Shape representation by B-spline curve modeling with applications in invariant curve matching, motion estimation and object tracking

This thesis deals with the problems of: (1) matching planar curves that are modeled as B-splines, independently of possible affine transformations that the original curve has been subjected to (e.g., rotation, translation, scale, semi-perspective projection), and possible occlusion; and (2) estimating the 3-D motion parameters and tracking a moving object with markings (curves) on its surface.; The thesis presents an iterative and a fast algorithm for estimating the control points of the B-spline that is robust to non-uniform sampling, noise, and local deformations.; Curve matching is achieved by judiciously comparing the B-splines' control points when no affine transformation and occlusion are present. The affine transformation and occlusion parameters are estimated through the use of a new class of weighted B-spline curve moments which are well defined whether a curve is open or closed. Based on a finite set of weighted moments, a closed-form solution for the affine transformation parameters are obtained. When the observed curve is an occluded affine transformed version of one the prototype curves, we need to locate the segment on the prototype curve that was affine transformed to yield the observed curve. This problem is compounded by the fact that the occlusion and the affine transformation are tangled together. We decouple the occlusion and the affine transformation problems by considering an affine invariant error measure based on a set of absolute invariants that are computed from the weighted B-spline moments, and minimizing this error with respect to the starting and ending points of the segment. The minimization problem does not require a lot of computation, due to the fact that the B-spline weighted moments are contour integrations that are additive, i.e., decomposable into smaller contour integrations. The method is used for classifying affine transformed silhouette of aircrafts.; The affine invariant B-spline curve matching process is used in tracking a moving object which has markings on its surface, by establishing the correspondence of the image curves that resulted from viewing the same object marking at different times. Implicit in this correspondence is the motion parameters.