Device Independence

1
Device Independence

• Calibration to standard space
• typically CIE XYZ
• Coordinate transforms through standard space
• Gamut mapping

2
Device independence

• Stone et. al. Color Gamut Mapping and the
  Printing of Digital Color Images, ACM
  Transactions on Graphics, 7(4) October 1998, pp.
  249-292.
• The following slides refer to their techniques.

3
Device to XYZ

• Sample gamut in device space on 8x8x8 mesh (7x7x7
  343 cubes).
• Measure (or model) device on mesh.
• Interpolate with trilinear interpolation
• for small mesh and reasonable function
  XYZf(device1, device2, device3) this
  approximates interpolating to tangent.

4
XYZ to Device

• Invert function XYZf(device1, device2, device3)
• hard to do in general if f is ill behaved
• At least make f monotonic by throwing out
  distinct points with same XYZ.
• e.g. CMY device
• (continued)

5
XYZ to CMY

• Invert function XYZf(c,m,y)
• Given XYZx,y,z want to find CMYc,m,y such
  that f(CMY)XYZ
• Consider X(c,m,y), Y(c,m,y), Z(c,m,y)
• A continuous function on a closed region has max
  and min on the region boundaries, here the cube
  vertices. Also, if a continuous function has
  opposite signs on two boundary points, it is zero
  somewhere in between.

6
XYZ to CMY

• Given X0, find c,m,y such that f(c,m,y) X0
• if ci,mi,yi cj,mj,yj are vertices on a given
  cube, and UX(c,m,y)- X0 has opposite sign on
  them, then it is zero in the cube. Similarly Y,
  Z. If find such vertices for all of X0,Y0,Z0,
  then the found cube contains the desired point.
  (and use interpolation). Doing this recursively
  will find the desired point if there is one.

7
Gamut Mapping

• Criteria
• preserve gray axis of original image
• maximum luminance contrast
• few colors map outside destination gamut
• hue, saturation shifts minimized
• increase, rather than decrease saturation
• do not violate color knowledge, e.g. sky is blue,
  fruit colors, skin colors

8
Gamut Mapping

• Special colors and problems
• Highlights this is a luminance issue so is about
  the gray axis
• Colors near black locus of these colors in image
  gamut must map into something reasonably similar
  shape else contrast and saturation is wrong

9
Gamut Mapping

• Special colors and problems
• Highly saturated colors (far from white point)
  printers often incapable.
• Colors on the image gamut boundary occupying
  large parts of the image. Should map inside
  target gamut else have to project them all on
  target boundary.

10
Gamuts
CRT
Printer