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There has been a great deal of research interest in contour tracking over the last five years. This article combines themes from tracking theory--elastic models and stochastic filtering--with the notion of affine invariance to synthesize a substantially new and demonstrably effective framework for contour tracking.A mechanism is developed for incorporating a shape template into a contour tracker via an affine invariant coupling. In that way the tracker becomes selective for shape and therefore able to ignore background clutter. Affine invariance ensures that the effect of varying viewpoint is accommodated. Use of a standard statistical filtering framework allows uncertainties to be treated systematically, which accommodates object flexibility and unmodeled distortions such as the deformation of a silhouette under motion.The statistical framework also facilitates a further development. In place of heuristically determined spatial scale for feature search, both spatial scale and temporal memory are controlled automatically and in a way that is responsive to the tracking process. Typically, the tracker operates initially in a coarse scale/short memory mode while it searches for a feature. Then spatial scale diminishes to allow more precise localization while memory (temporal scale) lengths to take advantage of motion coherence. All system parameters are determined by natural assumptions and desired tracking performance, leaving none to be fixed heuristically.Versions of the tracker have been implemented at video rate, both on SUN 4 and in parallel, using a network of 11 transputers. The theoretically established properties of automatic control of spatiotemporal scale and of affine invariance are demonstrated using the implemented tracker.

Magnetic resonance imaging (MRI) is unique in its ability to noninvasively and selectively alter tissue magnetization and create tagged patterns within a deforming body such as the heart muscle. The resulting patterns define a time-varying curvilinear coordinate system on the tissue, which we track with coupled B-snake grids. B-spline bases provide local control of shape, compact representation, and parametric continuity. Efficient spline warps are proposed which warp an area in the plane such that two embedded snake grids obtained from two tagged frames are brought into registration, interpolating a dense displacement vector field. The reconstructed vector field adheres to the known displacement information at the intersections, forces corresponding snakes to be warped into one another, and for all other points in the plane, where no information is available, a C1 continuous vector field is interpolated. The implementation proposed in this paper improves on our previous variational-based implementation and generalizes warp methods to include biologically relevant contiguous open curves, in addition to standard landmark points. The methods are validated with a cardiac motion simulator, in addition to in-vivo tagging data sets.

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A new framework for visual tracking of contours is presented, based on a synthesis of elastic models, stochastic filtering and geometric invariance. Flexibly coupled curve templates implement "soft" prior assumptions about shape. Affine invariance, built into the flexible coupling, ensures that the affine deformations that arise naturally from image projection are favoured. Finally, the stochastic hasis of the framework is shown to result naturally in an aut.omatic mechanism for the control of spatio-temporal scale.