Reduced complexity Retinex algorithm via the variational approach

Retinex theory addresses the problem of separating the illumination from the reflectance in a given image, and thereby compensating for non-uniform lighting. In a previous paper (Kimmel et al., 2003), a variational model for the Retinex problem was introduced. This model was shown to unify previous methods, leading to a new illumination estimation algorithm. The main drawback with the above approach is its numerical implementation. The computational complexity of the illumination reconstruction algorithm is relatively high, since in the obtained Quadratic Programming (QP) problem, the whole image is the unknown. In addition, the process requirements for obtaining the optimal solution are not chosen a priori based on hardware/ software constraints. In this paper we propose a way to compromise between the full fledged solution of the theoretical model, and a variety of efficient yet limited computational methods for which we develop optimal solutions. For computational methods parameterized linearly by a small set of free parameters, it is shown that a reduced size QP problem is obtained with a unique solution. Several special cases of this general solution are presented and analyzed: a Look-Up-Table (LUT), linear or nonlinear Volterra filters, and expansion using a truncated set of basis functions. The proposed solutions are sub-optimal compared to the original Retinex algorithm, yet their numerical implementations are much more efficient. Results indicate that the proposed methodology can enhance images for a reduced computational effort. 2003 Elsevier Inc. All rights reserved.

[1]  H. Saunders,et al.  Probability, Random Variables and Stochastic Processes (2nd Edition) , 1989 .

[2]  Zia-ur Rahman,et al.  A multiscale retinex for bridging the gap between color images and the human observation of scenes , 1997, IEEE Trans. Image Process..

[3]  E. Land,et al.  Lightness and retinex theory. , 1971, Journal of the Optical Society of America.

[4]  Michael Elad,et al.  A Variational Framework for Retinex , 2002, IS&T/SPIE Electronic Imaging.

[5]  Tomaso Poggio,et al.  Probabilistic Solution of Ill-Posed Problems in Computational Vision , 1987 .

[6]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  O. Faugeras.  Digital color image processing within the framework of a human visual model , 1979 .

[8]  E H Land,et al.  Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image. , 1983, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Jack M. Holm.  A Strategy for Pictorial Digital Image Processing (PDIP) , 1996, Color Imaging Conference.

[10]  Andrew Blake,et al.  Visual Reconstruction , 1987, Deep Learning for EEG-Based Brain–Computer Interfaces.

[11]  Florin Popentiu,et al.  Iterative identification and restoration of images , 1993, Comput. Graph..

[12]  E. Land.  The retinex theory of color vision. , 1977, Scientific American.

[13]  Stephen A. Dyer,et al.  Digital signal processing , 2018, 8th International Multitopic Conference, 2004. Proceedings of INMIC 2004..

[14]  穂鷹 良介.  Non-Linear Programming の計算法について , 1963 .

[15]  Jr. Thomas G. Stockham,et al.  Image processing in the context of a visual model , 1972 .

[16]  E H Land,et al.  An alternative technique for the computation of the designator in the retinex theory of color vision. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Andrew Blake,et al.  Boundary conditions for lightness computation in Mondrian World , 1985, Comput. Vis. Graph. Image Process..

[18]  Alexei A. Efros,et al.  Fast bilateral filtering for the display of high-dynamic-range images , 2002 .

[19]  K. Hohn,et al.  Determining Lightness from an Image , 2004 .

[20]  D H Brainard,et al.  Analysis of the retinex theory of color vision. , 1986, Journal of the Optical Society of America. A, Optics and image science.

[21]  Zia-ur Rahman,et al.  Properties and performance of a center/surround retinex , 1997, IEEE Trans. Image Process..

[22]  Demetri Terzopoulos,et al.  Image Analysis Using Multigrid Relaxation Methods , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.