Generalized equation for real-world image enhancement by Milano Retinex family

Milano Retinexes are spatial color algorithms grounded on the Retinex theory and widely applied to enhance the visual content of real-world color images. In this framework, they process the color channels of the input image independently and re-scale channel by channel the intensity of each pixel p by the so-called local reference white, i.e., a strictly positive value, computed by reworking a set of features sampled around p. The neighborhood of p to be sampled, its sampling, the features to be processed, as well as the mathematical model for the computation of the local reference white vary from algorithm to algorithm, determining different levels of enhancement. Based on the analysis of a group of Milano Retinexes, this work proves that the Milano Retinex local reference whites can be expressed by a generalized equation whose parameters model specific aspects of the Milano Retinex spatial color processing. In particular, tuning these parameters leads to different Milano Retinex implementations. This study contributes to a better understanding of the similarities and differences among the members of the Milano Retinex family, and provides new taxonomic schemes of them based on their own mathematical properties.