The primary goal of pattern recognition is supervised or unsupervised classification. Among the various frameworks in which pattern recognition has been traditionally formulated, the statistical approach has been most intensively studied and used in practice. More recently, neural network techniques and methods imported from statistical learning theory have bean receiving increasing attention. The design of a recognition system requires careful attention to the following issues: definition of pattern classes, sensing environment, pattern representation, feature extraction and selection, cluster analysis, classifier design and learning, selection of training and test samples, and performance evaluation. In spite of almost 50 years of research and development in this field, the general problem of recognizing complex patterns with arbitrary orientation, location, and scale remains unsolved. New and emerging applications, such as data mining, web searching, retrieval of multimedia data, face recognition, and cursive handwriting recognition, require robust and efficient pattern recognition techniques. The objective of this review paper is to summarize and compare some of the well-known methods used in various stages of a pattern recognition system and identify research topics and applications which are at the forefront of this exciting and challenging field.

Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linear-Gaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data. In particular, the main novel technical contributions of this thesis are as follows: a way of representing Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of applying Rao-Blackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.

We have been developing a theory for the generic representation of 2-D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a directed, acyclic shock graph, and complexity is managed by attending to the most significant (central) shape components first. The space of all such graphs is highly structured and can be characterized by the rules of a shock graph grammar. The grammar permits a reduction of a shock graph to a unique rooted shock tree. We introduce a novel tree matching algorithm which finds the best set of corresponding nodes between two shock trees in polynomial time. Using a diverse database of shapes, we demonstrate our system's performance under articulation, occlusion, and changes in viewpoint. Keywords: shape representation; shape matching; shock graph; shock graph grammar; subgraph isomorphism. 1 I...

this paper, we propose a Bayesian theory of hierarchical cortical computation based both on (a) the mathematical and computational ideas of computer vision and pattern the- ory and on (b) recent neurophysiological experimental evidence. We ,2 have proposed that Grenander's pattern theory 3 could potentially model the brain as a generafive model in such a way that feedback serves to disambiguate and 'explain away' the earlier representa- tion. The Helmholtz machine 4, 5 was an excellent step towards approximating this proposal, with feedback implementing priors. Its development, however, was rather limited, dealing only with binary images. Moreover, its feedback mechanisms were engaged only during the learning of the feedforward connections but not during perceptual inference, though the Gibbs sampling process for inference can potentially be interpreted as top-down feedback disambiguating low level representations? Rao and Ballard's predictive coding/Kalman filter model 6 did integrate generafive feedback in the perceptual inference process, but it was primarily a linear model and thus severely limited in practical utility. The data-driven Markov Chain Monte Carlo approach of Zhu and colleagues 7, 8 might be the most successful recent application of this proposal in solving real and difficult computer vision problems using generafive models, though its connection to the visual cortex has not been explored. Here, we bring in a powerful and widely applicable paradigm from artificial intelligence and computer vision to propose some new ideas about the algorithms of visual cortical process- ing and the nature of representations in the visual cortex. We will review some of our and others' neurophysiological experimental data to lend support to these ideas

This paper presents diffeomorphic transformations of three-dimensional (3-D) anatomical image data of the macaque occipital lobe and whole brain cryosection imagery and of deep brain structures in human brains as imaged via magnetic resonance imagery. These transformations are generated in a hierarchical manner, accommodating both global and local anatomical detail. The initial low-dimensional registration is accomplished by constraining the transformation to be in a low-dimensional basis. The basis is defined by the Green's function of the elasticity operator placed at predefined locations in the anatomy and the eigenfunctions of the elasticity operator. The high-dimensional large deformations are vector fields generated via the mismatch between the template and target-image volumes constrained to be the solution of a Navier--Stokes fluid model. As part of this procedure, the Jacobian of the transformation is tracked, insuring the generation of diffeomorphisms. It is shown that transformations constrained by quadratic regularization methods such as the Laplacian, biharmonic, and linear elasticity models, do not ensure that the transformation maintains topology and, therefore, must only be used for coarse global registration.

Abstract. We define distances between geometric curves by the square root of the minimal energy required to transform one curve into the other. The energy is formally defined from a left invariant Riemannian distance on an infinite dimensional group acting on the curves, which can be explicitly computed. The obtained distance boils down to a variational problem for which an optimal matching between the curves has to be computed. An analysis of the distance when the curves are polygonal leads to a numerical procedure for the solution of the variational problem, which can efficiently be implemented, as illustrated by experiments.

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For analyzing shapes of planar, closed curves, we propose di#erential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinite-dimensional spaces and their pairwise di#erences are quantified using the lengths of geodesics connecting them on these spaces. We use a Fourier basis to represent tangents to the shape spaces and then use a gradient-based shooting method to solve for the tangent that connects any two shapes via a geodesic.

In this paper we address the issue of recovering and segmenting the apparent velocity field in sequences of images. As for motion estimation, we minimize an objective function involving two robust terms. The first one cautiously captures the optical flow constraint, while the second (a priori) term incorporates a discontinuity-preserving smoothness constraint. To cope with the nonconvex minimization problem thus defined, we design an efficient deterministic multigrid procedure. It converges fast toward estimates of good quality, while revealing the large discontinuity structures of flow fields. We then propose an extension of the model by attaching to it a flexible object-based segmentation device based on deformable closed curves (different families of curve equipped with different kinds of prior can be easily supported). Experimental results on synthetic and natural sequences are presented, including an analysis of sensitivity to parameter tuning. INdex Terms--- Closed segmenting cu...

What does it mean for a deforming object to be "moving" (see Fig. 1)? How can we separate the overall motion (a finite-dimensional group action) from the more general deformation (a di#eomorphism)? In this paper we propose a definition of motion for a deforming object and introduce a notion of "shape average" as the entity that separates the motion from the deformation. Our definition allows us to derive novel and e#cient algorithms to register non-equivalent shapes using region-based methods, and to simultaneously approximate and register structures in grey-scale images. We also extend the notion of shape average to that of a "moving average" in order to track moving and deforming objects through time.