pigmentation of the sample coating formulation is different from the pigmentation used for the target coating. This means that the pigmentation of the sample coating is not optimal in order to match the target coating.

[0032] Within the scope of the present disclosure, a reflectivity curve (also referred to below as a spectral curve) describes the reflectivity behavior of a coating at different wavelength values ​​and a specific measurement geometry. For each measurement geometry, a separate reflectivity curve is determined (e.g., measured). Within the scope of the present disclosure, the terms "measurement geometry" and "measurement geometry" are used synonymously.

[0033] In the context of this disclosure, the term "sample coating" refers to a color, i.e., a paint layer that has been prepared according to a sample formula and applied to a surface. The term "target coating" refers to a color, i.e., a paint layer applied to a surface, the underlying formula of which is unknown and should be replicated as closely as possible.

[0034] According to a possible embodiment of the proposed method, step d) further comprises:

[0035] d2) With respect to wavelength, the normalized first derivative values ​​of the normalized reflectance curves of the target coating and the sample coating are converted into angle representations, respectively.

[0036] According to one embodiment of the proposed method, for each wavelength value, the normalized first derivative values ​​of the normalized reflectance curves of the target coating and the sample coating are respectively represented as two-dimensional vectors according to the following formula:

[0037]

[0038]

[0039]

[0040] in

[0041] as well as

[0042] and Δλ i =λ i+1 -λ i

[0043] in, Indicates the target coating at wavelength λ i The normalized reflectance value at Indicates the target coating at wavelength λ i+1 The normalized reflectance value at Indicates the sample coating at wavelength λ i The normalized reflectance value at Indicates the sample coating at wavelength λ i+1 The normalized reflectivity value at , k1 is the nonlinear damping parameter, where for example k1 = 0.005, and Indicates two normalized vectors and The angle between the vectors Indicates the target coating at λ i The normalized gradient of the reflectivity curve at , and the vector Indicates sample coating at λ i The normalized gradient of the reflectivity curve at . Therefore, Indicates the wavelength value λ i A normalized difference / angle between two spectral curves.

[0044] According to one aspect, the wavelength values ​​of the plurality of wavelength values ​​are selected from an interval from a minimum wavelength value to a maximum wavelength value, wherein the minimum wavelength value is approximately 420 nm and the maximum wavelength value is approximately 680 nm, i.e.:

[0045] λ i =λ min , ..., λ max

[0046] λ min ≈420nm

[0047] λ max ≈680nm

[0048] Among them, λ min and λ max The number of measured reflectance values ​​between is n, and the index of the corresponding reflectance value is i∈[0, ...(n-1)].

[0049] Since the human eye typically works in the range of 400 nm to 700 nm, this wavelength range is highly relevant. Due to measurement uncertainties caused by additives in the coating (e.g., UV blockers), the spectral range below 420 nm can be excluded from the analysis. Due to the limited hiding power of the coating layer and interference caused by the substrate color, the spectral range above 680 nm can be excluded from the analysis.

[0050] The proposed matching metric allows identifying differences between a target coating and a sample coating even if the color associated with the target coating and the color associated with the sample coating are located at the same point or adjacent points in the CIELab* space. Thus, non-optimal pigmentation with resulting metamerism effects can be taken into account and identified.

[0051] The normalized spectral reflectance curve of the target coating is composed of the normalized reflectance value Give / define.

[0052] The normalized spectral reflectance curve of the sample coating is composed of the normalized reflectance value Give / define.

[0053] For comparison purposes, the reflectance values ​​are normalized by a scaling function which is chosen to be a nonlinear scaling function f ref，smp , as follows:

[0054]

[0055] in

[0056]

[0057] in

[0058]

[0059] Among them, R ref， / smp，center It is given by:

[0060]

[0061] in, and

[0062] in, express and Both, among them, is the target coating at wavelength λ i The reflectivity value at is the sample coating at wavelength λ i The reflectivity value at .

[0063] Nonlinear scaling function f ref，smp Refers to the lightness (L*) algorithm used to convert colors from the XYZ color space to the CIELab* color space. The L* metric is designed to simulate the logarithmic response of the human eye to brightness. The scaling function attempts to linearize the perceptibility of brightness.

