WO2015167519A1

WO2015167519A1 - Color extrapolation from a first color space to a second color space

Info

Publication number: WO2015167519A1
Application number: PCT/US2014/036130
Authority: WO
Inventors: Nathan Moroney; Ingeborg Tastl
Original assignee: Hewlett-Packard Development Company, L.P.
Priority date: 2014-04-30
Filing date: 2014-04-30
Publication date: 2015-11-05

Abstract

Examples disclosed herein relate to color extrapolation from a first color space to a second color space. In one implementation, a processor extrapolates the color coordinates of a target color in a first color space to a second color space based on a set of colors with known coordinates in the first and second color space, a subset of combinations of the different colors, and aggregated mapping information from the first color space to the second color space. The processor outputs information about the color coordinates of the target color in the second color space.

Description

COLOR EXTRAPOLATION FROM A FIRST COLOR SPACE TO A SECOND COLOR

SPACE

BACKGROUND

Color approximation may be useful for color information about a color with known coordinates in a first color space. For example, in the case where color transformations are defined by a discrete set of color coordinates in a first color space and a corresponding set of color coordinates in a second color space target colors that are outside of the gamut of the color coordinates in the first color space may be extrapolated in order to determine corresponding color coordinates in the second color space.

BRIEF DESCRIPTION OF THE DRAWINGS

[0001] The drawings describe example embodiments. The following detailed description references the drawings, wherein:

[0002] Figure 1 is a block diagram illustrating one example of a computing system to determine color coordinates of a target color based on a color mapping from a fsrst color space to a second color space.

[0003] Figure 2 is a flow chart illustrating one example of a method to deTermine color coordinates of a target color based on a color mapping from a first color space to a second color space.

[0004] Figures 3A and 3B are diagrams illustrating one example of determining color coordinates of a target color based on a color mapping from a first color space to a second color space.

DETAILED DESCRIPTION

[0005] In one implementation, color extrapolation is performed based on colors determined to be similar to a target color. For example, the coordinates of the target color may be known in a first color space, but not in a second color space. A custom mapping from the first color space to a second color space may be created based on the first and second color space coordinates of colors similar to the target color. For example, the set of similar colors may be determined based on a comparison of the first color space coordinates of the target color compared to the first color space coordinates of the colors in the set of colors. Mapping information may be generated based on the similar colors, and the mapping information may be aggregated, such as by determining the median of the mapping information components. The aggregated mapping information may be used to convert the first color space coordinates of the target color to second color space coordinates. Aggregated coior extrapolations are more robust against noise. Furthermore they enable a balancing between an extrapolation that is defined locally versus more globally.

[0006] Color extrapolation may be useful, for example, for mobile applications where a user takes a picture including a color and would like to match the color. In some implementations, a processor may first determine if a target color is considered to be close enough to a particular color in a set of known colors, in cases where the target color is considered to be outside the range of the known colors, information about similar colors within the set of known colors may be used to approximate the target color to create a target coior specific color mapping from the first color space to a second color space. The second color space may be a device independent color space, such as CIELAB such that the mapping is specific to the target color and the particular type of device. A robust tunable extrapolation method may be useful, for example, for transformations of camera or scanner RGB values into device independent values, such as CIELAB values.

[0007] Figure 1 is a block diagram illustrating one example of a computing system to determine color coordinates of a target color based on a colo mapping from a first color space to a second color space. The computing system 100 may be used, for example, to approximate the color coordinates of a target color in a second color space based on the coordinates of the target color in a first color space. The computing system includes a storage device 107, a processor 101 , and machine- readable storage medium 102. In some implementations, the computing system 100 also includes a camera for capturing an image including a target color and color chart form which color coordinates in a first color space are being extracted. The components of the computing system 100 may communicate directly or via a network. In one implementation, the computing system 100 is embodied in a mobile device, such as a mobile phone,

[0008] The processor 101 may retrieve information from the storage device 107. The storage device 107 may be any suitable type of storage, such as a server or storage associated with a user device, The storage 107 may store color information 108. The color information 108 may be a color chart including color patches, a look up table of color information, and/or individual color patch information. The color information 108 may include information about a set of colors and the coordinates of the set of colors in a first color space and a second color space. For example, the first color space may be device R,G,B, and the second color space may be CIELAB. The color spaces may be, for example, scanner RGB values. f

[0009] The processor 101 may be a centred processing unit (CPU), a semiconductor-based microprocessor, or any other device suitable for retrieval and execution of instructions. As an alternative or in addition to fetching, decoding, and executing instructions, the processor 101 may include one or more integrated circuits (iCs) or other electronic circuits that comprise a plurality of electronic components for performing the functionality described below. The functionality described below may be performed by multiple processors.

