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Mappings between color spaces are ubiquitous in image processing problemssuch as gamut mapping, decolorization, and image optimization for color-blindpeople. Simple color transformations often result in information loss andambiguities (for example, when mapping from RGB to grayscale), and one wishesto find an image-specific transformation that would preserve as much aspossible the structure of the original image in the target color space. In thispaper, we propose Laplacian colormaps, a generic framework forstructure-preserving color transformations between images. We use the imageLaplacian to capture the structural information, and show that if the colortransformation between two images preserves the structure, the respectiveLaplacians have similar eigenvectors, or in other words, are approximatelyjointly diagonalizable. Employing the relation between joint diagonalizabilityand commutativity of matrices, we use Laplacians commutativity as a criterionof color mapping quality and minimize it w.r.t. the parameters of a colortransformation to achieve optimal structure preservation. We show numerousapplications of our approach, including color-to-gray conversion, gamutmapping, multispectral image fusion, and image optimization for color deficientviewers.

Structure-preserving color transformations using Laplacian commutativity