Methods and systems for sampling and modeling of colorant-limited, multi-colorant color spaces

• US 8,358,441 B2
• Filed: 04/01/2009
• Issued: 01/22/2013
• Est. Priority Date: 04/01/2009
• Status: Active Grant

• Current Assignee: Sharp Kabushiki Kaisha (Hon Hai Precision Industry Co., Ltd.)
• Original Assignee: Sharp Laboratories of America Incorporated (Hon Hai Precision Industry Co., Ltd.)
• Inventors: Chang, James Zhixin, Watanabe, Chizu
• Primary Examiner(s): Lee, Thomas D
• Assistant Examiner(s): Brinich, Stephen M
• Application Number:
  US12/416,590
• Publication Number:
  US 20100253698A1
• Time in Patent Office: 1,392 Days
• Field of Search: 358/1.9, 358/2.1, 358/500, 358/504, 358/1.16, 358515-523, 358/527, 358/530
• US Class Current: 358/2.1
• CPC Class Codes: H04N 1/6016 Conversion to subtractive colour signals
• CPC Class Codes: H04N 1/6033 using test pattern analysis H04N1/6055 takes precedence
• CPC Class Codes: H04N 1/6097 depending on the characteristics of the output medium, e.g. glossy paper, matt paper, transparency or fabrics

Abstract

Aspects of the present invention relate to methods and systems for determining output responses and device targets for multi-colorant output devices. Some aspects relate to methods and systems for multi-dimensional rectilinear sampling, transformation of samples from an unlimited colorant space to a colorant-limited space, obtaining additional samples within a colorant-limitation hyperplane and interpolation of values in a colorant-limited space.

Claims

1. A method for modeling a colorant-limited, multi-dimensional colorant space, said method comprising:

a) representing a full-colorant space as a multi-dimensional full-colorant hyper cube without colorant limitations;

b) sampling said full-colorant color space using a rectilinear sampling scheme, thereby producing rectilinear sample points;

c) representing a colorant-limited colorant space with a multi-dimensional hyper cube limited by a colorant-limitation hyperplane;

d) transforming said rectilinear sample points, using a bijective mapping process, to said colorant-limited colorant space, thereby producing transformed rectilinear sample points;

e) tessellating said rectilinear sample points into full-colorant-color space simplexes;

f) obtaining intersection sample points located at the intersection of the edges of said full-colorant-color-space simplexes and the intersection lines between the colorant limitation hyper-plane and said full colorant hypercube; and

g) using said transformed rectilinear sample points and said intersection sample points to model a device color gamut of the colorant-limited colorant space, by generating color patches on an output device and measuring said color patches with a measuring device.

2. A method as described in claim 1 wherein said using said transformed rectilinear sample points and said intersection sample points to model a colorant-limited device color gamut comprises printing color patches of said sample points to create a device characterization target image.

3. A method as described in claim 2 further comprising measuring said color patches with a color measuring device to determine color output values for said color patches.

4. A method as described in claim 3 further comprising correlating said color output values with the coordinates of their corresponding transformed rectilinear sample points and intersection sample points.

5. A method as described in claim 4 further comprising:

a) receiving an input color defined by an input color coordinate in said colorant-limited colorant space;

b) determining a color output value corresponding to said input color coordinate by interpolating between said transformed rectilinear sample points and intersection sample points.

6. A method as described in claim 1 wherein said bijective mapping process comprises identifying a point in said multi-dimensional hypercube limited by a colorant-limitation hyperplane, wherein said point defines a region into which points outside said colorant-limitation hyperplane are mapped.

