Color conversion method and apparatus

• US 5,937,089 A
• Filed: 10/13/1997
• Issued: 08/10/1999
• Est. Priority Date: 10/14/1996
• Status: Expired due to Fees

• Current Assignee: Oki Data Corporation (OKI Electric Industry Company Limited)
• Original Assignee: Oki Data Corporation (OKI Electric Industry Company Limited)
• Inventors: Kobayashi, Yasushi
• Primary Examiner(s): Boudreau, Leo H.
• Assistant Examiner(s): MEHTA, BHAVESH M
• Application Number:
  US08/949,299
• Time in Patent Office: 666 Days
• Field of Search: 382/162, 382/166, 382/167, 358/518, 358/520, 358/519, 358/521, 358/525, 345/425, 345/427, 345/431-432, 345/150, 345/153, 348/453, 395/101, 395/109
• US Class Current: 382/167
• CPC Class Codes: H04N 1/6027 Correction or control of colour gradation or colour contrast H04N1/6058 takes precedence

Abstract

A color conversion method maps input colors to output colors by first scaling the color coordinate system to reduce the difference between the gamut of reproducible input colors and the gamut of reproducible output colors. After scaling, input colors are mapped onto a polyhedron approximating the gamut of reproducible output colors. The polyhedron has vertices at the output white and black colors, and at least three of the most vivid reproducible output colors. In the mapping process, these most vivid colors are left fixed, and the input white and black colors are mapped to the output white and black colors.

Claims

1. A method of converting input colors reproducible by a first color image output device to output colors reproducible by a second color image output device, said input colors and said output colors being defined in a color coordinate system with separate lightness and chromaticity coordinates, comprising the steps of:

selecting an input white color having a maximum lightness reproducible by said first color image output device;

selecting an input black color having a minimum lightness reproducible by said first color image output device;

selecting an output white color having a maximum lightness reproducible by said second color image output device;

selecting an output black color having a minimum lightness reproducible by said second color image output device;

determining a scaling coefficient according to a ratio of a lightness difference between said output white color and said output black color to a lightness difference between said input white color and said input black color; and

scaling said color coordinate system according to said scaling coefficient.

2. The method of claim 1, wherein said step of scaling is performed on lightness coordinates in said color coordinate system.

3. The method of claim 1, wherein said step of scaling is performed on chromaticity coordinates in said color coordinate system.

4. The method of claim 1, wherein said step of scaling is performed on both lightness coordinates and chromaticity coordinates in said color coordinate system.

5. The method of claim 1, further comprising the steps of:

constructing an input white axis comprising all colors disposed on a straight segment joining said input white color to said input black color;

constructing an output white axis comprising all colors disposed on a straight segment joining said output white color to said output black color;

selecting at least three most vivid colors having different hues, said most vivid colors being shades of said hues reproducible by said second color image output device with maximum distance from said output white axis;

constructing a first polyhedron having as vertices said most vivid colors, said output white color, and said output black color;

mapping said input colors to output, colors within said first polyhedron, said most vivid colors being left fixed.

6. A method of converting input colors reproducible by a first color image output device to output colors reproducible by a second color image output device, said input colors and said output colors being defined in a color coordinate system with separate lightness and chromaticity coordinates, comprising the steps of:

selecting an input white color having a maximum lightness reproducible by said first color image output device;

selecting an input black color having a minimum lightness reproducible by said first color image output device;

selecting an output white color having a maximum lightness reproducible by said second color image output device;

selecting an output black color having a minimum lightness reproducible by said second color image output device;

constructing an input white axis comprising all colors disposed on a straight segment joining said input white color to said input black color;

constructing an output white axis comprising all colors disposed on a straight segment joining said output white color to said output black color;

selecting at least three most vivid colors having different hues, said most vivid colors being shades of said hues reproducible by said second color image output device with maximum distance from said output white axis;

constructing a first polyhedron having as vertices said most vivid colors, said output white color, and said output black color;

mapping said input colors to output colors within said first polyhedron, said most vivid colors being left fixed.

7. The method of claim 6, wherein said second color image output device reproduces colors by subtractive mixing of three primary colors, and said three primary colors are included among said most vivid colors.

8. The method of claim 7, wherein three secondary colors complementary to said three primary colors are also included among said most vivid colors.