[0064] According to one aspect of the proposed method, the matching metric called in the following dShape is chosen as follows:

[0065]

[0066] Where n is an integer and k2 is a linear scaling factor, where for example k2=0.65.

[0067] According to another aspect of the proposed method, the matching metric is chosen as follows:

[0068]

[0069] Where n is an integer, and is a linear scaling factor, where for example

[0070] Parameters k1 and k2, is freely selectable in order to define together (see the above formula) the scale of the first fit measure values ​​dShape, dShape*.

[0071] The proposed method provides a matching metric that produces values ​​in a scale (i.e., scale space) that is comparable to the scale space of the CIELab* color space and the scale space of color distance metrics defined in the CIELab* color space (such as, for example, the lightness difference metric dL* and the color difference metric dE*). Thus, all colorimetric data defined in this standard color space and usable for color matching, adjustment, and search processes can be provided in a comparable scale, facilitating the interpretation of the colorimetric data in a holistic view. Due to the scaling function, the gain value of the matching metric can be interpreted regardless of the absolute color coordinates of the target coating, in particular regardless of its lightness L*.

[0072] Generally, it is aimed to determine the formula retrieved from the database whose color difference dE*, optionally its texture difference, its sparkle difference dS and its granularity difference dG and whose newly calculated matching metric dShape is minimal when all metrics are considered individually (ie alone).

[0073] Further correction / modification of the optimal matching formula is performed using a cost function that combines all considered metrics, for example by adding all considered metrics together: dE* (or dL*+da*+db*)+dShape (optionally: +dS+dG+...), possibly with each addition being appropriately weighted and minimizing this cost function accordingly.

[0074] Alternatively, instead of preselecting a preliminary matching formula from the database, the optimal matching formula may be directly calculated using the cost function combining different metrics, that is, the optimal matching formula may be calculated from scratch.

[0075] According to another embodiment of the proposed method, the at least one measurement geometry is selected from the group consisting of -15°, 15°, 25, 45°, 75° and 110°, each measured relative to a mirror angle.

[0076] In particular, characteristic information about the pigmentation in the coating (i.e., in the target coating and the sample coating, respectively) is contained in the corresponding shape of the measured spectral curve (in particular, the measured reflectance curve). Within the scope of the present disclosure, the terms "spectral curve," "spectral reflectance curve," and "reflectance curve" are used synonymously. Pigments have typical absorption and scattering properties, which produce a characteristic fingerprint in the spectral curve. For the analysis of the desired / optimal pigmentation for the target color, the absolute intensity of the reflectance value is less important than the shape of the reflectance / spectral curve, which can be encoded by the first derivative value of the normalized spectral curve.

[0077] According to the present disclosure, a useful metric is the difference between the normalized first derivatives (values) of the corresponding normalized spectral curves of the target and sample coatings, i.e., the difference. This matching metric includes information about the shape of the spectral curves, but does not include information about the absolute intensity of the reflectance values.

[0078] As mentioned above, the strategy of using the normalized first derivatives (values) of the corresponding normalized spectral curves as matching metrics can also be combined with other metrics in the field of color search, matching and adjustment (e.g., with color difference metrics and optionally texture difference metrics).

[0079] The present disclosure further relates to a system for providing a matching metric for quantifying similarity of spectral profiles of a target coating and at least one sample coating, the system comprising:

[0080] A) Computing equipment;

[0081] B) A computer program product comprising computer executable code stored on a computer readable storage medium functionally coupled to a computing device and causing the computing device to perform a computing process when run, the computing process comprising the following steps:

[0082] B1) receiving, for a plurality of wavelength values, reflectivity values ​​of the target coating and reflectivity values ​​of the sample coating via a communication interface, wherein the reflectivity values ​​of the target coating are determined, in particular measured, at one or more measurement geometries, and the reflectivity values ​​of the sample coating are determined, in particular measured, at one or more measurement geometries;

[0083] B2) normalizing each of the reflectance values ​​of the target coating determined at the corresponding one or more measurement geometries and the reflectance values ​​of the sample coating determined at the corresponding one or more measurement geometries by using a nonlinear scaling function;

