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.