9. The method of claim 6, wherein:

said first color image output device reproduces colors by additive mixing of red, green, and blue;

said second color image output device reproduces colors by subtractive mixing of magenta, cyan, and yellow; and

the hues of said most vivid colors are cyan, magenta, yellow, red, green, and blue, said first polyhedron accordingly having just eight vertices and twelve faces.

10. A method of converting input colors reproducible by a first color image output device to output colors reproducible by a second color image output device, said input colors and said output colors being defined in a color coordinate system with separate lightness and chromaticity coordinates, comprising the steps of:

selecting an input white color having a maximum lightness reproducible by said first color image output device;

selecting an input black color having a minimum lightness reproducible by said first color image output device;

selecting an output white color having a maximum lightness reproducible by said second color image output device;

selecting an output black color having a minimum lightness reproducible by said second color image output device;

constructing an input white axis comprising all colors disposed on a straight segment joining said input white color to said input black color;

constructing an output white axis comprising all colors disposed on a straight segment joining said output white color to said output black color;

selecting at least three most vivid colors having different hues, said most vivid colors being shades of said hues reproducible by said second color image output device with maximum distance from said output white axis;

constructing a first polyhedron having as vertices said most vivid colors, said output white color, and said output black color;

receiving an input color having a certain input lightness coordinate;

projecting said input color and said input white axis onto a chromaticity diagram having only chromaticity coordinates;

projecting said most vivid colors onto said chromaticity diagram, thereby forming a first polygon having said most vivid colors as vertices in said chromaticity diagram;

determining a first intersection of said first polygon with a first line extending from said input white axis through said input color in said chromaticity diagram; and

mapping said input color to an output color having a hue, in relation to said output white axis, identical to a hue of said first intersection point, in relation to said output white axis, said output color being disposed on said output white axis if said input color is disposed on said input white axis, and said output color being equal to said input color if said input color is one of said most vivid colors.

11. The method of claim 10, wherein said first line extends from a first input gray color on said input white axis, said first input gray color having a lightness coordinate equal to said input lightness coordinate.

12. The method of claim 10, wherein said step of mapping said input color comprises the further steps of:

selecting, on said output white axis, a first output gray color equal in lightness to said input color, and projecting said first output gray color onto said chromaticity diagram;

constructing, in said chromaticity diagram, a second line from said first output gray color through said first intersection;

selecting, on said second line, an adjusted point such that distances from said input white axis to said first intersection and said input color are in equal ratio to distances from said first output gray color to said first intersection and said adjusted point;

selecting an adjusted color having chromaticity coordinates equal to chromaticity coordinates of said adjusted point and having a lightness coordinate equal to said input lightness coordinate; and

mapping said input color to an output color disposed within said first polyhedron on a line segment extending from said output white axis to said adjusted color.

13. The method of claim 12, wherein said line segment extends from said first output gray color to said adjusted color.

14. The method of claim 12, wherein said output color is equal to said adjusted color if said adjusted color is disposed within said first polyhedron, and said output color is disposed on a surface of said first polyhedron if said adjusted color is not disposed within said first polyhedron.

15. The method of claim 11, wherein said step of mapping said input color comprises the further steps of:

calculating a first distance from said first input gray color to said input color;

selecting an edge color disposed on an edge of said first polyhedron, said edge color and said first intersection having equal chromaticity coordinates;

selecting, on said output white axis, a first output gray color equal in lightness to said input color;

selecting, on said output white axis, a second output gray color equal in lightness to said edge color;

extending a third line from said first output gray color parallel to a line from said second output gray color to said edge color;

determining a second intersection of said third line with a surface of said first polyhedron;

determining a second distance from said first output gray color to said second intersection;

setting a third distance equal to said first distance if said first distance does not exceed said second distance, and equal to said second distance if said first distance exceeds said second distance; and

mapping said input color to an output color disposed on said third line at said third distance from said first output gray color.