[0084] B3) generating a normalized reflectance curve of the target coating based on the normalized reflectance value of the target coating at each wavelength value, and generating a normalized reflectance curve of the sample coating based on the normalized reflectance value of the sample coating at each wavelength value;

[0085] B4) generating, for a plurality of wavelength values, a normalized first derivative value of the normalized reflectivity curve of the target coating with respect to the wavelength and a normalized first derivative value of the normalized reflectivity curve of the sample coating with respect to the wavelength;

[0086] B5) generating, for each wavelength value of the plurality of wavelength values, a difference between a normalized first derivative value of the normalized reflectance curve of the target coating and a normalized first derivative value of the normalized reflectance curve of the sample coating;

[0087] B6) generating a match metric for similarity of the normalized reflectance curves of the target coating and the sample coating based at least on the difference values ​​across the plurality of wavelength values, and

[0088] B7) Outputting the generated matching metric to the user using an output device.

[0089] According to a possible embodiment of the proposed system, the system further comprises:

[0090] c) Color measurement equipment;

[0091] D) a formulation database comprising formulations of coating compositions and associated colorimetric data;

[0092] Therein, a computing device is functionally coupled to a color measurement device and a recipe database.

[0093] Typically, the color measurement device is a spectrometer, particularly a multi-angle spectrometer such as the Byk- I or XRite- -T series spectrometer.

[0094] Output devices can also be components of a system.

[0095] According to another embodiment of the system, the calculation process further comprises a color retrieval process for matching the colors of the target coating and the at least one sample coating, the matching process comprising at least the following steps:

[0096] B8) retrieving one or more preliminary matching formulas from a formula database based on the sample colorimetric data;

[0097] B9) Selecting at least one preliminary matching formula from the one or more preliminary matching formulas so as to minimize a matching metric other than other colorimetric metrics such as color difference (color difference metric) and texture difference (texture difference metric).

[0098] According to another embodiment of the system of the present invention, the calculation process further comprises the following steps:

[0099] B10) Modifying the initial formula of the sample coating, in particular at least one preliminary matching formula selected so as to minimize matching metrics in addition to other colorimetric metrics such as color difference and optionally texture difference.

[0100] Typically, at least the color measurement device, the computing device, and the recipe database are networked with each other via corresponding communication connections. Each of the communication connections between the different components of the system can be a direct connection or an indirect connection. Each communication connection can be a wired or wireless connection. Any suitable communication technology can be used. The recipe database, the color measurement device, and the computing device can each include one or more communication interfaces for communicating with each other. Such communication can be performed using a wired data transmission protocol, such as Fiber Distributed Data Interface (FDDI), Digital Subscriber Line (DSL), Ethernet, Asynchronous Transfer Mode (ATM), or any other wired transmission protocol. Alternatively, the communication can be performed wirelessly via a wireless communication network using any of a variety of protocols, such as General Packet Radio Service (GPRS), Universal Mobile Telecommunications System (UMTS), Code Division Multiple Access (CDMA), Long Term Evolution (LTE), Wireless Universal Serial Bus (USB), and / or any other wireless protocol. The corresponding communication can be a combination of wireless and wired communication.

[0101] The computing device may include or be in communication with one or more input devices, such as a touch screen, audio input, mobile input, mouse, keypad input, etc. In addition, the computing device may include or be in communication with one or more output devices, such as audio output, video output, screen / display output, etc.

[0102] Embodiments of the present invention can be used with or incorporated into a computer system, which can be a standalone unit or include one or more remote terminals or devices that communicate with a central computer located, for example, in the cloud, via a network (such as the Internet or an intranet). Thus, the computing devices and related components described herein can be part of a local computer system or a remote computer or online system, or a combination thereof. The recipe database and software described herein can be stored in a computer's internal memory or in a non-transitory computer-readable medium.

[0103] Within the scope of this disclosure, a database may be a part of a data storage unit or may represent the data storage unit itself.The terms "database" and "data storage unit" are used synonymously.

