Constrained pseudo-Brownian motion for image enhancement

The retinex theory of colour vision simulates certain features of the human visual system and is used as a method for image enhancement. Since its introduction in 1971 many flavours of retinex have been devised, which implement slight variations of the original concept. For example, Marini and Rizzi developed a retinex algorithm based on Brownian motion paths. However, while their approach delivers interesting results, it has a high computational complexity. We propose an efficient algorithm that generates pseudo-Brownian paths with a very important constraint: we can guarantee a lower bound to the number of visits to each pixel, as well as its average. We then present a retinex implementation that exploits the paths generated with this algorithm. In order to keep the number of visits per pixel low, we take a multi-scale approach: our path-based computation is performed at different scales of the input image and each result is averaged with the result obtained from larger scales. In doing so, we in effect combine the Brownian motion approach with the scale-space method of the McCann99 algorithm. In this paper we describe the details of our path generator, and we show some images processed with our retinex implementation compared with those obtained with the McCann99 retinex algorithm. The results show that, in general, the Brownian motion approach requires a smaller number of pixel comparisons per scale to achieve similar output images.