A Fast Algorithm for Exact Histogram Specification. Simple Extension to Colour Images

Abstract

In [12] a variational method using ${\mathcal C}^2$-smoothed ℓ₁-TV functionals was proposed to process digital (quantized) images so that the obtained minimizer is quite close to the input image but its pixels are all different from each other. These minimizers were shown to enable exact histogram specification outperforming the state-of-the-art methods [6], [19] in terms of faithful total strict ordering. They need to be computed with a high numerical precision. However the relevant functionals are difficult to minimize using standard tools because their gradient is nearly flat over vast regions.

Here we present a specially designed fixed-point algorithm enabling to attain the minimizer with remarkable speed and precision. This variational method applied with the new proposed algorithm is actually the best way (in terms of quality and speed) to order the pixels in digital images. This assertion is corroborated by exhaustive numerical tests.

We extend the method to color images where the luminance channel is exactly fitted to a prescribed histogram. We propose a new fast algorithm to compute the modified color values which preserves the hue and do not yield gamut problem. Numerical tests confirm the performance of the latter algorithm.