[0010] The processor 101 may communicate with the machine-readable storage medium 102. The machine-readable storage medium 102 may be any suitable machine readable medium, such as an electronic, magnetic, optical, or other physical storage device that stores executable instructions or other data (e.g., a hard disk drive, random access memory, flash memory, etc.). The machine-readable storage medium 102 may be, for example, a computer readable non-transitory medium. The machine- readable storage medium 102 may include similar color selection instructions 103, color mapping creation instructions 104, color coordinate extrapolation instructions 105, and color coordinate output instructions 106.

[001 1] The similar coior selection instructions 103 include instructions to determine colors in the stored color information 108 similar to the target color in the first color space. The processo 101 may receive or determine color coordinates of the target color in a first color space. In one implementation, the computing system 100 includes a camera for capturing an image inciuding the target color and the coior coordinates in a first coior space, and the processor 101 determines the coordinates of the target color in the first color space based on the image. The processor 101 may then determine colors similar to the target color based on the first color space coordinates of the target color or the first color space coior coordinates stored in the color information 108. The processor 101 may select colors in the color information 108 with a similarity score above a threshold and/or the top most similar colors,

[0012] The color mapping creation instructions 104 include instructions to create a mapping from the first color space to the second color space for the target coior. The mapping may be created by analyzing the first and second color space information associated with the selected similar colors. In one implementation, the mapping is determined by creating a linear inverse of order three polynomials. For example, groups of three colors of the selected similar colors may be selected, The three colors in the group may be used to determine the linear inverse and the associated coefficients for a component of the second color space. A similar process may be performed for each of the components of the second color space. The process may be performed in multiple iterations where new groups of three colors are selected for each iteration. Any suitable number of iterations may be performed, and a selected similar color may be included in multiple groups (ex. appear in multiple iterations). The mapping may be performed using larger groups based on the order of the poiynomial used to generate the coefficients. The resulting mapping information may be aggregated. For example, the median of the mapping information may be determined.

[0013] The color coordinate extrapolation instructions 105 includes instructions to determine the second color space coordinates of the target color based on the custom aggregated mapping information and the first color space coordinates of the target color. For example, an operation may be performed on the first color space coordinates using the coefficients in the mapping information.

[0014] The color coordinate output instructions 106 include instructions to output the color information. For example, the second coior space coordinates of the target color may be stored, transmitted, and/or displayed. I one implementation, the second color space coordinates are used in a second application_s such as to determine colors coordinating with the target color.

[0015] Figure 2 is a flow chart illustrating one example of a method to determine color coordinates of a target coior based on a color mapping from a first coior space to a second color space. A customized color mapping from the first color space to the second color space may be created for a target color with known coordinates in the first color space, and the color mapping may be used to determine the second color space coordinates of the target color. The method may be Implemented, for example, by th processor 101 of Figure 1.

[0018] Beginning at 200, a processor selects a set of colors within color reference data with coordinates in a first and second coior space based on the similarity to a target color in the first color space. For example, the coior space of the target color in the first color space may be determined or retrieved from a storage device. A processor may determine the first color space based on an image including the target color. For example, the processor may be associated with a mobile device that captures an image for the processor to analyze. Based on the image, the processor may determine the coordinates of the target color in the first color space. For example, the processor may determine the R,G,B coordinates of the target coior,

[0017] The reference color data may be, for example, stored color data including color coordinates for a group of colors in both a first and second color space. For example, the R,G,B and CIELAB coordinates of the colors may be stored. The color reference data may include a coior chart. For example, color patches may be associated with their color coordinates i the first and second coior space.

[0016] In one implementation, the processor first checks to determine if the target coior is represented by one of the reference colors. For example, the target color may be determine to be the same as or within a suitable range of one of the reference colors. The comparison may be based on image analysis and/or a comparison of the first colo space coordinates of the reference colors and the target color. If the target coior is associated with one of the reference colors, the second coior space coordinates of the associated reference coior may be output. If the target color is not found to be associated with one of the reference colors, the processor may approximate the target color coordinates in the second color space based on the reference color data.

[0019] The processor may determine a set of simiiar colors within the reference color data. The set of colors may be determined based on a similarity score threshold and/or based on the relative similarity such that the top N most similar colors are selected. The similarity may be determined based on a comparison of the reference color and target color coordinates in the first color space.

[0020] The method is described in conjunction with the examples in Figures 3A and 38. Figure 3A is a diagram illustrating a sample color chart of reference color data and a target color, and Figure 3B is a diagram illustrating one example of determining color coordinates of the target color based on the reference color data. In Figure 3A, color chart 300 includes 5 reference colors and their coordinates in an R_SG₅8 first color space and in a CIELA8 second color space. For example, color 1 has R.G.B, coordinates R1 ,G1 , and B1 and has CIELAB coordinates L1 , A1 , and 81. The target color 301 includes coordinates in the first color space, for example, coordinates R. G, B.