[0104] This disclosure describes the matching metric as a metric that can be combined with other metrics in the field of color search, matching, and adjustment, such as, for example, color difference, sparkle difference, flop difference, etc. Since the value ranges of all such different metrics lie in a comparable scale space, it is helpful to interpret the matching metric in the context of the other metrics in this overview.

[0105] The proposed method and system achieves better convergence in the color matching and adjustment process. Furthermore, it reduces the workload required for color development and customer service matching within the corresponding laboratory. The overall color matching process is more reliable and faster.

[0106] The present invention is further defined in the following examples. It should be understood that these examples, while indicating preferred embodiments of the present invention, are given by way of illustration only. From the above discussion and examples, one skilled in the art will be able to ascertain the essential characteristics of the present invention and, without departing from its spirit and scope, may make various changes and modifications to adapt the present invention to various uses and conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 Spectral reflectance graphs of target coating and sample coating are shown;

[0108] Figure 2 Show Figure 1 spectral reflectance curves of the target coating, and an average reflectance value of the target coating for each spectral reflectance curve;

[0109] Figure 3a Show Figure 1 Spectral reflectance curve of the graph, where specific areas are circled;

[0110] Figure 3b Showing an enlarged representation Figure 3a The circled area;

[0111] Figure 3c Show representation Figure 3b The vector of the gradient of the reflectivity curve of the target coating in the circled area;

[0112] Figure 3d Show instructions Figure 3b The vector of the gradient of the reflectivity curve of the sample coating in the circled area;

[0113] Figure 3e Show Figure 3c The vector sum Figure 3d The angle between the vectors;

[0114] Figure 4 Figures 4a to 4k An example of a matching metric value provided by an embodiment of the proposed method is shown in .

[0115] Figure 5 An embodiment of the proposed system is schematically shown. DETAILED DESCRIPTION

[0116] Figure 1 The normalized spectral measurement values ​​are shown, i.e., the normalized spectral reflectance curves of the target coating and the sample coating at different viewing angles. The in-plane bidirectional reflectance of the metallic colored sample coating is measured using a multi-angle spectrometer (e.g., Byk- I or XRite -T series spectrometer). The reflectance of the sample coating was measured from several geometries, namely with a given illumination angle of 45° measured relative to the coating surface normal, and viewing angles of -15°, 15°, 25°, 45°, 75°, and 110°, each measured relative to the specular angle.

[0117] The wavelength of the incident light flux is plotted along the horizontal axis 110. The normalized reflectance of the sample coating and the target coating is plotted along the vertical axis 120. Using the scaling function f ref,smp Normalize the measured reflectance values:

[0118]

[0119] in

[0120]

[0121] in

[0122]

[0123] Among them, R ref， / smp，center Given by:

[0124]

[0125] in, and

[0126] Curve 130 indicates the reflectivity of the target coating measured at a viewing angle of -15°, and curve 135 indicates the reflectivity of the sample coating measured at a viewing angle of -15°. Respectively, curve 140 indicates the reflectivity of the target coating measured at a viewing angle of 15°, and curve 145 indicates the reflectivity of the sample coating measured at a viewing angle of 15°. Respectively, curve 150 indicates the reflectivity of the target coating measured at a viewing angle of 25°, and curve 155 indicates the reflectivity of the sample coating measured at a viewing angle of 25°. Respectively, curve 160 indicates the reflectivity of the target coating measured at a viewing angle of 45°, and curve 165 indicates the reflectivity of the sample coating measured at a viewing angle of 45°. Respectively, curve 170 indicates the reflectivity of the target coating measured at a viewing angle of 75°, and curve 175 indicates the reflectivity of the sample coating measured at a viewing angle of 75°. The reflectivity curves of the target coating and the sample coating, each measured at a viewing angle of 110°, are not distinguishable from the reflectivity curves 170 and 175, respectively, in the representation presented here, as only very small reflectivity values ​​are measured at flip angles of 45°, 75°, and 110°, respectively. Furthermore, only small changes in the shape of the respective curves, depending on wavelength, are observed.