16. The method of claim 11, wherein said step of mapping said input color comprises the further steps of:

calculating a first distance from said first input gray color to said input color;

selecting an edge color disposed on an edge of said first polyhedron, said edge color and said first intersection having equal chromaticity coordinates;

selecting, on said output white axis, a second output gray color equal in lightness to said edge color;

projecting said edge color, said second output gray color, said output white color, and said output black color onto a saturation-lightness plane;

selecting, in said saturation-lightness plane, a target point having a saturation coordinate equal to said first distance and a lightness coordinate equal to said input lightness coordinate;

determining a single third intersection, in said saturation-lightness plane, of a line extending from said second output gray color through said target color and lines extending from said edge color through said output white color and said output black color;

determining a fourth distance from said second output gray color to said third intersection;

determining a fifth distance from said second output gray color to said target point;

setting an output lightness coordinate equal to said input lightness coordinate if said fifth distance does not exceed said fourth distance, and to a lightness coordinate of said third intersection if said fifth distance exceeds said fourth distance;

setting an output saturation value equal to said first distance if said fifth distance does not exceed said fourth distance, and to a saturation coordinate of said third intersection if said fifth distance exceeds said fourth distance;

selecting, on said output white axis, a third output gray color having a lightness coordinate equal to said output lightness coordinate;

constructing a fourth line extending from said third output gray color parallel to a line from said second output gray color to said edge color; and

mapping said input color to an output color disposed on said fourth line at a distance equal to said output saturation value from said third output gray color.

17. A method of converting input colors reproducible by a first color image output device to output colors reproducible by a second color image output device, said input colors and said output colors being defined in a color coordinate system with separate lightness and chromaticity coordinates, comprising the steps of:

selecting an input white color having a maximum lightness reproducible by said first color image output device;

selecting an input black color having a minimum lightness reproducible by said first color image output device;

selecting an output white color having a maximum lightness reproducible by said second color image output device;

selecting an output black color having a minimum lightness reproducible by said second color image output device;

constructing an input white axis comprising all colors disposed on a straight segment joining said input white color to said input black color;

constructing an output white axis comprising all colors disposed on a straight segment joining said output white color to said output black color;

selecting at least three most vivid colors having different hues, said most vivid colors being shades of said hues reproducible by said second color image output device with maximum distance from said output white axis;

constructing a first polyhedron having as vertices said most vivid colors, said output white color, and said output black color;

selecting, on said input white axis, a white vertex color such that said white vertex color and said output white color have equal lightness coordinates;

selecting, on said input white axis, a black vertex color such that said black vertex color and said output black color have equal lightness coordinates;

constructing a second polyhedron having as vertices said most vivid colors, said white vertex color, and said black vertex color;

mapping said input colors into said second polyhedron, said most vivid colors being left fixed, and input colors disposed on said input white axis being mapped onto said input white axis; and

mapping colors in said second polyhedron to colors in said first polyhedron, said most vivid colors being left fixed, lightness coordinates being left unchanged, and colors on said input white axis being mapped to colors on said output white axis.

18. The method of claim 17, wherein said step of mapping said input colors into said second polyhedron preserves hue.

19. The method of claim 17, wherein said step of mapping said input colors into said second polyhedron comprises the further steps of:

receiving an input color having a certain input lightness coordinate;

projecting said input color and said input white axis onto a chromaticity diagram having only chromaticity coordinates;

projecting said most vivid colors onto said chromaticity diagram, thereby forming a first polygon having said most vivid colors as vertices in said chromaticity diagram;

determining a first intersection of said first polygon with a first line extending from said input white axis through said input color in said chromaticity diagram;

determining an edge color disposed on an edge of said second polyhedron such that said edge color and said first intersection have equal chromaticity coordinates;

determining a second input gray color disposed on said input white axis, said edge color and said second input gray color having equal lightness coordinates;

constructing a fifth line from said second input gray color through said input color; and

mapping said input color to a surface color disposed at an intersection of said fifth line with a surface of said second polyhedron if said input color is disposed exterior to said second polyhedron, said input color being left fixed if said input color is disposed within said second polyhedron.

20. A color conversion apparatus mapping input colors reproducible by a first color image output device to output colors reproducible by a second color image output device, said input colors and said output colors being defined in a color coordinate system with separate lightness and chromaticity coordinates, comprising:

a color parameter memory storing coordinates of an input white color having a maximum lightness reproducible by said first color image output device, an input black color having a minimum lightness reproducible by said first color image output device, an output white color having a maximum lightness reproducible by said second color image output device, and an output black color having a minimum lightness reproducible by said second color image output device;

a scaling coefficient calculator coupled to said color parameter memory, for determining a scaling coefficient according to a ratio of a lightness difference between said output white color and said output black color to a lightness difference between said input white color and said input black color; and

a scaling processor for scaling said color coordinate system according to said scaling coefficient.

