Two-Stage Decolorization Based on Histogram Equalization and Local Variance Maximization

Image decolorization is widely used in single-channel image processing, black-and-white printing, etc. Decolorization aims to generate a perceptually satisfactory gray image that preserves the contrast of the color image. It is known that histogram equalization can enhance the global image contrast by effectively spreading out the most frequent intensity values. Meanwhile, local contrast features such as salient edges and local details have large local variances, which can be enhanced by maximizing local variance. Inspired by these facts, we propose a two-stage decolorization method based on histogram equalization and local variance maximization. In the first stage, we assume that the decolorized gray image is a linear combination of the three channels of the color image, and the combination coefficients are three global weights. Then we propose a constrained variational histogram equalization model to optimize the global weights. The resulting gray image has good global contrast. To further enhance the local contrast, in the second stage, we use local weight combination to express the color image and maximize the local variance by forcing the local weights to be close to the global weights. Numerically, the global weights can be estimated by a gradient-based solver or a discrete searching solver, and the local weights are solved by an iterative solver. Theoretically, we discuss the properties of the energy functions and the convergence of the algorithm. Our proposed method better preserves global and local contrast than state-of-the-art decolorization algorithms.