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.
© 2005 Optical Society of America
Original Manuscript: January 18, 2005
Revised Manuscript: April 27, 2005
Manuscript Accepted: May 3, 2005
Published: December 1, 2005
Edoardo Provenzi, Daniele Marini, Luca De Carli, and Alessandro Rizzi, "Mathematical definition and analysis of the Retinex algorithm," J. Opt. Soc. Am. A 22, 2613-2621 (2005)