Binary Restoration Research Articles

Guest editors' introduction to the special section on energy minimization methods in computer vision and pattern recognition

ENERGY minimization techniques are central to many methods in computer vision and pattern recognition. Stated simply, if a task can be posed as the minimization of an energy measure, which may, for instance, be the negative logarithm of a probability or an entropy, then a variety of optimization methods may be applied to locate the solution. The solution may be a vector of parameters representing the shapes of a curve, a surface, or a volume, it may be a set of symbolic labels representing the semantic or syntactic content of a signal, or it may be a graph representing arrangement or structure. The optimization methods that can be applied to the cost function to recover the solution include gradient descent, simulated annealing, mean-field annealing, evolutionary search, and tabu search, to mention just a few. Many of the classical methods in the fields of computer vision and pattern recognitionmake use of energyminimization techniques. Familiar examples include relaxation labeling, regularization, active contours, and Markov models. More recent examples include the use of graph-cuts, spectral graph theory, and semidefinite programming. Energy minimization techniques have also been pivotal in the development of algorithms for learning, inference, and classification. One of the characteristics of this field is that it draws strongly on recent developments in other disciplines such as mathematics, statistics, operations research, biology, and economics. Moreover, the basic methodology is being developed at a great rate in these related disciplines. In this respect, energy minimization is different from other widely used techniques such as geometry or probability, where the basic methods have been available in the mathematics literature for well over 100 years. It is probably fair to say that the problems of optimization and, in particular, combinatorial optimization, are ones of a computational nature and have hence only emerged over the past few decades. Our own involvement in this field has been, in part, through a biennial series of workshops (EMMVCPR) that commenced in 1997 and which have been aimed at providing a focus for research in this area. From the interest shown in these workshops and the number of papers on the topic appearing in the main conferences (CVPR, ECCV, ICCV), it seemed to us that a special edition of IEEE Transactions on Pattern Analysis and Machine Intelligence would be both timely and valuable to the community. The call for papers was issued in mid-2001 and we received 50 papers by the deadline on 1 May 2002. Each paper was reviewed by at least three reviewers according to the standard TPAMI reviewing procedure. This meant that we needed the assistance of some 150 reviewers. By late October 2002, we had first reviews for all of the papers and met in Venice to make initial decisions. Based on the reviews, and giving authors the chance to revise their papers in the light of reviewers comments, we selected the six papers that appear in the current special section, together with three papers that will appear in a subsequent special section. The papers span a diverse set of methods and applications. The techniques covered include semidefinite programming, Markov models, and simulated annealing, while the problems addressed include deformable models, shape-from-shading, and clustering. The first regular paper in this special section is “Binary Partitioning, Perceptual Grouping, and Restoration with Semidefinite Programming” by J. Keuchel, C. Schnorr, C. Schellewald, and D. Cremers. The authors describe a new optimization method based on semidefinite programming relaxations. The method is applied to the computer vision problems of unsupervised partitioning, figure-ground discrimination, and binary restoration. The interesting feature of the proposed method is that it does not require any parameter tuning. Moreover, apart from the symmetry condition, no assumptions aremade concerning the objective criterion. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 25, NO. 11, NOVEMBER 2003 1361

Binary partitioning, perceptual grouping, and restoration with semidefinite programming

We introduce a novel optimization method based on semidefinite programming relaxations to the field of computer vision and apply it to the combinatorial problem of minimizing quadratic functionals in binary decision variables subject to linear constraints. The approach is (tuning) parameter-free and computes high-quality combinatorial solutions using interior-point methods (convex programming) and a randomized hyperplane technique. Apart from a symmetry condition, no assumptions (such as metric pairwise interactions) are made with respect to the objective criterion. As a consequence, the approach can be applied to a wide range of problems. Applications to unsupervised partitioning, figure-ground discrimination, and binary restoration are presented along with extensive ground-truth experiments. From the viewpoint of relaxation of the underlying combinatorial problem, we show the superiority of our approach to relaxations based on spectral graph theory and prove performance bounds.

Binary restoration of thin objects in multidimensional imagery

We present a method for restoration of noisy tomographic images for detecting thin objects, such as explosives. Use of a weighted mean-square estimate optimizes the solution to place emphasis on the infrequent, but significant local structure associated with thin objects. Experimental results show successful restoration at very high noise levels.