Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 353

FIGURE 7.28 Three-dimensional view of node colors when super imposed on a printer gamut
(left: sRGB to L*a*b*), (middle: ROMMRGB to L*a*b*), and (right: ProPhoto RGB to L*a*b*).

shows the image path in the forward direction when we start from the intermediate
RGB space. The reverse path to PCS space can be found in Figure 7.1. The overall
pro le accuracy depends on the choice of this intermediate color space since the

spacing between the nodes in this color space has different effects in different
regions of the printer gamut. This in turn can affect the interpolation accuracy of
pixels that are not located on the nodes since all interpolation operations inside the
ICC pro

ow use linear interpolation such as the tetrahedral interpolation to
process images at high speed. Thus, a correspondence in the reverse direction (i.e.,
from nodes in the RGB color space to L*a*b*

le work

= XYZ values in the PCS) and a
correspondence in the forward direction from the RGB nodes to L*a*b* nodes are
generated just before constructing the printer inverse (i.e., L*a*b*toCMY).

7.5.2.1 Inverse by Working on the Printer Model

Different numerical algorithms can be used to compute the printer inverse map
starting from the printer model [71 s algorithm [89],

the moving matrix (MM) algorithm [90], iteratively clustered interpolation (ICI)
algorithm [91], 3-D root

- 88]. They include Shepard

'

finding algorithm [92], conjugate gradient algorithm [93].
Various other methods described in Refs. [71 88] and [94] can be used in the

inversion. Comparison of the inversion performance of some of these methods is
described in Section 6.4.6. Although round trip accuracy (Section 7.7) is a good
quantitative metric for comparison between various known inversion methods,
execution time, computational complexity (i.e., number of complex operations
such as multiplications, matrix inversions performed, etc.) also play an important
role in the choice of the inversion approach. For example, (1) Shepard

-

is method is
easy to implement but relatively less accurate than others, (2) the MM method
has accuracy better than Shepard

'

s but because of complex operations involved in
it, it has high execution time and the method often fails for nodes near the boundary,
and (3) the ICI algorithm provides by far the best results in terms of accuracy,
execution time, and complexity. Although ICI algorithm is iterative, its use for a
nondeterministic system is dif

'

cult. Hence a more general control-based approach is
developed and is described in the next section. It is more suitable for accurately
inverting color maps with three or more separations by either working on the printer
forward map or by directly iterating on the printer with color sensors.