7. A method as described in claim 1 further comprising:

a) transforming said full-colorant-space simplexes into transformed simplexes for said transformed rectilinear sample points;

b) tessellating said intersection sample points on top of said transformed simplexes to form intersection point simplexes for a complete tessellation of said transformed rectilinear and intersection sample points;

c) receiving an input color defined by an input color coordinate in said colorant-limited colorant space;

d) inverse transforming said colorant-limited input color coordinate using an inverse bijective mapping process that is the inverse of said bijective mapping process to obtain full-colorant-space input coordinate;

e) determining an input color simplex from among said full-colorant-space simplexes, wherein said input color simplex contains said full-colorant-space input coordinate;

f) finding a transformed input color simplex from among said transformed simplexes, wherein said transformed input color simplex corresponds to said input color simplex;

g) determining whether said colorant-limited input color coordinate is contained in said transformed input color simplex;

h) if said colorant-limited input color coordinate is not found in said transformed input color simplex, searching a neighborhood of simplexes among said complete tessellation of said transformed rectilinear and intersection sample points in the vicinity of said transformed input color simplex to locate a simplex containing said colorant-limited input color coordinate; and

i) interpolating a color output value by using simplicial interpolation between the vertices of said simplex containing said colorant-limited input color coordinate.

8. A method for modeling a colorant-limited, 4-colorant space using multiple interpolation methods, said method comprising:

a) establishing a total colorant limit, L₄;

b) representing a full colorant space as a 4-dimensional hypercube without colorant limitations;

c) partitioning a 4-D rectilinear sampling target in said full colorant space according to a fourth dimension, such that said partitioning results in multiple sets of first, second and third dimension rectilinear samples within 3-D full colorant cubes, wherein each of said 3-D full colorant cubes has a fixed fourth dimension value, D4, and wherein said fixed fourth dimension values are scaled to extend between 0 and L₄ if said total colorant limit, L₄, is less than 100% of the maximum amount of a single colorant;

d) producing a plurality of 3-D rectilinear sampling targets with fixed fourth dimension values, D4;

e) calculating 3-D colorant limits, L₃, for each of said fourth dimension values, D4, in said 3-D rectilinear sampling targets, wherein L₃=L₄−

D4;

f) for each of said fourth dimension values, D4, representing a 3-D colorant-limited colorant space with one of said 3-D full colorant cubes limited by a colorant-limitation plane, which is at least partially defined by a corresponding one of said 3-D colorant limits, L₃;

g) for each fourth dimension value, D4, transforming said 3-D full colorant cube samples, using a bijective mapping process, to said colorant-limited colorant space, thereby producing transformed 3-D colorant-limited cube sample points;

h) for each fourth dimension value, D4, tessellating said 3-D full colorant cube samples into full-colorant-space simplexes having full-colorant space simplex lines between simplex vertices;

i) for each fourth dimension value, D4, obtaining intersection sample points located at the intersections of said full-colorant space simplex lines, on the surfaces of said full colorant space cube, and said 3-D colorant-limitation plane; and

j) for each fourth dimension value, D4, using said colorant-limited cube sample points and said intersection sample points to model a device color gamut, in a 3-D colorant-limited colorant space, of a virtual 3-colorant device with said fixed fourth dimension value, D4, by generating color patches on an output device and measuring said color patches with a measuring device.

9. A method as described in claim 8 further comprising adding a first designated sample point at the value (100%, 100%, 100%, L₄−

300%) when said total colorant limit, L₄, is between 300% and 400% of a maximum value for a single colorant.

10. A method as described in claim 8 further comprising adding a second designated sample point at the value (0, 0, 0, L₄) when said total colorant limit, L₄, is less than 100% of a maximum value for a single colorant.

11. A method as described in claim 8 wherein said using said 3-D colorant-limited cube sample points and said intersection sample points to model a device color gamut further comprises, for all the fourth-dimension values, modeling a 4-D colorant-limited device color gamut, wherein said modeling comprises printing 4-colorant color patches of said 3-D colorant-limited cube sample points and said intersection points for a plurality of said fixed fourth dimension values to create a device characterization target image.

12. A method as described in claim 11 further comprising measuring said color patches with a color measuring device to determine color output values for said color patches.

