Abstract:
A method for generating the characteristics of a set of colors involves selecting at least two, and typically more reference colors. Each of the selected reference colors is described by a set of color characteristic data indicating the reflectance of each color at each of a set of predetermined wavelengths; and descriptions of the intermediate color samples are generated by computer the relative proportions of each base color which characterizes each intermediate color and calculating a reflectance value at each wavelength for the color to be generated proportionate to the reflectance values for each base color at the corresponding wavelength. A set of color samples is created as a result of the method for generating the characteristics of the colors and arranged in a geometry indicative of the method. A system for generating the color samples data has storage for storing the photometric characteristics and other data; a central processor under software control for accessing the stored data, computing the relative proportion of each reference color comprising each color to be generated, and computing the reflectances at each wavelength for which color reflectance data is stored for each intermediate color; and an output for outputting the data generated by the central processor.

Description:
This is a continuation of application Ser. No. 07/175,519, filed Mar. 31, 1988 now abandoned. 
    
    
     FIELD OF THE INVENTION 
     This invention relates to color description and notation systems, in particular a system which describes and notates a set of colors whose characteristics are derived from weighting the characteristics of a set of reference colors. 
     BACKGROUND 
     The appearance of a colored object is affected by three primary factors: the photometric characteristics of the light source which illuminates the color, the photometric characteristics of the colored object, and the perception of these characteristics by an observer. Additional factors such as texture, gloss, etc. may affect how a color is perceived by an observer, but have varying affects on the spectrophotometric characteristics of that color. 
     Colorimetric systems have been developed in an effort to objectively describe how colors are perceived by observers. The International Commission on Illumination (CIE) has, for example, developed a system for objective description of color by light source, object, and observer. The CIE developed a standardization of the illuminant and observer data. The color of the object under these standard conditions is identified by tristimulus values X,Y and Z. Each XYZ value is obtained by multiplying the reflectance of the colored sample, the power of the standard illuminant, and the calculated amount of each of the three primary colors (red, green, and blue) which, when combined, are found through observational tests to be the color equivalent of the object being described. 
     The tristimulus values X,Y, and Z are of somewhat limited value as color specifications because 
     they do not correlate well to visual attributes. As a result, the CIE adopted the use of chromaticity coordinates x, y, and z which are the amounts of each tristimulus value divided by the sum of all three. 
     The CIE chromaticity calculations have been further transformed by the use of the L *  a *  b transformation. The L *  a *  b system identifies color by lightness or darkness as its L *  value. The saturation, or amount of dullness or brightness (deviation from gray) a color has, as well as hue, or what is commonly called color (blue, green, etc.), are both identified using +a, +b values. The L * , a * , and b values may be used as coordinates to lay out the color system in a three-dimensional space. Typically, the L *  value is shown in the vertical z-direction. The +a * , +b values are set in the XY plane. Plus a is red, -a *  is green, +b is yellow, and -b is blue. L *  =0 is black, and L *  =100 is white. Between these extremes of each value, all colors can be identified. See FIG. 1. 
     In addition to the above-described color description systems, a number of other color order systems are commercially used to identify color samples and for other purposes. Among the most popular is the Munsell system. The Munsell system has a lightness value essentially corresponding to the L *  value of the L *  a *  b system. Unlike the L *  a *  b system, hue and saturation are defined by a letter-number system corresponding to the hue and chroma characteristics of the color. 
     It would be desirable for a commercial color sample system to have several characteristics. Among them are that the system have representations and be layed out in a geometry which is generally consistent with the typical user&#39;s intuitions as to the components and relationships of the represented colors. Moreover, a system adapted to the L *  a *  b system would have advantages including ease of transformation between systems and ease of access in processing data available through the L *  a *  b system. 
     Colors subject to metamerism may have other types of characteristics which are identical. A system which only identifies colors as similar when there is no metamerism between the colors is desirable. A color sample system would be desirable that simplifies matching efforts between a sample color and a color to be manufactured from a given set of colorants identifying the color sample in a manner readily processible by a system which determines how to mix the available colorants. Ideally, such matching could be accurately achieved even for sample colors not identified in the system through an objective description of the color based on identified sample colors. 
     SUMMARY OF THE INVENTION 
     An objective color notation system is described including methods for generating the color sample characteristics of each color in the system, a processing system adapted to the methods, and a color system including samples derived by such a method. 