21. The apparatus of claim 20, wherein said color parameter memory also stores coordinates of at least three most vivid colors of different hues, said most vivid colors being shades of said hues most vividly reproducible by said second color image output device, further comprising:

a mapping processor for mapping said input colors, after scaling by said scaling processor, into a first polyhedron in said color coordinate system, said first polyhedron having as vertices said output white color, said output black color, and said most vivid colors.

22. The apparatus of claim 21, wherein said mapping processor maps input colors disposed on an input white axis joining said input white color to said input black color to output colors disposed on an output white axis joining said output white color to said output black color.

23. The apparatus of claim 22, wherein said mapping processor leaves said most vivid colors fixed.

24. A color conversion apparatus mapping input colors reproducible by a first color image output device to output colors reproducible by a second color image output device, said input colors and said output colors being defined in a color coordinate system with separate lightness and chromaticity coordinates, comprising:

a color parameter memory storing coordinates of an input white color having a maximum lightness reproducible by said first color image output device, an input black color having a minimum lightness reproducible by said first color image output device, an output white color having a maximum lightness reproducible by said second color image output device, an output black color having a minimum lightness reproducible by said second color image output device, and at least three most vivid colors of different hues, said most vivid colors being shades of said hues most vividly reproducible by said second color image output device, said input white color and said input black color defining an input white axis, said output white color and said output black color defining an output white axis, and said output white color, said output black color, and said most vivid colors defining vertices of a first polyhedron in said color coordinate system;

a color adjustment processor for receiving an input color having a certain input lightness coordinate, projecting said input color and said input white axis onto a chromaticity diagram having only chromaticity coordinates, projecting said most vivid colors onto said chromaticity diagram, thereby forming a first polygon having said most vivid colors as vertices in said chromaticity diagram, determining a first intersection of said first polygon with a first line extending from said input white axis through said input color in said chromaticity diagram, selecting, on said output white axis, a first output gray color equal in lightness to said input color, projecting said first output gray color onto said chromaticity diagram, constructing, in said chromaticity diagram, a second line from said first output gray color through said first intersection, selecting, on said second line, an adjusted point such that distances from said first input gray color to said first intersection and said input color are in equal ratio to distances from said first output gray color to said first intersection and said adjusted point, and selecting an adjusted color having chromaticity coordinates equal to said adjusted point and having a lightness coordinate equal to said input lightness coordinate;

a reproducible color determiner for projecting a section through said first polyhedron at a lightness level equal to said input lightness coordinate onto said chromaticity diagram, thereby obtaining a second polygon in said chromaticity diagram; and

a mapping decision processor coupled to said color adjustment processor and said reproducible color determiner, for finding a fourth intersection of an edge of said second polygon with said second line, and mapping said input color to an output color having a lightness coordinate equal to said input lightness coordinate, said output color having chromaticity coordinates equal to chromaticity coordinates of said adjusted color, if said adjusted point is disposed within said second polygon, and having chromaticity coordinates equal to chromaticity coordinates of said fourth intersection, if said adjusted point is not disposed within said second polygon.

25. A color conversion apparatus mapping input colors reproducible by a first color image output device to output colors reproducible by a second color image output device, said input colors and said output colors being defined in a color coordinate system with separate lightness and chromaticity coordinates, comprising:

a color parameter memory storing coordinates of an input white color having a maximum lightness reproducible by said first color image output device, an input black color having a minimum lightness reproducible by said first color image output device, an output white color having a maximum lightness reproducible by said second color image output device, an output black color having a minimum lightness reproducible by said second color image output device, and at least three most vivid colors of different hues, said most vivid colors being shades of said hues most vividly reproducible by said second color image output device, said input white color and said input black color defining an input white axis, said output white color and said output black color defining an output white axis, and said output white color, said output black color, and said most vivid colors defining vertices of a first polyhedron in said color coordinate system;

an input gray calculator for receiving an input color having a certain input lightness coordinate, and selecting, on said input white axis, an input gray color having a lightness coordinate equal to said input lightness coordinate;

an input saturation calculator for calculating a first distance from said an input gray color to said input color;

an edge color calculator for projecting said input color and said input gray color onto a chromaticity diagram having only chromaticity coordinates, projecting said most vivid colors onto said chromaticity diagram, thereby forming a first polygon having said most vivid colors as vertices in said chromaticity diagram, determining a first intersection of said first polygon with a first line extending from said input gray color through said input color in said chromaticity diagram, and determining an edge color disposed on an edge of said first polyhedron such that said edge color and said first intersection have equal chromaticity coordinates;

