Color Image and Video Enhancement pp 131-154 | Cite as

# Spatial and Frequency-Based Variational Methods for Perceptually Inspired Color and Contrast Enhancement of Digital Images

## Abstract

In the past 20 years, variational principles in image processing and computer vision flourished, often allowing a deep comprehension and a more efficient solution to many problems. As this chapter presents, this also holds true for color image processing. We start by discussing the fundamental result about the interpretation of histogram equalization as the minimization of a suitable functional. This functional is given by two opponent terms: the first being a global quadratic adjustment to the middle gray level, and the second representing a global contrast enhancement term. It is proven here that this analytical form is shared by the so-called perceptual functionals, which allow an enhancement of color images in line with the most important human visual system features. For perceptual functionals, the adjustment is entropic and contrast enhancement is local and invariant under global illumination changes. It is also highlighted that the variational setting provides a unified framework where existing perceptually inspired color improvement models can be seen as particular instances. In the end, the wavelet version of this framework is discussed in detail.

## Notes

### Acknowledgements

The author would like to dedicate this work to the memory of Prof. Vicent Caselles with infinite gratitude for sharing his deep intelligence, culture, passion for science, and, last but not least, honesty.

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