# A Variational Framework for Retinex

@article{Kimmel2004AVF, title={A Variational Framework for Retinex}, author={Ron Kimmel and Michael Elad and Doron Shaked and Renato Keshet and Irwin Sobel}, journal={International Journal of Computer Vision}, year={2004}, volume={52}, pages={7-23} }

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…

## 601 Citations

### Variational famework for Retinex

- Mathematics, Computer ScienceIS&T/SPIE Electronic Imaging
- 2002

A variational model for the Retinex problem that unifies previous methods and shows that the illumination estimation problem can be formulated as a Quadratic Programming optimization problem.

### Reduced complexity Retinex algorithm via the variational approach

- Computer ScienceJ. Vis. Commun. Image Represent.
- 2003

### Non-Local Retinex - A Unifying Framework and Beyond

- Mathematics, Computer ScienceSIAM J. Imaging Sci.
- 2015

This paper reinterpret the gradient thresholding model as variational models with sparsity constraints as well as defining the unifying Retinex model in two similar, but more general, steps.

### A Multi-Exposure Variational Method for Retinex

- Mathematics
- 2017

Retinex theory explains how the human visual system perceives colors. The goal of retinex is to decompose the reflectance and the illumination from the given images and thereby compensating for…

### A novel Retinex algorithm based on alternating direction optimization

- Computer Science, MathematicsPrecision Mechanical Measurements
- 2013

An efficient and effective algorithm based on alternating direction optimization to solve the illumination image and reflectance image without converting images to the logarithmic domain and has less computational cost and can be applied to real-time processing.

### A unifying retinex model based on non-local differential operators

- Computer Science, MathematicsElectronic Imaging
- 2013

Within a single framework new retinex instances particularly suited for texture-preserving shadow removal, cartoon-texture decomposition, color and hyperspectral image enhancement are defined, and entirely novel retineX formulations are derived by using more interesting non-local versions for the sparsity and fidelity prior.

### A parallel operator splitting algorithm for solving constrained total-variation retinex

- Computer ScienceInverse Problems & Imaging
- 2020

A parallel operator splitting algorithm tailored for the constrained total-variation retinex model, in which all the resulting subproblems admit closed form solutions or can be tractably solved by some subroutines without any internally nested iterations is developed.

### A modulus iteration method for retinex problem

- MathematicsNumer. Linear Algebra Appl.
- 2018

A variational minimization model with physical constraints imposed on reflectance values is proposed and it is shown that the proposed model is equivalent to a linear complementarity problem, and a modulus iteration method is applied to solve it.

### Framelet regularization for uneven intensity correction of color images with illumination and reflectance estimation

- MathematicsNeurocomputing
- 2018

### Retinex by Two Bilateral Filters

- MathematicsScale-Space
- 2005

This result stands as a theoretic justification and refinement for the recently proposed heuristic use of the bilateral filter for retinex by Durand and Dorsey and shows that similar speedup methods apply to the algorithm.

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