A fuzzy set approach to Retinex spray sampling

The color sensation at a point, for the Human Visual System (HVS), derives not only from the color stimulus at that point, but also from the relative spatial arrangement of the stimuli in the image. Based on this observation, the Retinex algorithm, an early and widely studied model of the HVS, determines the output – for each chromatic channel – by rescaling the input intensity of a pixel w.r.t. a reference white level, computed by sampling the brightest points in the neighborhood of the target pixel. In this work, we argue that several elements, inherent to the above observation, can benefit from a fuzzy formalization. We show that the adoption of the fuzzy formalism allows to better encode the mutual influence of pixels. Overall, the fuzzy formalization can provide a general framework for designing and tuning image enhancement algorithms inspired by the HVS. We demonstrate its use by the construction of a fuzzy version of the point-sampling algorithm Random Spray Retinex (RSR). Using RSR as a guide, we build a more efficient algorithm, based on the fact that each spray (a set of sampled points used in RSR to determine the reference white of a specific target) can be assumed to belong to some degree to all the target pixels of the image, provided that a suitable membership function is defined. The features of this alternative formalization of RSR are discussed here, using synthetic and natural test images.