Local flatness

Abstract: A topic of continued interest in Retinex over the years has been finding ways to implement it with computational models of improved accuracy and efficiency. We have devised a new approach to digitally implementing the Retinex using a local deviation based variational model. The new model leads to improvements in the computed image quality with respect to illumination correction and image enhancement. Several contributions are made: 1) a new prior constraint, which we call local flatness, is proposed, and a new measure of Local Deviation ( LD ) is developed to quantify the degree of local illumination flatness; 2) a variational problem is defined and the solution is found by a logical sequence of steps; 3) discrete implementation of the variational solution is shown to effectively estimate and remove uneven illumination, yielding an accurate recovered image. Unlike other physical prior based variational Retinex models, which use the L2 norm of the illumination gradient to enforce smoothness of illumination, our LD prior selectively imposes local flatness on illumination by calculating the deviation between the estimated illumination surface to a reference plane. In the experiments, pseudo ground truth images are created by superimposing uneven illumination on real scenes, providing an effective way to objectively assess algorithm performance. The experimental results show that our method can reconstruct more accurate recovered images than other state-of-the-art methods, while maintaining good contrast.

Abstract: In the paper we present the analysis of connections on frame bundles of higher order contact, with special emphasis on the question of local flatness.