Renato Keshet

A Variational Framework for Retinex

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.

Variational famework for Retinex

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.

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.

Rejection based classifier for face detection

Pattern detection problems require a separation between two classes, Target and Clutter, where the probability of the former is substantially smaller compared to that of the latter. In this paper we propose a new classifier that exploits this property, yielding a low complexity yet effective target detection algorithm. This algorithm, called the maximal rejection classifier (MRC), is based on linear successive rejection operations. An application of detecting faces in images is demonstrated using the MRC with encouraging results. 2002 Published by Elsevier Science B.V.

Inf-Semilattice Approach to Self-Dual Morphology

Today, the theoretical framework of mathematical morphology is phrased in terms of complete lattices and operators defined on them. The characterization of a particular class of operators, such as erosions or openings, depends almost entirely upon the choice of the underlying partial ordering. This is not so strange if one realizes that the partial ordering formalizes the notions of foreground and background of an image. The duality principle for partially ordered sets, which says that the opposite of a partial ordering is also a partial ordering, gives rise to the fact that all morphological operators occur in pairs, e.g., dilation and erosion, opening and closing, etc. This phenomenon often prohibits the construction of tools that treat foreground and background of signals in exactly the same way. In this paper we discuss an alternative framework for morphological image processing that gives rise to image operators which are intrinsically self-dual. As one might expect, this alternative framework is entirely based upon the definition of a new self-dual partial ordering.

Mathematical Morphology on Complete Semilattices and its Applications to Image Processing

This work extends the scope of mathematical morphology from complete lattices to complete semilattices, and presents some applications of this extension. More specifically, we first define and briefly analyze basic morphological operators in complete inf-semilattices. Then, difference and reference semilattices are introduced. Finally, some video processing applications in these semilattices are presented, namely: Detection of fast motion, innovation extraction, and contour compression for segmentation-based coding.

Pattern detection using a maximal rejection classifier

Summary form only given. In target detection applications, the aim is to detect occurrences of a specific target in a given signal. In general, the target is subjected to some particular type of transformation, hence we have a set of target signals to be detected. In this context, the set of non-target samples are referred to as clutter. In practice, the target detection problem can be characterized as designing a classifier C(z), which, given an input vector z, has to decide whether z belongs to the target class X or the clutter class Y. In example based classification, this classifier is designed using two training sets -X/spl circ/={xi}/sub i=1..Lx/ (target samples) and Y/spl circ/={y/sub i/}/sub i=1..Ly/ (clutter samples), drawn from the above two classes.

Vanishing points estimation by self-similarity

This paper presents a novel self-similarity based approach for the problem of vanishing point estimation in man-made scenes. A vanishing point (VP) is the convergence point of a pencil (a concurrent line set), that is a perspective projection of a corresponding parallel line set in the scene. Unlike traditional VP detection that relies on extraction and grouping of individual straight lines, our approach detects entire pencils based on a property of 1D affine-similarity between parallel cross-sections of a pencil. Our approach is not limited to real pencils. Under some conditions (normally met in man-made scenes), our method can detect pencils made of virtual lines passing through similar image features, and hence can detect VPs from repeating patterns that do not contain straight edges. We demonstrate that detecting entire pencils rather than individual lines improves the detection robustness in that it improves VP detection in challenging conditions, such as very-low resolution or weak edges, and simultaneously reduces VP false-detection rate when only a small number of lines are detectable.

Shape-Tree Semilattice

A new, self-dual approach for morphological image processing, based on a semilattice framework, is introduced. The related morphological erosion, in particular, shrinks all ’objects‘ in an image, regardless to whether they are bright or dark.The theory is first developed for the binary case, where it is closely related to the adjacency tree. Under certain constraints, it is shown to yield a lattice structure, which is complete for discrete images. It is then generalized to grayscale functions thanks to the tree of shapes, a recently introduced generalization of adjacency trees.

Human upper body identification from images

Estimating human pose in static images is challenging due to the high dimensional state space, presence of image clutter and ambiguities of image observations. In this paper we propose a method to automatically segment human subjects in images, based on dominant colors, and given the face captured by a face detector. The posture is estimated using a 2D model combined with anthropometric data. Experimental results showed that the proposed technique performs well in non trivial images.