     A method for generating the characteristics of a set of colors in accordance with the present invention comprises the steps of selecting at least two, and typically more reference colors; describing each of the selected reference colors by a set of color characteristic data indicating the reflectance of each color at each of a set of predetermined wavelengths; and generating descriptions of the intermediate color samples by computing the relative proportions of each base color which characterizes each intermediate color and calculating a reflectance value at each wavelength for the color to be generated proportionate to the reflectance values for each base color at the corresponding wavelength. Also described is a set of color samples created as a result of the method for characteristics of the colors and arranged geometry indicative of the method. 
     A system for generating the color sample data in accordance with the present invention is described which comprises storage means for storing the photometric characteristics and other data; a central processing means under software control for accessing the stored data, computing the relative proportion of each reference color comprising each color to be generated, and computing the reflectances at each wavelength for which color reflectance data is stored for each intermediate color; and output means for outputting the data generated by the central processing means. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a graph representing the three-dimensional L *  a *  b color characteristics chart. 
     FIG. 2 is a graph representing a two-dimensional portion of the L *  a *  b chart with L *  held constant. 
     FIG. 3. is a block diagram of a processing system in accordance with the present invention. 
     FIG. 4 is a drawing depicting a portion of a color chart generated in accordance with the present invention. 
     FIGS. 5A and 5B comprise a flow chart depicting the processing of color characteristic data in accordance with the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The creation of a color system in accordance with the present invention is described herein, by way of example, through a two-dimensional plane in the L *  a *  b *  system wherein L *  is held constant. However, the principles described are adaptable to other systems and geometries, as will be clear. 
     FIG. 2 shows a grid in the L *  a *  b *  geometry where L is a constant. The +a direction equates to a specific red (R), the -a direction to a specific green (g), the +b *  direction to a specific yellow (y), and the -b *  direction to a specific blue (B). Inbetween the +a and +b *  axes are middle coordinates corresponding to the mixed colors orange (o), yellow-green (yg) blue-green (Bg), and purple (p). Along a line extending from the center of the map outward in any direction, the amount of saturation or grayness (white-black or wb) decreases. Thus, the amount of grayness is constant along the vectors (labeled wb in FIG. 2) perpendicular to lines extending from the center of the map. FIG. 2 also shows vectors for the various reference colors, labeled with the abbreviation for the pertinent reference color, which show lines along which the labeled color has a constant L *  value and a constant proportion of the labeled color. For example, the line labeled R in the triangle formed by the points W/B&#39;, O, and R in FIG. 2 represents a line along which all represented colors have a proportion of the chosen Red color equal to 40%. 
     To generate the spectrophotometric and other characteristics of a set of color samples represented by a portion of the map shown in FIG. 2, a set of reference points are selected. For example, a quadrilateral-shaped region on the map shown in FIG. 1 may be created with four reference points. An example region described herein is bound by the points labeled 1, 2, 3, and 4, corresponding to the reference colors red, purple, blue, and gray. More or fewer reference points may be used to define the boundaries of the region represented by the map wherein color sample characteristics are to be generated. The reference points used may represent the reference colors represented by the abbreviations shown in FIG. 2, or by reference points which include combinations of the colors represented by these abbreviations. 
     The reference colors 1, 2, 3, and 4 are defined by their spectrophotometric characteristics. These characteristics are represented by numerical data representing the reflectance of each reference color at each of a selected group of wavelengths. Each reference color may also be characterized by tristimulus values and L *  a *  b *  values. Other characteristic data may also describe the reference colors. Such data may be derived by evaluating a color sample matching the reference color. Alternatively, the reference color data may be obtained from sources of data representing the desired reference colors, and may or may not be based on an actual color sample. 
     With the data describing the color characteristics of each of the selected reference colors, the generation of data describing the color characteristics of a selected number of color samples is accomplished by processing the characteristics of the reference colors. A representative process and processing unit are described herein. As will be clear from the disclosure, systems equivalent to the present system may utilize a different sequence of steps in a different manner, yet reach the same result. 
     FIG. 4 shows a set of data generated between two reference colors: a color equivalent to one hundred percent of a specific red (designated RP0), and a color equivalent to one hundred percent of a specific purple (designated RP7). These two reference colors have no components of other hues, nor of gray. However, reference colors may be chosen having components of multiple colors. The data for these two reference colors serves as the starting point from which the data may be generated for the intermediate colors, designated RP1, RP2, . . . RP6. The locations of each of these colors is shown in FIG. 2 along a straight line extending from reference point 1 to reference point 2. 
