A Wavelet Perspective on Variational Perceptually-Inspired Color Enhancement
The issue of perceptually-inspired correction of color and contrast in digital images has been recently analyzed with the help of variational principles. These techniques allowed building a general framework in which the action of many already existing algorithms can be more easily understood and compared in terms of intensification of local contrast and control of dispersion around the average intensity value. In this paper we analyze this issue from the dual perspective of wavelet theory, showing that it is possible to build energy functionals of wavelet coefficients that lead to a multilevel perceptually-inspired color correction. By computing the Euler–Lagrange equations associated to the wavelet-based functionals we were able to find an analytical formula for the modification of wavelet detail coefficients that overcomes the problem of an ad-hoc selection based on empirical considerations. Besides these theoretical results, the wavelet perspective provides the computational advantage of generating much faster algorithms in comparison with the spatial variational framework.
KeywordsLocal contrast enhancement Wavelets Color image processing Variational methods
Mathematics Subject Classification68U10 94A08 35A15
The authors acknowledge partial support by MICINN Project, reference MTM2009-08171, and by GRC reference 2009 SGR 773 funded by the Generalitat de Catalunya. Edoardo Provenzi also acknowledges FUI Project CEDCA. V. Caselles also acknowledges partial support by ”ICREA Acadèmia” prize for excellence in Research funded by the Generalitat de Catalunya and by the ERC Advanced Grant INPAINTING (Grant Agreement No.: 319899).
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