[0021] In Figure 38, at 302, a processor compares the target color to the reference colors in the color chart 300 to determine that coiors 1 , 3, 4, and 5 are closest to the target color in the R,G,B color space. The comparison may be determined in an suitable manner, such as based on the difference in each of the components between the target color and each of the colors in the color chart.

[0022] Referring back to Figure 2 and Proceeding to 201 , a processor creates combinations of the selected colors. Th combinations may be used to create multiple mappings from the first color space to the second color space. For example, the mapping may var based on which set of similar colors are used in a particular combination. The subsets may include any suitable number of coiors in any suitable combinations, and the same color may be included in multiple combinations. For example, the combinations may include triplets of the subset of similar colors, such as a first triplet color 1 , color 2, color 3 and a second triplet color 2, color 3, color 4. The subsets may include any suitable number of colors. The triplets may include sets of coiors to be used to determine mappings from the first coiors space to the second color space,

[0023] In some implementations, a subset of the closest colors is used, for example, selected randomly or selected based on data in addition to the similarity level. The number of color combinations selected may be determined based on whether a global or local solution is desired. For example, using all possible combinations of groupings may provide a more global sample from which to perform the estimation,

[0024] At 303 In Figure 3, a processor selects triplet combinations of the four colors. The selected combinations are colors 1 , 4, 5, colors 1 , 3, 5, and colors 3, 4, 5. For example, the triplet combinations may be selected based groupings of three of the closest colors. The number of triplet combinations may vary. The grouping of three colors may be selected for using incomplete first order polynomials. A polynomial of the order of 1 may contain up to 11 coefficients, and thus, corresponding number of colors are selected. Grouping of a greater number of colors may be used for higher order polynomials.

[0025] Referring back to Figure 2 and Proceeding to 202, a processor determines mapping information between the first color space to the second color space based on the combinations of the first color space and second color space coordinates of the colors within the combinations. The manner of determining the mapping information may depend on the number of colors in the groupings. For example, inverse linear polynomials may be used to create the mapping information, and the order of the polynomials may be based on the number of colors in the subsets. The processor may determine mapping coefficients from each of the inverse linear polynomials of each of the color groups,

[0026] In Figure 3 at 304, a processor performs the linear inverse to determine the L, A, B coefficients for each of the triplet combinations. A linear inverse may be determined for each of the L, A, and B values. As an example, the first order polynomials for each triplet combination may be determined as follows for the L value for color 1 , color 4, and color 5:

[0027] L1 = (R1x1 ) + (G1y1 ) + (B1 1 )

[0028] 14 = (R4x1 } + (G4y1 ) + (B4z1 ) [0029] L5 = (R5x1) + (G5y1 ) + (B5z1)

0030J The inverse of the polynomials may then be determined as the following for solving for values x1 , y 1 , and z1 :

-(81G4LS)+(GlB+tS)+Btl4<&-LtGS~GllABS+LX>G*BS

[0031] x1 - [0032] Y1 ~

GlB4L5~RW4l$ --Gll4R$ +llG4R$ + till4G$-~UFi4G5

[0033] Z1

-~i.SlG4«S)+GlB4RS+eii54C5~fl1.84ffS~ei«4SS -iflC48^'S

[0034] The coefficients x1 , y1 , zl may be stored, and the same process may be performed on the other triplet groups, such as on the combination of colors 1. 3. and 5, and the colors 3, 4, and 5. For example, the values x1i, yis, and z1, where i is the number related to the subset i, may be determined based on the inverse of the polynomials for colors 1 , 3, and 5, and the values XI 3, y _f and ZI 3 may be determined based on the polynomials for colors 3, 4, and 5,

[0035] Referring back to Figure 2 and proceeding to 203, a processor aggregates the mapping information. The mapping information may vary according to the subset of similar colors used to create the mapping, and the processor may aggregate the varying mapping information to converge on a single mapping from the first color space to the second color space for the target coior. The aggregatio may include any suitable method for aggregating the coefficients. In one implementation, the aggregated mapping information includes the median, mean, or other value for each of the coefficient values. For example, the median value may be selected from a different color triplet combination for each coefficient value. In one implementation, the mapping information is aggregated for each coordinate of the second color space. For example, there may be multiple coefficients for each coordinate of the second coior space, and the median of each of the coefficients of each of the second color space coordinates may be determined.

[0036] in Figure 3 at 305, the median coefficient values are determined for the L value. The same process may be repeated for the coefficients for the a^* and b^* values. Block 305 shows a set of coefficients on each row where each row is associated with the output based on a different set of color triplets. There are x, y_« and z. coefficients for each color sets, and the median of each of the x_:. y;, and Z;

B coefficients are determined independently. Other aggregation methods, such as the mean of the values, may also be used.

