It is well known that significant differences exist between a digital reproduction of a scene, and the perception of the same real scene by a human observer. These differences are mainly due to the color constancy property of the human visual system (HVS), allowing human subjects to perceive the intrinsic color of objects independent of illuminating conditions.

Many computational manipulations have been proposed in the literature to reduce illuminating effects; the oldest one is the Retinex theory, proposed by Land and McCann in 1971. In the basic version of Retinex, the relative reflectance of a colored patch is computed as the mean value of relative reflectance along N random paths across the image, ending at that patch. The main parameters of the algorithm are thus the number of paths, their length, and their randomness, each one impacting directly on the displayed image quality and the computation time.

In this paper, the authors propose a computational improvement of their previous work [1], with the goal of using Brownian paths to compute relative reflectance. Brownian paths are chosen to significantly reduce the number of needed paths; they also approximate the cortical area responsible for color vision.

As underlined in their previous work [1], although the use of Brownian paths resolves the color constancy problem, two problems remain: the high computation time, and the noise level introduced by Brownian paths. Both problems are resolved in this paper, in which the authors present two efficient versions of the Brownian Retinex. The first one, called look up table (LUT), applies the Brownian Retinex to a sub-sampled version of the image, and then builds a mapping function for each color channel to retrieve the filtered pixel values. The second one, called multilevel (MLV), is based on a pyramidal decomposition resulting in a set of mosaic versions of the original image, allowing a speed up of the relative reflectance computation.

The authors offer a new random walk version of the Retinex approach in this paper that significantly reduces the number of paths required to compute relative reflectance. The noise level is also reduced, especially in the MLV version. The presentation of this version suffers from a lack of comparison with other Retinex variants (surround filtering [2], variational [3], and so on), especially in terms of parameter tuning, displayed image quality, noise level, and color constancy.

Finally, it is important to note that the proposed approach has recently been applied by the authors to the color image retrieval problem [4], for which Retinex image pre-processing provides a significant improvement in terms of retrieval results.