A Variational Framework for Retinex

  • Authors:

  • Ron Kimmel;Michael Elad;Doron Shaked;Renato Keshet;Irwin Sobel

  • Affiliations:

  • Computer Science Department, Technion—I.I.T., Technion City, Haifa 32000, Israel. ron@cs.technion.ac.il;The Computer Science Department, Stanford University, Gates 2B, Room 282, Stanford 94305-9025, CA, USA. elad@sccm.stanford.edu;HP Laboratories Israel, Technion City, Haifa 32000, Israel. doron.shaked@hp.com;HP Laboratories Israel, Technion City, Haifa 32000, Israel. renato.keshet@hp.com;HP Laboratories, 1501 Page Mill Rd., Palo Alto, CA 94304, USA. Irwin.sobel@hp.com

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 2003

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Abstract

Retinex theory addresses the problem of separating the illumination from the reflectance in a given image and thereby compensating for non-uniform lighting. This is in general an ill-posed problem. In this paper we propose a variational model for the Retinex problem that unifies previous methods. Similar to previous algorithms, it assumes spatial smoothness of the illumination field. In addition, knowledge of the limited dynamic range of the reflectance is used as a constraint in the recovery process. A penalty term is also included, exploiting a-priori knowledge of the nature of the reflectance image. The proposed formulation adopts a Bayesian view point of the estimation problem, which leads to an algebraic regularization term, that contributes to better conditioning of the reconstruction problem.Based on the proposed variational model, we show that the illumination estimation problem can be formulated as a Quadratic Programming optimization problem. An efficient multi-resolution algorithm is proposed. It exploits the spatial correlation in the reflectance and illumination images. Applications of the algorithm to various color images yield promising results.