Structure-preserving color transformations using Laplacian commutativity
This work addresses a domain-specific problem in image processing for tasks such as gamut mapping and image optimization for color-blind viewers, offering incremental improvements over existing methods.
The authors tackled the problem of information loss and ambiguities in color space transformations by proposing Laplacian colormaps, a framework that uses Laplacian commutativity to preserve image structure, achieving improved results in applications like color-to-gray conversion and gamut mapping.
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.