In 1964 Edwin H. Land formulated the Retinex theory, the first attempt to simulate and explain how the human visual system perceives color. Unfortunately, the Retinex Land-McCann original algorithm is both complex and not fully specified. Indeed, this algorithm computes at each pixel an average of a very large set of paths on the image. For this reason, Retinex has received several interpretations and implementations which, among other aims, attempt to tune down its excessive complexity. But, Morel et al. have shown that the original Retinex algorithm can be formalized as a (discrete) partial differential equation.

While the Retinex theory aimed at explaining human color perception, its derivations have led to efficient algorithms enhancing local image contrast, thus permitting among other features, to “see in the shadows”. Among these derived algorithms, Multiscale Retinex is probably the most successful center-surround image filter. In [1], we offer an analysis and implementation of Multiscale Retinex. We point out and resolve some ambiguities of the method. In particular, we show that the important color correction final step of the method can be seriously improved.

Poisson Image Editing is a new technique permitting to modify the gradient vector field of an image, and then to recover an image with a gradient approaching this modified gradient field. This amounts to solve a Poisson equation, an operation which can be efficiently performed by Fast Fourier Transform (FFT), see [2].

In order to attenuate the effects of non-uniform illumination in digital images an extension of the TV model is proposed in [3]. We compare the simplest possible linear algorithm and the simplest possible total-variation based algorithm. The comparison demonstrates once again that the total variation model improves images with minimal halo artifacts. In [5] we propose to analyze the formal properties of the center/surround versions of Retinex. We propose a new kernel which founds an acceptable compromise between scale invariance and integrability.

**Figure 1.** Experiment on the Multiscale Retinex algorithm [4]. Left: Original image. Right: Enhanced image.

**Figure 2**. Experiment by applying the Poisson equation [2]. Left: Original image. Right: Enhanced image.

**Figure 3**. Experiment applying the new kernel [5]. Left: Original image. Right: Enhanced image.

**Main references:**

[1] J. M. Morel, A. B. Petro, C. Sbert, “A PDE formalization of retinex theory”, IEEE Transactions on Image Processing, Vol 19(11), pp: 2825-2837, 2010.

[2] J. M. Morel, A. B. Petro, C. Sbert, “Fourier implementation of Poisson image editing”, Pattern Recognition Letters, Vol 33,pp: 342-348, 2012.

[3] A. B. Petro, C. Sbert, J. M. Morel, “Automatic correction of image intensity non-uniformity by the simplest total variation model”, Methods and Applications of Analysis, Vol 21(1), pp: 107-120, 2014.

[4] A. B. Petro, C. Sbert, and J. M. Morel, *Multiscale Retinex*, Image Processing On Line, (2014), pp. 71–88.http://dx.doi.org/10.5201/ipol.2014.107

[5] A. B. Petro, C. Sbert, and J. M. Morel, What is the right center/surround for Retinex? in *Image Processing (ICIP), 2014 IEEE International Conference on*, pp. 4552-4556, Oct. 2014.