     To generate the characteristics of the intermediate colors, the only initial data needed are the reflectance values for the reference colors (accessed at 120 in the flowchart shown in FIG. 5A), characteristics of the reference points RP0 and RP7 and the number of intermediate color samples to be characterized (accessed at 110 in FIG. 5A). In FIG. 4, by way of example, the number of intermediate colors chosen is 6. 
     The intermediate color characteristics are generated such that each of the samples has proportions of the reference colors RP0 and RP7 representative of the intermediate color sample&#39;s relative location between the reference points, or, equivalently, representative of the RP number 1-6 of the intermediate color. In FIG. 3, the proportion of red is shown as decreasing by a decimal representation of 1/7 (approximately 14.28%) for each successive sample, with the proportion of purple increasing by an amount equal to the amount of the decrease of the intermediate color&#39;s proportion of the red reference color. These calculations are made at step 130 of FIG. 5A. The proportions of each color RP0-RP7 are shown directly below the reference color proportions portion of Table A. 
     For samples located closer to the center of the map shown in FIG. 2, the reference and intermediate color samples will also have proportions of gray. Other intermediate color samples will have other combinations of reference colors. In all cases, the proportions of all reference colors which comprise an intermediate color (or a reference color) will add to 100%. The data shown in FIG. 3 and Table A is a rounded-off representation of the proportion and reflectance data actually used by the system, which may be carried to several decimal places for greater accuracy. 
     Among the characteristics generated are the spectrophotometric characteristics of each intermediate color sample. The spectrophotometric data is generated at each wavelength for which there is a reflectance value for the reference colors. The reflectance value for each intermediate color sample is derived by weighting the reflectance values for each reference color at the same wavelength. 
     For example, as shown in part in FIG. 3 (at the reference color stored data means 20) and more fully in Table A, at 400 nanometers the RP0 reflectance is 35.25 units and the RP7 reflectance is 67.24 units. The difference between these numbers, 31.99, is divided by 7 to derive the 4.57 unit difference in the 400 nanometer reflectance for each sample RP0-RP7. This difference is shown by the successive reflectance values for each color sample at the 400 nanometer wavelength. 
     Similar results are achieved by weighting the reference color reflectances at the 400 nanometer wavelength according to the relative proportions of those reference colors represented by each respective intermediate color. Thus, RP1&#39;s reflectance (comprised of 86% RP0 and 14% RP1, approximately) at 400 nanometers is approximately equal to the sum of 86%×35.25 and 14%×67.24, or 39.82, units. 
     The above process may be used to generate the reflectance value for each wavelength for which data exists for the reference colors. The process is shown at step 140 in FIG. 5A. The process is also repeated for each intermediate color RP1-RP6. 
     A similar process of calculating data may be used to generate tristimulus (XYZ) values. As for the reflectance values at each wavelength, the XYZ values are weighted in accordance with the reference color XYZ values. This process is shown by steps 150 and 160 in FIGS. 5A and 5B. However, the L *  a *  b *  characteristics are not generated in this manner. Instead, they are derived from the photometric or XYZ characteristics of each intermediate color, using transformations or other stored information. The process is indicated by step 170 in FIG. 5B. Thus, the described process generates color sample data in the L *  a *  b *  geometry which is proportionate to the more objective color description of photometric or tristimulus characteristics, yet readily describes each sample&#39;s L *  a *  b *  values. Although other transformations or color characteristic data are not described herein, it is clear from the description that, through stored transformations or other data, other characteristics of colors (e.g. Munsell notations) may also be generated. 
     The characteristics of intermediate color samples may be generated between reference colors and previously-generated intermediate color sample characteristics or between two intermediate color samples. Such additional color sample characteristics are generated using the above-described process or its equivalent, using the color samples between which the sample to be generated would be located on the map shown in FIG. 2. Thus, an unlimited set of color sample characteristics can be generated from a limited set of reference color characteristics data. 
     With the above-described notation system, colors not represented in the generated data can be accurately and easily described. For example, based on the data shown in FIG. 4 and Table A, a color may be designated as RP2.4. The spectrophotometric, XYZ, L *  a *  b * , and any other desired characteristics of such a 5 designated color may be readily generated by a processing system similar to a processing system which would generate the intermediate color characteristics as described above. The RP2.4 description indicates a weighting of 60% RP2 and 40% RP3. The photometric and tristimulus characteristics of the RP2.4 sample may be generated in accordance with this weighting. Other characteristics, such as L *  a *  b *  characteristics, may also be derived by transformations or similar methods. Thus, even colors not expressly described by the set of reference and intermediate color sample characteristics can be intuitively described by the user in an accurate manner without an actual color sample or previously-generated characteristics data corresponding to the selection. 
