Embedding non-Euclidean color spaces into Euclidean color spaces with minimal isometric disagreement

Abstract

Isometric embedding of non-Euclidean color spaces into Euclidean color spaces is investigated. Owing to regions of nonzero Gaussian curvature within common non-Euclidean color spaces, we focus on the determination of transformations into Euclidean spaces with minimal isometric disagreement. A computational method is presented for deriving such a color space transformation by means of a multigrid optimization, resulting in a simple color look-up table. The multigrid optimization is applied on the CIELAB space with the CMC, CIE94, and CIEDE2000 formulas. The mean disagreement between distances calculated by these formulas and Euclidean distances within the new spaces is far below 3% for all investigated color difference formulas. Color space transformations containing the inverse transformations are provided as MATLAB scripts at the first author's website.