Shape matching is an important subfield of computer vision and has a host of applications in object recognition, non-rigid registration in medical imaging, and indexing in image databases. In medical imaging for example, a fundamental advance in shape matching will have important ramifications for the automated segmentation and classification of anatomical structures. In object recognition, advances in shape matching will be enormously useful in constructing new distance measures that can be used for indexing and retrieval.
Shape matching involves establishing correspondences between homologous structures in different objects. While the correspondence problem can be avoided if intensity-based approaches are used, these methods often rely on the brightness constancy assumption that is often invalid. Feature-based approaches to shape matching have to solve the correspondence problem in situations where there are significant global and local shape differences between the objects being compared. In non-rigid registration, a shape matching approach is required to objects into register. In this work, a relational shape matching approach for simultaneously solving for correspondence and non-rigid deformations is proposed. In contrast to most previous work, the shape matching objective function is set up as a pairwise correspondence and deformation problem. The template consists of a point-set and a known topology that can easily accommodate curves and surfaces. In sharp contrast to previous graph matching approaches, the data is represented as an unstructured point-set. While the resulting optimization problem may appear formidable, efficient algorithms can be designed based on recent and fundamental advances in Bayesian networks. The Bayesian network approach recasts the pairwise correspondence as a joint probability and this results in an alternating algorithm that iteratively updates joint probabilities and deformations. Assuming that efficient algorithms can be designed based on this approach, both non-rigid registration and object recognition applications can be tackled using the same framework and algorithm. Validation and evaluation of these algorithms will be done using medical imaging datasets. Comparisons will also be undertaken against our own previous NSF-funded non-rigid point matching (TPS-RPM) algorithms.
Despite mostly being confined to computer vision, shape matching has the potential to reach a much broader audience with computer graphics and theoretical physics being two concrete examples. In computer graphics, there is burgeoning interest in matching point clouds and more structured representations such as surfaces. While theoretical physics seems like an unlikely candidate at first glance, there is a deep connection between the shape matching objective functions proposed here and by many other vision researchers and general relativity; evidence of this connection can be seen in the recent work of Julian Barbour, The End of Time, Oxford Univ. Press, 2000 (Chapter 11). These connections are just beginning to be noticed and come as a surprise to both vision and theoretical physics researchers. As shape matching in computer vision continues to make incremental (and hopefully inexorable) progress in both frameworks and efficient algorithms, it is hoped that these deep connections will result in unexpected and productive cross-fertilizations.