     The color sample processing and generating system and method described herein is also readily adaptable to accurate color matching. Colors can be accurately matched in a number of ways. For example, use of reference colors corresponding to the colors available for mixing to generate intermediate color samples will enable a close match of a selected color. RP2, for example, may be achieved by mixing about 71% of the red reference color with about 29% of the purple reference color. In this manner, even hybrid colors, which may be selected by a user and not shown by the color notation system or samples generated thereby, e.g. a sample designated RP2.4 based on the data shown in FIG. 3, can be matched in an equally accurate manner. Thus, an infinite number of colors can be accurately described and matched from a limited number of reference colors. 
     The above-described process may be performed 5 using a system such as that shown in FIG. 3. The color characteristics of the reference colors are stored in data storage means 20 by way of random access memory or the like. The number of samples to be generated is input into the system by input/output means 28, for example a video terminal having a keyboard. This input is stored in storage means, which may also be random access memory such as storage means 20, but are shown separately as storage means 22 for clarity. The central processing unit (CPU) 24 is under the control of software 80 shown stored in storage means 20 or, alternatively, in CPU 24. Software 80 represents the control instructions for executing the instructions indicated in the flowcharts shown in FIGS. 5A and 5B. The CPU may process the stored data to generate the characteristics of each intermediate color, which is shown as stored at storage location 58 for example. 
     The steps performed by the software-controlled processing means used to generate color samples in accordance with the present invention are shown at their most basic level in the flowcharts shown in FIGS. 5A and 5B. The system starts by accessing the selected number of reference colors to be used to generate the intermediate colors, designated by the symbol f. This number will typically be 4 for a quadrilateral-shaped color chart. The system also accesses the number indicating the number of samples to be generated by the system, designated by the letter s. Finally, the system accesses the number of wavelength increments for which there is stored data for the reference colors, indicated by the letter v. This accessing step is indicated by step 110 of the flowchart. 
     The system also accesses the reflectance data for each reference color. Each piece of data stored in the storage means may be designated as shown by the designation R C .sbsb.N w G . This symbol indicates a reflectance value for reference color C N  at wavelength W G . Thus, a complete set of this data will include integer values for N of between 1 and f, and for G between 1 and v, as shown at step 120. 
     Also shown, at step 130, is the step of generating the relative proportions of each reference color which comprise a given sample to be generated. These values are stored in a matrix with each value represented by the symbol P C .sbsb.N K G . This designation represents the proportion of reference color C N  for color sample K G  to be generated. Thus, the P values will be generated for integer values of N ranging from 1 to f and for values of G ranging from 1 to s. 
     The accessed reflectance data and generated reference color proportion data is utilized at step 140 to generate the reflectance values at each wavelength for each color sample to be generated. As stated above, the reflectance value at a particular wavelength for a particular color to be generated will equal the sum of the products of the relative proportions of each reference color and the reflectance value for that reference color. This summation process is described by the equation shown in step 140. 
     The tristimulus, or XYZ values, may be generated in a similar manner. Step 150 shows the accessing of the tristimulus data for the reference colors. X C .sbsb.n, Y C .sbsb.n and Z C .sbsb.N represent the X, Y and Z values, respectively of reference color CN. 
     The XYZ values for each color to be generated, as for the reflectance values, is defined by the summation of a product of the characteristic values for each reference color and the relative proportion of the reference color which comprises the color to be generated. These summations for each characteristic, X, Y, and Z, are shown in the equations described in step 160. 
     Finally, the L *  a *  b *  values for each color to be generated may be calculated based on the XYZ values. As indicated in step 170, the L *  value for a given color sample to be generated, KQ, is a function of the Y-value of that generated color sample. The a *  value of that color sample is a function of the X and Y values of that color sample, and the b *  value is a function of the Y and Z values of that color sample. 
     TABLE A is an example of a set of data generated in accordance with the present invention. The four reference colors red, purple, gray, and blue are listed across the top of the chart with their corresponding percentages. Based on these percentages and the stored data for the reference colors, characteristics for each intermediate color are generated. 