13. A method as described in claim 12 further comprising correlating said color output values with the coordinates of their corresponding 3-D colorant-limited cube sample points and said intersection sample points with fixed fourth dimension values, D4, for all the fourth dimension values.

14. A method as described in claim 13 further comprising using the result of said correlating to interpolate a color output value for an input color value in said colorant-limited colorant space.

15. A method as described in claim 14 further comprising:

a) receiving an input color defined by an input color coordinate in said colorant-limited colorant space, wherein said input color coordinate is represented by (C, M, Y, K), wherein K is a value in said fourth dimension;

b) obtaining neighboring values, K1 and K2, on either side of K, wherein said neighboring values were established in said partitioning and K1<

=K<

=K2;

c) obtaining a 3-D CMY colorant limit for K2 using the expression;

L₃ (K2)=L₄−

K2;

d) if C+M+Y<

=L₃ (K2), assign K3=K2;

e) if C+M+Y>

L₃ (K2), assign K3=L₄−

C−

M−

Y;

f) determining color output values for neighboring colors described by the coordinates (C,M,Y,K1) and (C,M,Y,K3) using interpolation based on values determined during said measuring said color patches; and

g) determining a color output value for said input color, (C,M,Y,K), by interpolating in the K dimension between K1 and K3 based on said color output values for neighboring colors.

16. A method as described in claim 15 wherein said determining color output values for said neighboring colors by interpolation, wherein said neighboring colors are identified by the coordinates (C,M,Y,Kn) where n is either 1 or 3, further comprises:

a) determining whether Kn is a value determined in said partitioning said 4-D rectilinear sampling target;

b) if Kn is a value determined in said partitioning a rectilinear sampling target,

i) transforming said full colorant cube simplexes from said tessellation of said 3-D full colorant cube for fixed Kn into transformed simplexes for said transformed 3-D colorant-limited cube sample points;

ii) tessellating said intersection sample points on top of said transformed simplexes to form intersection point simplexes for a complete tessellation of said transformed rectilinear and intersection sample points;

iii) inverse transforming (C,M,Y) in said (C,M,Y,Kn) using an inverse bijective mapping process that is the inverse of said bijective mapping process to obtain a full-colorant-space input coordinate for transformed (C,M,Y) in said 3-D full colorant cube;

iv) determining an input color simplex from among said CMY full-colorant-space simplexes, wherein said input color simplex contains said transformed (C,M,Y);

v) finding a transformed input color simplex from among said transformed simplexes, wherein said transformed input color simplex corresponds to said input color simplex;

vi) determining whether said (C,M,Y) is contained in said transformed input color simplex;

vii) if said (C,M,Y) is not found in said transformed input color simplex, searching a neighborhood of simplexes among said complete tessellation of said transformed rectilinear and intersection sample points in the vicinity of said transformed input color simplex to locate a simplex containing said (C,M,Y); and

viii) interpolating a color output value by using simplicial interpolation between the vertices of said simplex containing said (C,M,Y).

c) if Kn is not a value determined in said partitioning said 4-D rectilinear sampling target,

i) if L₄ is between 300% and 400% of a maximum value for a single colorant and K1<

=L₄−

300%<

=K2;

ii) adding a first designated sample point at the value (100%, 100%, 100%, L₄−

300%) and

iii) tessellating said colorant-limited cube sample points, which satisfy the constraint C+M+Y=L₄−

K2, obtained when K=K2 and said first designated sample point thereby creating first modified simplexes;

iv) if L4 is not between 300% and 400% of a maximum value for a single colorant;

v) tessellating said 3-D colorant-limited cube sample points, which satisfy the constraint C+M+Y=L₄−

K1, obtained when K=K1 and said 3-D colorant-limited cube sample points, which satisfy the constraint C+M+Y=L₄−

K1, obtained when K=K2 thereby creating second modified simplexes;

d) using simplicial interpolation to interpolate a color output value for said (C,M,Y,Kn), using at least one of said first or said second modified simplexes.