In order to investigate the local filtering behavior of the Retinex model, we propose a new implementation in which paths are replaced by 2-D pixel sprays, hence the name "random spray Retinex." A peculiar feature of this implementation is the way its parameters can be controlled to perform spatial investigation. The parameters' tuning is accomplished by an unsupervised method based on quantitative measures. This procedure has been validated via user panel tests. Furthermore, the spray approach has faster performances than the path-wise one. Tests and results are presented and discussed.

We present a detailed mathematical analysis of the original Retinex algorithm due to Land and McCann [J. Opt. Soc. Am. 61, 1 (1071)]. To this end, we propose an analytic formula that describes the algorithm behavior. More than one Retinex version (e.g., with and without threshold) is examined. The behavior of Retinex varying the number of paths is predicted, and its recursive iterations are mathematically analyzed using the formula. The mathematical setting presented serves as a common ground for the various Retinex implementations. Its validity is confirmed by the tests on images that we have performed.

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