, IEEE Computer Society
Pages: pp. 1361-1363
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 recognition make use of energy minimization 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. Schnörr, 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 are made concerning the objective criterion.
In their paper "Hidden Markov Measure Field Models for Image Segmentation," J.L. Marroquin, E.A. Santana, and S. Botello present a novel Bayesian formulation of parametric image segmentation using a doubly stochastic prior model for the label field. Exact optimal estimators for both the label field and the model parameters are obtained by an efficient minimization algorithm. The applications of segmentation of Magnetic Resonance volumes and motion segmentation are explored.
In their paper "Generating Discriminating Cartoon Faces Using Interaction Snakes," R-.L. Hsu and A.K. Jain describe a new method for manipulating interacting snakes in the face recognition domain. The authors propose the use of semantic face graphs which employ interacting snakes to align the general facial topology onto the sensed face images. Good classification performance is demonstrated using cartoon faces.
S. Ghebreab and A.W.M. Smeulders introduce a new class of deformable model that they refer to as a string in "Strings: Variational Deformable Models of Multivariate Continuous Boundary Features." This model is characterized in a functional setting and does not rely on vectors of labeled landmark points as input. The method is used to learn closed boundary curves by performing principal components analysis on the functional representation. When compared with existing deformable models, the technique offers a number of advantages. For instance, it does not require accurate landmark correspondence and can deal with missing landmark points.
The first short paper in this section is "Bagging for Path-Based Clustering" by B. Fischer and J.M. Buhmann. It contains a mathematical description of the method of Path-Based Clustering. The paper focuses on the use of the bootstrap resampling technique for agglomerative clustering, which is necessary for making the method work. The proposed method is evaluated on a large color image data set of human segmentations.
A. Crouzil, X. Descombes, and J.-D. Durou tackle the classical problem of shape from shading in "A Multiresolution Approach for Shape from Shading Coupling Deterministic and Stochastic Optimization." They develop a multiresolution approach to the problem. By using simulated annealing, they overcome problems associated with local minima. They demonstrate that the underlying cost function is related to the energy of an MRF. The method is shown to offer advantages for surfaces involving complex patterns of concave and convex structure.
We hope that the collection of papers assembled in this special section will provide a timely and interesting sample of research in the field of energy minimization. In addition to the authors and reviewers, we received considerable help and support from a number of individuals in bringing it to fruition. These include Kevin Boyer, Rama Chellappa, and David Kriegman who, as EICs, supported our proposal, Hilda Hosillos and Suzanne Werner at the IEEE Computer Society who helped with the collection of papers, undertook the final preparation of the special section, and kept us on schedule, and Corinne Zuzia, who assisted with the processing of the reviews.
Mário A.T. Figueiredo
Edwin R. Hancock