a first output gray calculator for determining a second output gray color disposed on said output white axis such that said edge color and said second output gray color have equal lightness coordinates;

a vector calculator for constructing a vector from said second output gray color to said edge color;

an edge saturation calculator for measuring a sixth distance from said second output gray color to said edge color;

a unit vector calculator for dividing said vector by said sixth distance to obtain a unit vector;

a first intersection calculator for selecting a fourth output gray color on said output white axis, projecting said output white color, said output black color, said fourth output gray color, and said edge color onto a saturation-lightness plane, selecting, in said saturation-lightness plane, a target point having a saturation coordinate equal to said first distance and a lightness coordinate equal said input lightness coordinate, finding a fifth intersection of a line extending from said fourth output gray point through said target point with lines extending from said edge point through said output white point and said output black point in said saturation-lightness plane, setting an output saturation value equal to said first distance if said target point is not farther than said fifth intersection from said fourth gray color, setting said output saturation value equal to a saturation coordinate of said fifth intersection point if said target point is farther than said fifth intersection point from said fourth gray color, setting an output lightness coordinate equal to said input lightness coordinate if said target point is not farther than said fifth intersection from said fourth gray color, and setting said output lightness coordinate equal to a lightness coordinate of said intersection point if said target point is farther than said fifth intersection point from said fourth gray color;

a second output gray calculator for selecting, on said output white axis, a fifth output gray color having a lightness coordinate equal to said output lightness coordinate; and

an output chromaticity calculator for multiplying said unit vector by said output saturation value and adding a resulting product to said fifth output gray color, thereby obtaining output chromaticity coordinates, said input color thus being mapped to an output color having said output lightness coordinate and said output chromaticity coordinates.

26. The apparatus of claim 25, wherein said fourth output gray color has a lightness coordinate equal to said input lightness coordinate.

27. The apparatus of claim 26, wherein said fourth output gray color is identical to said second output gray color.

28. A color conversion apparatus mapping input colors reproducible by a first color image output device to output colors reproducible by a second color image output device, said input colors and said output colors being defined in a color coordinate system with separate lightness and chromaticity coordinates, comprising:

a color parameter memory storing coordinates of an input white color having a maximum lightness reproducible by said first color image output device, an input black color having a minimum lightness reproducible by said first color image output device, said input white color and said input black color defining an input white axis, an output white color having a maximum lightness reproducible by said second color image output device, an output black color having a minimum lightness reproducible by said second color image output device, said output white color and said output black color defining an output white axis, a white vertex color disposed on said input white axis, said white vertex color and said output white color having equal lightness coordinates, and a black vertex color disposed on said input white axis, said black vertex color and said output black color having equal lightness coordinates, and at least three most vivid colors of different hues, said most vivid colors being shades of said hues most vividly reproducible by said second color image output device, and said output white color, said output black color, and said most vivid colors defining vertices of a first polyhedron in said color coordinate system, and said white vertex color, said black vertex color, and said most vivid colors defining vertices of a second polyhedron in said color coordinate system;

a maximum saturator for projecting said input color and said input white axis onto a chromaticity diagram having only chromaticity coordinates, projecting said most vivid colors onto said chromaticity diagram, thereby forming a first polygon having said most vivid colors as vertices in said chromaticity diagram, and determining a first intersection of said first polygon with a first line extending from said input white axis through said input color in said chromaticity diagram;

a lightness calculator for determining an edge color disposed on an edge of said first polyhedron, said edge color and said first intersection having equal chromaticity coordinates;

a second intersection calculator for determining a second input gray color disposed on said input white axis, said edge color and said second input gray color having equal lightness coordinates, constructing a fifth line from said second input gray color to said input color, and determining a surface color disposed at an intersection of said fifth line with a surface of said second polyhedron;

a color projector for mapping said input color to an intermediate color, said intermediate color being equal to said input color if said input color is disposed in said second polyhedron, and said intermediate color being equal to said surface color, if said input color is not disposed in said second polyhedron; and

a white adjuster for mapping said intermediate color to a color in said first polyhedron.

29. The apparatus of claim 28, wherein said white adjuster leaves said most vivid colors fixed, does not change lightness coordinates, maps said white vertex color to said output white color, and maps said black vertex color to said output black color.

