Methods and Systems for Sampling and Modeling of Colorant-Limited, Multi-Colorant Color Spaces
First Claim
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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.
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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.
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Citations
16 Claims
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1. A method for modeling a colorant-limited, multi-dimensional colorant space, said method comprising:
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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. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A method for modeling a colorant-limited, 4-colorant space using multiple interpolation methods, said method comprising:
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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. - View Dependent Claims (9, 10, 11, 12, 13, 14, 15, 16)
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Specification