A PDE Formalization of Retinex Theory

Abstract

In 1964 Edwin H. Land formulated the Retinex theory, the first attempt to simulate and explain how the human visual system perceives color. His theory and an extension, the "reset Retinex" were further formalized by Land and McCann. Several Retinex algorithms have been developed ever since. These color constancy algorithms modify the RGB values at each pixel to give an estimate of the color sensation without a priori information on the illumination. Unfortunately, the Retinex Land-McCann original algorithm is both complex and not fully specified. Indeed, this algorithm computes at each pixel an average of a very large set of paths on the image. For this reason, Retinex has received several interpretations and implementations which, among other aims, attempt to tune down its excessive complexity. In this paper, it is proved that if the paths are assumed to be symmetric random walks, the Retinex solutions satisfy a discrete screened Poisson equation. This formalization yields an exact and fast implementation using only two FFTs. Several experiments on color images illustrate the effectiveness of the Retinex original theory.

Segmentation of Trophectoderm in Microscopic Images of Human Embryos using Watershed Method

“…This paper proposes an automatic segmentation technique, which is considered as a strong method for segmenting the TE region, does not require any manual pre-processing work. The presented work utilized the Retinex algorithm [10] to highlight the cells which are present in the cavity area or region and then level-set algorithm is applied to segment the TE region from corresponding selected blastocyst image. Finally to enhance the segmentation operation it is proposed to use the watershed technique.…”

“…These low frequency components are removed by Retinex algorithm by Moral et al [10]. A set of starting pixel say, "y" and ending pixel "z" defines the path on an image.…”

Retinex Poisson Equation: a Model for Color Perception

“…But, Morel et al have shown [3] that the original Retinex algorithm can be formalized as a (discrete) partial differential equation. More precisely, it can be shown that if the Retinex paths are interpreted as symmetric random walks, then Retinex is equivalent to a Neumann problem for a Poisson equation.…”

“…The formalization proved by Morel et al [3] yields a fast implementation of the Land-McCann original theory using only two DFT's.…”

“…It is proven [3] that the output of the Retinex algorithm proposed by Land and McCann is the solution of the discrete partial differential equation with Neumann boundary conditions…”