30. A recording medium storing lightness and chromaticity coordinates of an input white color, an input black color, an output white color, and an output black color, said input white color having a maximum lightness reproducible by a first color image output device, said input black color having a minimum lightness reproducible by said first color image output device, said output white color having a maximum lightness reproducible by a second color image output device, and said output black color having a minimum lightness reproducible by a second color image output device, also storing a computer program for implementing a method of mapping input colors reproducible by said first color image output device to output colors reproducible by said second color image output device, the method comprising the steps of:

determining a scaling coefficient according to a ratio of a lightness difference between said output white color and said output black color to a lightness difference between said input white color and said input black color; and

scaling said color coordinate system according to said scaling coefficient.

31. The recording medium of claim 30, wherein said recording medium also stores coordinates of at least three most vivid colors of different hues, said most vivid colors being shades of said hues most vividly reproducible by said second color image output device, and said method further comprises the steps of:

constructing an input white axis comprising colors disposed on a straight segment joining said input white color to said input black color;

constructing an output white axis comprising colors disposed on a straight segment joining said output white color to said output black color;

constructing a first polyhedron having as vertices said most vivid colors, said output white color, and said output black color;

mapping said input colors to output colors within said first polyhedron, said most vivid colors being left fixed.

32. A recording medium storing lightness and chromaticity coordinates of an input white color, an input black color, an output white color, an output black color, and at least three most vivid colors of different hues, said input white color having a maximum lightness reproducible by a first color image output device, said input black color having a minimum lightness reproducible by said first color image output device, said input white color and said input black color defining an input white axis, said output white color having a maximum lightness reproducible by a second color image output device, said output black color having a minimum lightness reproducible by a second color image output device, said output white color and said output black color defining an output white axis, said most vivid colors being shades of said hues most vividly reproducible by said second color image output device, also storing a computer program for implementing a method of mapping input colors reproducible by said first color image output device to output colors reproducible by said second color image output device, the method comprising the steps of:

receiving an input color having a certain input lightness coordinate;

projecting said input color and said input white axis onto a chromaticity diagram having only chromaticity coordinates;

projecting said most vivid colors onto said chromaticity diagram, thereby forming a first polygon having said most vivid colors as vertices in said chromaticity diagram;

determining a first intersection of said first polygon with a first line extending from said input white axis through said input color in said chromaticity diagram; and

mapping said input color to an output color having a hue, in relation to said output white axis, identical to a hue of said first intersection point, in relation to said output white axis, said output color being disposed on said output white axis if said input color is disposed on said input white axis, and said output color being equal to said input color if said input color is one of said most vivid colors.

33. The recording medium of claim 32, wherein said step of mapping said input color comprises the further steps of:

selecting, on said output white axis, a first output gray color equal in lightness to said input color, and projecting said first output gray color onto said chromaticity diagram;

constructing, in said chromaticity diagram, a second line from said first output gray color through said first intersection;

selecting, on said second line, an adjusted point such that distances from said input white axis to said first intersection and said input color are in equal ratio to distances from said first output gray color to said first intersection and said adjusted point;

selecting an adjusted color having chromaticity coordinates equal to chromaticity coordinates of said adjusted point and having a lightness coordinate equal to said input lightness coordinate; and

mapping said input color to an output color disposed within said first polyhedron on a line segment extending from said output white axis to said adjusted color.

34. The recording medium of claim 33, wherein said line segment extends from said first output gray color to said adjusted color.

35. The recording medium of claim 33, wherein said output color is equal to said adjusted color of said adjusted color is disposed within said first polyhedron, and said output color is disposed on a surface of said first polyhedron if said adjusted color is not disposed within said first polyhedron.

36. The recording medium of claim 32, wherein said step of mapping said input color comprises the further steps of:

selecting, on said input white axis, a first input gray color having a lightness coordinate equal to said input lightness coordinate.

calculating a first distance from said first input gray color to said input color;

selecting an edge color disposed on an edge of said first polyhedron, said edge color and said first intersection having equal chromaticity coordinates;

selecting, on said output white axis, a first output gray color equal in lightness to said input color;

selecting, on said output white axis, a second output gray color equal in lightness to said edge color;

extending a third line from said first output gray color parallel to a line from said second output gray color to said edge color;

determining a second intersection of said third line with a surface of said first polyhedron;

determining a second distance from said first output gray color to said second intersection;

setting a third distance equal to said first distance if said first distance does not exceed said second distance, and equal to said second distance if said first distance exceeds said second distance; and

mapping said input color to an output color disposed on said third line at said third distance from said first output gray color.

