  Mappings between color spaces are ubiquitous in image processing problems
such as gamut mapping, decolorization, and image optimization for color-blind
people. Simple color transformations often result in information loss and
ambiguities (for example, when mapping from RGB to grayscale), and one wishes
to find an image-specific transformation that would preserve as much as
possible the structure of the original image in the target color space. In this
paper, we propose Laplacian colormaps, a generic framework for
structure-preserving color transformations between images. We use the image
Laplacian to capture the structural information, and show that if the color
transformation between two images preserves the structure, the respective
Laplacians have similar eigenvectors, or in other words, are approximately
jointly diagonalizable. Employing the relation between joint diagonalizability
and commutativity of matrices, we use Laplacians commutativity as a criterion
of color mapping quality and minimize it w.r.t. the parameters of a color
transformation to achieve optimal structure preservation. We show numerous
applications of our approach, including color-to-gray conversion, gamut
mapping, multispectral image fusion, and image optimization for color deficient
viewers.
