Continued fractions, diophantine approximations, and design of color transforms

摘要

We study a problem of approximate computation of color transforms (with real and possibly irrational factors) using integer arithmetics. We show that precision of such computations can be significantly imp roved if we allow input or output variables to be scaled by some constant. The problem of finding such a constant turns out to be related to the classic Diophantine approximation problem. We use this relation to explain how best scaled approximations can be derived, and provide several examples of using this technique for design of color transforms.