Towards Direct Motion and Shape Parameter Recovery from Image Sequences

This thesis introduces a flexible and general representation of image deformations using a correspondence matrix H. It is shown that these image deformations can be performed and detected using the optimal basis operators derived from the Singular Value Decomposition (SVD) of H. Among other uses, the decomposition can convert the description of an image deformation into a matrix multiplication. The correspondence matrix is used to perform a variety of image transforms, including scale change, image plane rotation and translation. The methodology is also used to independently reproduce the steerable basis operators for the rotation of functions. The correspondence matrix framework is extended to recover the parameters of an image deformation model using appearance-based methods, producing a probability density function of model parameters in a local, strictly feed-forward, fashion. This method solves the inverse mapping problem by learning the forward mapping. One of the goals of this thesis is to show how much shape and motion information can be directly extracted from a scene by local inspection, leading directly to confidence bound