Deformable templates are a mechanism for modeling shape classes, and have been used recently for the identification of structures in medical imagery such as x-rays of hands and magnetic resonance images of brains, and for the identification and tracking of targets in simulated military applications. Templates are chosen from prototypical members of the object class; the deformations are chosen from a distribution on transformations. Deformations act on templates to produce observable shapes. The ensemble of presentations of a particular object is thereby modeled as the result of acting on a template with a random deformation. The advantage of this approach is that it conveniently captures both the global regularities (embodied in the template) and the typically local departures from the prototype that characterize a particular instance of an object. It is important that the deformations are mostly local, because they can then be described by a local random field, and this has essential computational advantages.
The framework is quite general. The deformation might represent a diffeomorphism that takes a prototype ``atlas" brain into the MRI scan of an individual patient (thereby automatically labelling the structures of the patient's brain), or it might represent the dynamics that carry a target from frame to frame in a detection/tracking application. Object recognition and scene interpretation are reformulated as the computational problems of identifying a template/transformation pair that accounts for the observable data. A new Monte Carlo algorithm, involving jump diffusion processes, has been introduced and shown, analytically, to converge to a correct sampling from the posterior distribution on template/transformation pairs, thereby providing a tool for Bayes-optimal inference. The algorithm, which amounts to an inference engine, is computationally intensive, but implementation on a massively parallel computer has achieved satisfactory convergence times in several applications.