Retinex by Two Bilateral Filters

Retinex theory deals with the removal of unfavorable illumination effects from images. This ill-posed inverse problem is typically regularized by forcing spatial smoothness on the recoverable illumination. Recent work in this field suggested exploiting the knowledge that the illumination image bounds the image from above, and the fact that the reflectance is also expected to be smooth. In this paper we show how the above model can be improved to provide a non-iterative retinex algorithm that handles better edges in the illumination, and suppresses noise in dark areas. This algorithm uses two specially tailored bilateral filters – the first evaluates the illumination and the other is used for the computation of the reflectance. This result stands as a theoretic justification and refinement for the recently proposed heuristic use of the bilateral filter for retinex by Durand and Dorsey. In line with their appealing way of speeding up the bilateral filter, we show that similar speedup methods apply to our algorithm.