Continued fractions, diophantine approximations, and design of color transforms | Zendy

Yuriy A. Reznik | Zendy

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Continued fractions, diophantine approximations, and design of color transforms

Author(s) -

Yuriy A. Reznik

Publication year - 2008

Publication title -

proceedings of spie, the international society for optical engineering/proceedings of spie

Language(s) - English

Resource type - Conference proceedings

SCImago Journal Rank - 0.192

H-Index - 176

eISSN - 1996-756X

pISSN - 0277-786X

DOI - 10.1117/12.797245

Subject(s) - irrational number , diophantine approximation , computation , constant (computer programming) , diophantine equation , integer (computer science) , diophantine set , mathematics , approximations of π , relation (database) , computer science , algorithm , arithmetic , discrete mathematics , geometry , programming language , database

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.

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