Structure-preserving color transformations using Laplacian commutativity

TL;DR

This paper introduces Laplacian colormaps, a framework for structure-preserving color transformations that maintain image structure across color spaces by leveraging Laplacian eigenvector similarity and matrix commutativity.

Contribution

It proposes a novel method using Laplacian eigenvectors and matrix commutativity to optimize color transformations for structure preservation in images.

Findings

Effective color-to-gray conversion preserving structure

Improved gamut mapping with minimal structural distortion

Enhanced image fusion and optimization for color-deficient viewers

Abstract

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.