Authors:
Frank Hammond
1
;
Catalina Sbert
2
and
Joan Duran
2
Affiliations:
1
Higher Polytechnic School, University of the Balearic Islands, Spain
;
2
Department of Mathematics and Computer Science & IAC3, University of the Balearic Islands, Cra. de Valldemossa, km. 7.5, E-07122 Palma, Illes Balears, Spain
Keyword(s):
Retinex Theory, Illumination, Reflectance, Image Decomposition, Low-Light Enhancement, Variational Method, Total Variation, Nonlocal Regularization.
Abstract:
Retinex theory assumes that an image can be decomposed into illumination and reflectance components. In this work, we introduce two variational models to solve the ill-posed inverse problem of estimating illumination and reflectance from a given observation. Nonlocal regularization exploiting image self-similarities is used to estimate the reflectance, since it is assumed to contain fine details and texture. The difference between the proposed models comes from the selected prior for the illumination. Specifically, Tychonoff regularization, which promots smooth solutions, and the total variation, which favours piecewise constant solutions, are independently proposed. A comprehensive theoretical analysis of the resulting functionals is presented within appropriate functional spaces, complemented by an experimental validation for thorough examination.