[0037] Referring back to Figure 2 and proceeding to 204, a processor exirapofates second color space coordinates of the target color based on the first color space of the target color and the aggregated mapping information. For example, there may be multiple coefficients associated with each of the second colors space coordinates. The coefficients may foe used to transform the first color space coordinates to the second color space coordinates, such as based on a multiplication operation.

[0038] In Figure 3 at 306, the LAB coordinates of the target color R. G, B are determined based on the R,G,B coordinates of the target color and the median values of the coefficients. Block 306 shows a median matrix where x1 , y1 , z1 correspond to the L coefficients 2.8, 3.6, 4.8 determined at block 305. The coefficients x2, y2, and z2 correspond to the median coefficients determined for the color sets for the a^* component, and the coefficients x3, y3, z3 correspond to the median coefficients determined for the color sets for the b* component.

[0039] Some implementations may involve more than three colors in the color groupings. Using different numbers of colors in the combinations ma allow for a larger order polynomial. A larger order polynomial generating more coefficients could be used. The additional coefficients could then be used to determine the LAB values of the target color. For example, the matrix could be Nx3 based where N is based on the order of the polynomial.

[0040] Referring back to Figure 2 and proceeding to 205, a processor outputs the second color space coordinates of the target color. The processor may display, transmit, or store the second color space coordinate information. Estimating color coordinates in a second coior space of a target color may be useful where a target color is not in the gamut of known colors. For example, the extrapolation method may useful for scanners with a range book or colors outside the range of a standardized swatch book. The color coordinate information that is output may be further processed, such as to create or match a color.

Claims

1 , A computing system, comprising;

a storage to store color information related to first color space coordinates and second color space coordinates for a set of colors; and

a processor to;

extrapolate second color space coordinates of a target color with known first color space coordinates, including:

selecting colors stored co!or information based on similarity to the target color;

creating aggregated mapping information from the first color space to the second color space based on combinations of the selected colors; and

performing the approximation of the target color second color space coordinates based on the target color first color space coordinates and the aggregated mapping information; and output the target color second color space coordinates,

2, The computing system of claim 1 , wherein the mapping information comprises determining coefficients from a linear polynomial inverse of the first color space coordinate components to a second color space coordinate component.

3, The computing system of claim 2, wherein creating the mapping information

comprises; creating a matrix including three coefficients for each of the components of the coordinates in the second color space.

4, The computing system of claim 3, creating aggregated the mapping information comprises selecting the median coefficient value for each color space coordinate component.

5, The computing system of claim 1 , wherein the first color space is a device

independent and wherein the second color space is a device independent color space.

6. The computing system of claim 1 , wherein creating the aggregated mapping information comprises creating aggregated mapping information robust against noise.

7. The computing system of claim 1 , further comprising a camera to capture an image of the target color and wherein the processorfurther determines the first color space coordinates of the target color based on the image and wherein the processor extracts the coior coordinates of the first color space for a color chart that has been captured together with the image

8. A method, comprising:

selecting, by a processor, a set of colors within coior reference data with coordinates In a first and second color space based on the similarity to a target color in the first coior space;

creating combinations of the selected colors;

determining mapping information between the first color space to the second color space based on the combinations and the first color space and second color space coordinates of the colors within the combinations;

aggregating the mapping information;

extrapolating second color space coordinates of the target color based on the first coior space of the target color and the aggregated mapping information; and outputting the second color space coordinates of the target color.

9. The method of claim 8, wherein determining the mapping comprises determining the linea polynomials and their inverses for the sample colors,

10. The method of claim 8, wherei determining mapping information based o the combinations comprises:

selecting a subset of the combinations; and

determining mapping information based on the selected subset.

11. The method of claim 8, wherein the aggregated mapping information comprises a 3x3 matrix with an x, y, and z coefficient for each of three color coordinates of the first color space; and wherein determining the second color space coordinates comprises determining a dot product between the 3x3 matrix and a 3 x1 matrix of the values of the three coordinates of the target color in the first color space.

12. A computer readable non-transitory storage medium comprising instructions executable by a processor to:

extrapolate the color coordinates of a target color in a first color space to a second device specific color space based on a set of colors with known coordinates in the first and second color space, a subset of combinations of the different colors, and aggregated mapping information from the first color space to the second color space; and

output information about the color coordinates of the target color in the second color space,

13. The machine-readable non-transitory storage medium of claim 12, wherein the aggregated mapping information comprises a 3x3 matrix with 3 coefficient values for each first color space coordinates.

14. The machine-readable non-transitory storage medium of claim 12, wherein the aggregated mapping information comprises median data of the individual color component mappings.

15. The machine-readable non-transitory storage medium of claim 12, further

comprising instructions to select the set of colors based on the similarity between the first color space coordinates of the colors in the set of colors to the first color space coordinates to the target color,