37. The recording medium of claim 32, wherein said step of mapping said input color comprises the further steps of:

selecting, on said input white axis, a first input gray color having a lightness coordinate equal to said input lightness coordinate.

calculating a first distance from said first input gray color to said input color;

selecting an edge color disposed on an edge of said first polyhedron, said edge color and said first intersection having equal chromaticity coordinates;

selecting, on said output white axis, a second output gray color equal in lightness to said edge color;

projecting said edge color, said second output gray color, said output white color, and said output black color onto a saturation-lightness plane;

selecting, in said saturation-lightness plane, a target point having a saturation coordinate equal to said first distance and a lightness coordinate equal to said input lightness coordinate;

determining a single third intersection, in said saturation-lightness plane, of a line extending from said second output gray color through said target color and lines extending from said edge color through said output white color and said output black color;

determining a fourth distance from said second output gray color to said third intersection;

determining a fifth distance from said second output gray color to said target point;

setting an output lightness coordinate equal to said input lightness coordinate if said fifth distance does not exceed said fourth distance, and to a lightness coordinate of said third intersection if said fifth distance exceeds said fourth distance;

setting an output saturation value equal to said first distance if said fifth distance does not exceed said fourth distance, and to a saturation coordinate of said third intersection if said fifth distance exceeds said fourth distance;

selecting, on said output white axis, a third output gray color having a lightness coordinate equal to said output lightness coordinate;

constructing a fourth line extending from said third output gray color parallel to a line from said second output gray color to said edge color; and

mapping said input color to an output color disposed on said fourth line at a distance equal to said output saturation value from said third output gray color.

38. A recording medium storing lightness and chromaticity coordinates of an input white color, an input black color, an output white color, an output black color, and at least three most vivid colors of different hues, said input white color having a maximum lightness reproducible by a first color image output device, said input black color having a minimum lightness reproducible by said first color image output device, said output white color having a maximum lightness reproducible by a second color image output device, said output black color having a minimum lightness reproducible by a second color image output device, said most vivid colors being shades of said hues most vividly reproducible by said second color image output device, also storing a computer program for implementing a method of mapping input colors reproducible by said first color image output device to output colors reproducible by said second color image output device, the method comprising the steps of:

constructing an input white axis comprising all colors disposed on a straight segment joining said input white color to said input black color;

constructing an output white axis comprising all colors disposed on a straight segment joining said output white color to said output black color;

constructing a first polyhedron having as vertices said most vivid colors, said output white color, and said output black color;

selecting, on said input white axis, a white vertex color such that said white vertex color and said output white color have equal lightness coordinates;

selecting, on said input white axis, a black vertex color such that said black vertex color and said output black color have equal lightness coordinates;

constructing a second polyhedron having as vertices said most vivid colors, said white vertex color, and said black vertex color;

mapping said input colors into said second polyhedron, said most vivid colors being left fixed, and input colors disposed on said input white axis being mapped onto said input white axis; and

mapping colors in said second polyhedron to colors in said first polyhedron, said most vivid colors being left fixed, lightness coordinates being left unchanged, and colors on said input white axis being mapped to colors on said output white axis.

39. The method of claim 38, wherein said step of mapping said input colors into said second polyhedron preserves hue.

40. The method of claim 38, wherein said step of mapping said input colors into said second polyhedron comprises the further steps of:

receiving an input color having a certain input lightness coordinate;

projecting said input color and said input white axis onto a chromaticity diagram having only chromaticity coordinates;

projecting said most vivid colors onto said chromaticity diagram, thereby forming a first polygon having said most vivid colors as vertices in said chromaticity diagram;

determining a first intersection of said first polygon with a first line extending from said input white axis through said input color in said chromaticity diagram;

determining an edge color disposed on an edge of said second polyhedron such that said edge color and said first intersection have equal chromaticity coordinates;

determining a second input gray color disposed on said input white axis, said edge color and said second input gray color having equal to lightness coordinates;

constructing a fifth line from said second input gray color through said input color; and

mapping said input color to a surface color disposed at an intersection of said fifth line with a surface of said second polyhedron if said input color is disposed exterior to said second polyhedron, said input color being left fixed if said input color is disposed within said second polyhedron.