[0127] The wavelength values ​​of the multiple wavelength values ​​for analyzing the reflectivity are selected from the interval from the minimum wavelength value to the maximum wavelength value, wherein the minimum wavelength value is about 420nm and the maximum wavelength value is about 680nm, that is:

[0128] λ i =λ min , ..., λ max

[0129] λ min ≈420nm

[0130] λ max ≈680nm

[0131] Among them, λ min and λ max The number of analyzed reflectance values ​​between is n, and the index of the corresponding reflectance value is i∈[0,...(n-1)].

[0132] Figure 2 Show Figure 1 spectral reflectance curves of the target coating, and for each spectral reflectance curve, the average reflectance value 131, 141, 151, 161, 171 of the target coating, each is indicated by a dotted line.

[0133] Figure 3a Show Figure 1 FIG1 is a normalized spectral reflectance graph of FIG1 , wherein a specific area 133 is circled.

[0134] Figure 3bShown in enlarged form Figure 3a The circled area 133. Next, consider the intersection 134 of the two anti-blocking rate curves 130 and 135.

[0135] Figure 3c Shows a vector indicating Figure 3b The normalized gradient (equal to the normalized derivative value) of the reflectivity curve of the target coating in the circled region 133 of FIG, particularly at the intersection 134. Therefore, only the gradient from λ i ≈605,3nm to λ i +Δλ i The enlarged portion 110' of the horizontal axis 110 is shown, and only the enlarged portion 120' of the vertical axis 120 is shown, which includes the arrive By means of the vector representation of the normalized first-order derivative value of the reflectance curve of the target coating and the normalized first-order derivative value of the reflectance curve of the sample coating, respectively, the difference between the normalized first-order derivative value of the reflectance curve of the target coating and the normalized first-order derivative value of the reflectance curve of the sample coating can be indicated as an angle (See Figure 3e ).

[0136] like Figure 3c As shown in i ≈605,3nm, the normalized first derivative value of the reflectivity curve of the target coating at the intersection 134 is expressed as a two-dimensional vector according to the following formula

[0137]

[0138] in

[0139] as well as

[0140] Δλ i =λ i+1 -λ i

[0141] in, Indicates the target coating at wavelength λ i The normalized reflectance value at Indicates the target coating at wavelength λ i+1 =λ i +Δλ i The normalized reflectivity value at . k1 is the nonlinear damping parameter, where k1 = 0.005.

[0142] Figure 3d Shows the normalized vector, indicating Figure 3bThe gradient of the reflectivity curve of the sample coating in the circled region of λ (particularly at the intersection 134). Again, only the gradient from λ i ≈605,3nm to λ i +Δλ i In addition, only the enlarged portion 120′ of the vertical axis 120 is shown, which includes the arrive The reflectivity value.

[0143] like Figure 3d As shown in i ≈605,3 nm, the normalized first derivative value of the reflectivity curve of the sample coating at the intersection 134 is expressed as a two-dimensional vector according to the following formula:

[0144]

[0145] as well as

[0146] Δλ i =λ i+1 -λ i .

[0147] Indicates the sample coating at wavelength λ i The normalized reflectance value at Indicates the sample coating at wavelength λ i+1 =λ i +Δλ i The normalized reflectivity value at . k1 is the nonlinear damping parameter.

[0148] Figure 3e Show Figure 3c Vector and Figure 3d Vector Angle between This indicates that at the intersection point 134 (i.e., the wavelength value λ i ≈605.3 nm) is the difference between the gradient (equal to the normalized derivative value) of the reflectance curve 130 of the target coating and the gradient (equal to the normalized derivative value) of the reflectance curve 135 of the sample coating. Indicates two normalized vectors and The angle between them, and the vector Indicates the target coating at λ i The gradient of the reflectivity curve at , and the vector Indicates sample coating at λ i The gradient of the reflectivity curve at . Therefore, Indicates a difference angle / value and is determined according to the following formula (Law of Cosines):

[0149]

[0150]

[0151] Figure 4 Figures 4a to 4k Examples of values ​​of the matching metric dShape provided by an embodiment of the proposed method are shown in FIG.

[0152] Figures 4a to 4k Graphs each show a normalized spectral curve for a target coating and a normalized spectral curve for a sample coating. Wavelength values ​​are plotted along horizontal axis 410 and are selected from a range of minimum wavelength values ​​to maximum wavelength values, wherein the minimum wavelength value is 420 nm and the maximum wavelength value is 680 nm. Normalized reflectance values ​​for the target coating and the sample coating are plotted along vertical axis 420, respectively, with the range of 0.0 to 0.5.

