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.
Mathematical definition and analysis of the Retinex algorithm / E. Provenzi, A. Rizzi, L. De Carli, D. Marini. - In: JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION. - ISSN 1084-7529. - 22:12(2005), pp. 2613-2621.
Mathematical definition and analysis of the Retinex algorithm
E. ProvenziPrimo
;A. RizziSecondo
;L. De CarliPenultimo
;D. MariniUltimo
2005
Abstract
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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