Ana Belén Petro

A PDE Formalization of Retinex Theory

In 1964, Edwin H. Land formulated the Retinex theory, the first attempt to simulate and explain how the human visual system perceives color. His theory and an extension, the “reset Retinex” were further formalized by Land and McCann. Several Retinex algorithms have been developed ever since. These color constancy algorithms modify the RGB values at each pixel to give an estimate of the color sensation without a priori information on the illumination. 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. In this paper, it is proved that if the paths are assumed to be symmetric random walks, the Retinex solutions satisfy a discrete Poisson equation. This formalization yields an exact and fast implementation using only two FFTs. Several experiments on color images illustrate the effectiveness of the Retinex original theory.

A Nonparametric Approach for Histogram Segmentation

In this work, we propose a method to segment a 1-D histogram without a priori assumptions about the underlying density function. Our approach considers a rigorous definition of an admissible segmentation, avoiding over and under segmentation problems. A fast algorithm leading to such a segmentation is proposed. The approach is tested both with synthetic and real data. An application to the segmentation of written documents is also presented. We shall see that this application requires the detection of very small histogram modes, which can be accurately detected with the proposed method

Simplest Color Balance

In this paper we present the simplest possible color balance algorithm. The assumption underlying this algorithm is that the highest values of R, G, B observed in the image must correspond to white, and the lowest values to obscurity. The algorithm simply stretches, as much as it can, the values of the three channels Red, Green, Blue (R, G, B), so that they occupy the maximal possible range [0, 255] by applying an affine transform ax+b to each channel. Since many images contain a few aberrant pixels that already occupy the 0 and 255 values, the proposed method saturates a small percentage of the pixels with the highest values to 255 and a small percentage of the pixels with the lowest values to 0, before applying the affine transform. Source Code The source code (ANSI C), its documentation, and the online demo are accessible at the IPOL web page of this article.

Retinex Poisson Equation: a Model for Color Perception

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. This article describes the PDE-Retinex, a fast implementation of the Land-McCann original theory using only two DFT’s.

Fast implementation of color constancy algorithms

Color constancy is a feature of the human color perception system which ensures that the perceived color of objects remains relatively constant under varying illumination conditions, and therefore closer to the physical reflectance. This perceptual effect, discovered by Helmholtz, was formalized by Land and McCann in 1971, who formulated the Retinex theory. Several theories have ever since been developed, known as Retinex or color constancy algorithms. In particular an important historic variant was proposed by Horn in 1974 and another by Blake in 1985. These algorithms modify the RGB values at each pixel in an attempt to give an estimate of the physical color. Lands original algorithm is both complex and not fully specified. It computes at each pixel a stochastic integral on an unspecified set of paths on the image. For this reason, Lands algorithm has received many recent interpretations and implementations that attempt to tune down the excessive complexity. In this paper, a fast and exact FFT implementation of Lands, Horn and Blake theories is described. It permits for the first time a rigorous comparison of these algorithms. A slight variant of these three algorithms will be proposed, that makes them into contrast enhancing algorithms. Several comparative experiments on color images illustrate the superiority of Lands model to manipulate image contrast.

Screened Poisson Equation for Image Contrast Enhancement

In this work we propose a discussion and detailed implementation of a very simple gradient domain method that tries to eliminate the effect of nonuniform illumination and at the same time preserves the images details. This model, which to the best of our knowledge has not been explored in spite of its simplicity, acts as a high pass filter. We show that with a single contrast parameter (which keeps the same value in most experiments), the model delivers state of the art results. They compare favorably to results obtained with more complex algorithms. Our algorithm is designed for all kinds of images, but with the special specification of making minimal image detail alteration thanks to a first order fidelity term, instead of the usual zero order term. Experiments on non-uniform medical images and on hazy images illustrate significant perception gain.

Color image segmentation using acceptable histogram segmentation

In this paper, a new method for the segmentation of color images is presented. This method searches for an acceptable segmentation of 1D-histograms, according to a “monotone” hypothesis. The algorithm uses recurrence to localize all the modes in the histogram. The algorithm is applied on the hue, saturation and intensity histograms of the image. As a result, an optimal and accurately segmented image is obtained. In contrast to previous state of the art methods uses exclusively the image color histogram to perform segmentation and no spatial information at all.

Fourier implementation of Poisson image editing

Poisson editing, introduced in 2003, is becoming a technique with major applications in many different domains of image processing and computer graphics. This letter presents an exact and fast Fourier implementation of the Poisson editing equation proposed in (Perez et al., 2003). The proposed algorithm can handle well all Poisson editing methods that are currently implemented with finite differences and multigrid methods. But it also authorizes fast complex editing strategies where the edited region is obtained by an algorithm instead of a manual selection. The selected region can therefore have a complex topology without additional computational cost. In this letter the proposed method is applied to a classic local contrast enhancement principle introduced in (Caselles et al., 1999). The manual selection of the dark regions is replaced by a lower threshold and the method becomes fast, efficient, level-line preserving, and interactive. The proposed method can be tried on line on any uploaded image at http://www.ipol.im/pub/demo/lmps_selective_contrast_adjustment/.

Color and Contrast Enhancement by Controlled Piecewise Affine Histogram Equalization

This paper presents a simple contrast enhancement algorithm based on histogram equalization (HE). The proposed algorithm performs a piecewise affine transform of the i ntensity levels of a digital image such that the new histogram function will be approximately uniform (as with HE), but where the stretching of the range is locally controlled to avoid brutal noise enhancement. We call this algorithm Piecewise Affine Equalization (PAE). Several experiments show that, in general, the new algorithm improves HE results. Source Code The proposed algorithm has been implemented in ANSI C. The source code, the code documentation, and the online demo are accessible from the web page of this article 1 .

What is the right center/surround for Retinex?

In this work we propose to analyze the formal properties of the center/surround versions of Retinex. Our main goal is to clarify what the “best” surround should be. Two conditions are sound or necessary from an image theoretical viewpoint: scale invariance and integrability. Then, we present a new kernel, which finds an acceptable compromise between these two conditions. This new kernel is compared with different kernels obtained from some center-surround methods.