[0153] Above each figure, the corresponding values ​​of the matching metric dShape, the minimum wavelength value wlmin, the maximum wavelength value wlmax, the nonlinear damping parameter k1 and the linear scaling factor k2 are illustrated.

[0154] Figure 5 An embodiment of the proposed system is schematically illustrated. The system 500 shown here includes a computing device 510, a recipe database 520, a color measurement device 530, an output device 540, an input device 550, and a computer-readable storage medium 560. The system further includes a computer program product comprising computer executable code stored on the computer-readable storage medium 560. In the example shown here, the computer-readable storage medium 560 is loaded into the internal memory of the computing device 510. Therefore, the computer-readable storage medium 560 is functionally coupled to the computing device 510. Any other functional coupling of the computer-readable storage medium 560 and the computing device 510 is possible. When executed, the computer-readable storage medium 560 causes the computing device 510 to perform a computing process comprising the following steps:

[0155] B1) receiving, for a plurality of wavelength values, reflectivity values ​​of the target coating and reflectivity values ​​of the sample coating via a communication interface, wherein the reflectivity values ​​of the target coating are determined, in particular measured, at one or more measurement geometries, and the reflectivity values ​​of the sample coating are determined, in particular measured, at one or more measurement geometries;

[0156] B2) normalizing each of the reflectance values ​​of the target coating determined at the corresponding one or more measurement geometries and the reflectance values ​​of the sample coating determined at the corresponding one or more measurement geometries by using a nonlinear scaling function;

[0157] B3) generating a normalized reflectance curve of the target coating based on the normalized reflectance value of the target coating at each wavelength value, and generating a normalized reflectance curve of the sample coating based on the normalized reflectance value of the sample coating at each wavelength value;

[0158] B4) generating, for a plurality of wavelength values, a normalized first derivative value of the normalized reflectivity curve of the target coating with respect to the wavelength and a normalized first derivative value of the normalized reflectivity curve of the sample coating with respect to the wavelength;

[0159] B5) generating, for each wavelength value of the plurality of wavelength values, a difference between a normalized first derivative value of the normalized reflectance curve of the target coating and a normalized first derivative value of the normalized reflectance curve of the sample coating;

[0160] B6) generating a match metric for similarity of the normalized reflectance curves of the target coating and the sample coating based at least on the difference values ​​across the plurality of wavelength values, and

[0161] B7) Output the generated matching metric to the user using the output device 540.

[0162] Recipe database 520 includes recipes for coating compositions and interrelated colorimetric data and is functionally coupled to computing device 510 .

[0163] Typically, the color measurement device 530, which is also functionally coupled to the computing device 510, is a spectrometer, particularly a multi-angle spectrometer, such as a Byk- I or XRite- -T series spectrometer.

[0164] The calculation process may further include a color retrieval process for matching the colors of the target coating and the at least one sample coating, the matching process including at least the following steps:

[0165] B8) retrieving one or more preliminary matching formulas from the formula database 520 based on the sample colorimetric data;

[0166] B9) Selecting at least one preliminary matching formula from the one or more preliminary matching formulas so as to minimize a matching metric other than other colorimetric metrics such as color difference (color difference metric) and texture difference (texture difference metric).

[0167] In addition, the calculation process may further include the following steps:

[0168] B10) Modifying the initial formula of the sample coating, in particular at least one preliminary matching formula selected so as to minimize matching metrics in addition to other colorimetric metrics such as color difference and optionally texture difference.

[0169] Typically, at least the color measurement device 530, the computing device 510, and the recipe database 520 are networked with each other via corresponding communication connections. In addition, the input device 550 and the output device 540 are part of the computing device 510 or at least functionally coupled to the computing device 510. Both the target coating (i.e., the spectral curve of the target coating) and the sample coating (i.e., the spectral curve of the sample coating) can be simultaneously illustrated on the output device 540 to allow for visual comparison "on the fly," i.e., during operation of the matching process.