     
                                           TABLE A__________________________________________________________________________ADDITIVE REFLECTANCE DATA AND L*a*b CALCULATIONSREFERENCE COLOR PROPORTIONS__________________________________________________________________________    100%        RED   86%                 RED   71%                          RED   57% RED    0%  PURPLE              14%                 PURPLE                       29%                          PURPLE                                43% PURPLE    0%  GRAY  0% GRAY  0% GRAY  0%  GRAY    0%  BLUE  0% BLUE  0% BLUE  0%  BLUESAMPLE CODE  RP0      RP1      RP2       RP3WAVELENGTH(nm)    REFLECTANCES400      35.25     39.82    44.39    48.96420      51.92     56.66    61.41    66.15440      45.70     51.48    57.27    63.04460      28.90     35.66    42.43    49.19480      11.98     18.27    24.55    30.84500       5.89     10.45    15.00    19.56520       9.13     11.58    14.04    16.49540      13.37     13.69    14.01    14.33560      25.17     23.79    22.41    21.03580      52.46     49.62    46.79    43.95600      76.14     72.53    68.93    65.32620      85.67     81.92    78.16    74.41640      90.11     86.53    82.95    79.37660      92.11     88.66    85.22    81.77680      90.74     87.13    83.53    79.93700      89.41     85.66    81.91    78.16X        51.95     51.04    50.13    49.22Y        34.05     34.05    34.05    34.05Z        36.56     42.93    49.29    55.66L*       65.00     65.00    65.00    65.00a*       59.98     57.57    55.14    52.67b         0.00     -7.67    -14.62   - 21.00__________________________________________________________________________    43% RED   29%                 RED   14%                          RED   0%  RED    57% PURPLE              71%                 PURPLE                       86%                          PURPLE                                100%                                    PURPLE    0%  GRAY  0% GRAY  0% GRAY  0%  GRAY    0%  GRAY  0% GRAY  0% BLUE  0%  BLUESAMPLE CODE  RP4      RP5      RP6       RP7WAVELENGTH(nm)     REFLECTANCES400      53.53     58.10    62.67    67.24420      70.90     75.64    80.38    85.13440      68.83     74.61    80.40    86.18460      55.96     62.72    69.49    76.25480      37.13     43.41    49.70    55.99500      24.12     28.68    33.23    26.30520      18.94     21.39    23.85    37.79540      14.64     14.96    15.28    15.60560      19.64     18.26    16.88    15.50580      41.11     38.27    35.44    32.60600      61.72     58.11    54.51    50.90620      70.65     66.90    63.14    59.39640      75.79     72.21    68.64    65.06660      78.32     74.87    71.43    67.98680      76.32     72.71    69.11    65.51700      74.42     70.67    66.92    63.17X        48.30     47.39    46.48    45.57Y        34.05     34.05    34.05    34.05Z        62.03     68.40    74.76    81.13L*       65.00     65.00    65.00    65.00a*       50.18     47.65    45.09    42.49b        -26.91    -32.42   -37.60   -42.50__________________________________________________________________________ 
    
     Color sample identifiers or codes may also be generated by the processing unit as shown at storage locations 50, 52, 54, and 56, shown in FIG. 3. The generated data may be outputted at the with the input means. The generated data may also be stored in storage means 26. 
     The system is best utilized with an actual color chart having samples created as a result of the characteristic data generated and having sample identifiers or codes representative of the proportion of the reference colors used to generate the samples. FIG. 4 shows a representative portion of a color chart 30 set in the L *  a *  b *  geometry, L *  =constant, having color samples generated from the data shown in FIG. 3 corresponding to the RP0, RP1 . . . , RP7 identification system (32, 34, 36, 38, 40, 42, 44 and 46, respectively). With color samples having equal areas as is typical, the location of each sample on the color chart may not exactly correspond to the equivalent relation between the color sample and the center axis of the L *  a *  b *  plane as shown. However, the sample will be accurately positioned relative to all other samples. 
     Moreover, even when the color samples are not available for matching or have faded or are otherwise no longer accurate representations of the colors, the system enables matching which minimizes metamerism. Every color sample identifiable by the system is readily describable by its spectrophotometric characteristics. Computer or other processing of the spectrophotometric characteristics of the colors available for mixing may ensure a close match between the desired and actual spectrophotometric characteristics which will minimize metamerism. 
     The system may generate color samples readily identifiable in the L *  a *  b *  system, and thus can accurately present colors to users in the L *  a *  b *  geometry. Other advantages of the system should be clear from the description.