ABSTRACT
Multidimensional functions play an important role in digital color imaging systems. For example, a digital color printer can be modeled as a forward map from fourdimensional (4-D) device-dependent CMYK color space to three-dimensional (3-D) device-independent L*a*b* color space. The mapping can be defined by the following three multidimensional functions:
L* ¼ f1(C,M,Y ,K) a* ¼ f2(C,M,Y ,K) b* ¼ f3(C,M,Y ,K)
(6:1)
Unfortunately, exact closed-form expressions are not easily available for the above equations. Therefore, we have two options. The first option is to have a lookup table (LUT) of all possible combinations of CMYK; that is, change each separation from 0 to 255 in steps of one, which requires a LUT size of 2554 entries that is equivalent to 3 2554 bytes ¼ 12.6856 bytes of CMYK – L*a*b* data. This is not practical. Another approach would be to have a LUT of size smaller than the full size, for example, 174 or lesser, that is, CMYK – L*a*b* data and use interpolation to find other colors. Multidimensional interpolation is also extensively used in displays, scanners, and inverse printer maps.
