Continued fractions, diophantine approximations, and design of color transforms

Yuriy A. Reznik

doi:10.1117/12.797245

13 September 2008 Continued fractions, diophantine approximations, and design of color transforms

Yuriy A. Reznik

Proceedings Volume 7073, Applications of Digital Image Processing XXXI; 707309 (2008) https://doi.org/10.1117/12.797245
Event: Optical Engineering + Applications, 2008, San Diego, California, United States

Abstract

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 improved 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.

Citation Download Citation

Yuriy A. Reznik "Continued fractions, diophantine approximations, and design of color transforms", Proc. SPIE 7073, Applications of Digital Image Processing XXXI, 707309 (13 September 2008); https://doi.org/10.1117/12.797245

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