[0170] Reference Signs List

[0171] 110 horizontal axis

[0172] 120 vertical axis

[0173] Reflectivity curve at 130-15°

[0174] Reflectivity curve at 135-15°

[0175] 140 Reflectivity curve at 15°

[0176] 145 Reflectivity curve at 15°

[0177] Reflectivity curve at 150 25°

[0178] 155 Reflectivity curve at 25°

[0179] 160 Reflectivity curve at 45°

[0180] 165 Reflectivity curve at 45°

[0181] 170 Reflectivity curve at 75°

[0182] Reflectivity curve at 175 75°

[0183] Average reflectivity value at 131-15°

[0184] 141 Average reflectivity at 15°

[0185] 151 Average reflectivity value at 25°

[0186] 161 Average reflectivity value at 45°

[0187] 171 Average reflectivity value at 75°

[0188] 133 Specific Areas

[0189] 134 Intersection

[0190] 110' Enlarged section of horizontal axis 110

[0191] 120' Enlarged section of vertical axis 120

[0192] 410 horizontal axis

[0193] 420 vertical axis

[0194] 500 system

[0195] 510 Computing Equipment

[0196] 520 recipe database

[0197] 530 Color Measurement Equipment

[0198] 540 output devices

[0199] 550 Input Devices

[0200] 560 Computer readable storage medium

Claims

1. A computer-implemented method for providing a match metric for quantifying spectral similarity between a target coating and at least one sample coating, the method comprising at least the steps of: a) obtaining reflectance values ​​of the target coating and reflectance values ​​of the sample coating for a plurality of wavelength values, wherein the reflectance values ​​of the target coating are determined at one or more measurement geometries and the reflectance values ​​of the sample coating are determined at the one or more measurement geometries; and By using one or more processors: b) normalizing each of the reflectance values ​​of the target coating determined at a corresponding one of the one or more measurement geometries and the reflectance values ​​of the sample coating determined at the corresponding one of the one or more measurement geometries by using a scaling function; c) generating a normalized reflectivity curve of the target coating based on the normalized reflectivity value of the target coating at each wavelength value, and generating a normalized reflectivity curve of the sample coating based on the normalized reflectivity value of the sample coating at each wavelength value; d) generating, for the plurality of wavelength values, normalized first derivative values ​​of the normalized reflectivity curve of the target coating with respect to the wavelength and normalized first derivative values ​​of the normalized reflectivity curve of the sample coating with respect to the wavelength; e) generating, for each wavelength value in the plurality of wavelength values, a difference between the normalized first derivative value of the normalized reflectance curve of the target coating and the normalized first derivative value of the normalized reflectance curve of the sample coating; f) generating a matching metric of similarity between the normalized reflectance curves of the target coating and the sample coating based at least on the difference across all of the plurality of wavelength values, g) outputting the generated match metric to a user using an output device; h) retrieving one or more preliminary matching formulas from a recipe database comprising formulas of coating compositions and associated colorimetric properties based on the reflectance value of the sample coating and / or further predetermined color properties of the sample coating or a combination thereof; i) modifying one of the one or more preliminary matching formulas so as to minimize the matching metric of the similarity of the normalized reflectance curves of the target coating and the sample coating as an additional constraint in addition to an existing color difference metric, wherein the modifying is performed by minimizing a cost function including a weighted sum of color difference, texture difference, sparkle difference, granularity difference, and the matching metric; Wherein, for each wavelength value, the normalized first-order derivative value of the normalized reflectivity curve of the target coating and the normalized first-order derivative value of the normalized reflectivity curve of the sample coating are respectively expressed as two-dimensional vectors according to the following formulas: in as well as as well as Dl i =λ i+1 -l i in, Indicates the target coating at wavelength value λ i The normalized reflectance value at Indicates the target coating at wavelength value λ i+1 The normalized reflectance value at Indicates that the sample coating is at the wavelength value λ i The normalized reflectance value at Indicates that the sample coating is at the wavelength value λ i+1 The normalized reflectivity value at , k1 is the nonlinear damping parameter, where k1 = 0.005, and Indicates two normalized vectors and The angle between the vector Indicates the target coating at λ i The normalized gradient of the reflectivity curve at , and the vector Indicates that the sample coating is at λ i The normalized gradient of the reflectivity curve at .

2. The method according to claim 1, wherein The wavelength values ​​of the plurality of wavelength values ​​are selected from an interval from a minimum wavelength value to a maximum wavelength value, wherein the minimum wavelength value is approximately 420 nm and the maximum wavelength value is approximately 680 nm.

3. The method according to claim 1, wherein The scaling function is chosen to be a nonlinear scaling function f ref,smp , the nonlinear scaling function f ref,smp The following are selected: in in Among them, R ref, / smp,center Given by: in, and 4. The method according to claim 1, wherein The matching metric is chosen as follows: Where n is an integer and k2 is a linear scaling factor, where k2=0.

65.

5. The method according to claim 1, wherein The matching metric is chosen as follows: Where n is an integer, and is the linear scaling factor, where 6. A system (500) for providing a matching metric for quantifying spectral similarity between a target coating and at least one sample coating, the system comprising: A) computing device (510); B) A computer program product comprising computer executable code stored on a computer readable storage medium (560) functionally coupled to the computing device (510) and causing the computing device (510) to perform a computing process when run, the computing process comprising the following steps: B1) receiving reflectance values ​​of the target coating and reflectance values ​​of the sample coating for a plurality of wavelength values, wherein the reflectance values ​​of the target coating are determined at one or more measurement geometries and the reflectance values ​​of the sample coating are determined at the one or more measurement geometries; B2) normalizing each of the reflectance values ​​of the target coating determined at a corresponding one of the one or more measurement geometries and the reflectance values ​​of the sample coating determined at the corresponding one of the one or more measurement geometries by using a nonlinear scaling function; B3) generating a normalized reflectance curve of the target coating based on the normalized reflectance value of the target coating at each wavelength value, and generating a normalized reflectance curve of the sample coating based on the normalized reflectance value of the sample coating at each wavelength value; B4) generating, for the plurality of wavelength values, normalized first derivative values ​​of the normalized reflectivity curve of the target coating with respect to the wavelength and normalized first derivative values ​​of the normalized reflectivity curve of the sample coating with respect to the wavelength; B5) generating, for each wavelength value in the plurality of wavelength values, a difference between the normalized first derivative value of the normalized reflectance curve of the target coating and the normalized first derivative value of the normalized reflectance curve of the sample coating; B6) generating a match metric of similarity between the normalized reflectance curves of the target coating and the sample coating based at least on the difference across all of the plurality of wavelength values; B7) retrieving one or more preliminary matching formulas from a formula database (520) based on the sample colorimetric data; B8) selecting at least one preliminary matching formula from the one or more preliminary matching formulas so as to minimize the matching metric other than other colorimetric metrics; B9) modifying a formula for the sample coating to minimize the match metric in addition to other colorimetric metrics, wherein the modifying is performed by minimizing a cost function comprising a weighted sum of color difference, texture difference, sparkle difference, granularity difference, and the match metric; Wherein, for each wavelength value, the normalized first-order derivative value of the normalized reflectivity curve of the target coating and the normalized first-order derivative value of the normalized reflectivity curve of the sample coating are respectively expressed as two-dimensional vectors according to the following formulas: in as well as as well as Dl i =λ i+1 -l i in, Indicates the target coating at wavelength value λ i The normalized reflectance value at Indicates the target coating at wavelength value λ i+1 The normalized reflectance value at Indicates that the sample coating is at the wavelength value λ i The normalized reflectance value at Indicates that the sample coating is at the wavelength value λ i+1 The normalized reflectivity value at , k1 is the nonlinear damping parameter, where k1 = 0.005, and Indicates two normalized vectors and The angle between the vector Indicates the target coating at λ i The normalized gradient of the reflectivity curve at , and the vector Indicates that the sample coating is at λ i The normalized gradient of the reflectivity curve at .

7. The system according to claim 6, further comprising: C) color measurement equipment (530); D) a formulation database (520) comprising formulas for coating compositions and associated colorimetric data; The computing device (510) is functionally coupled to the color measurement device (530) and the recipe database (520).

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