Use of PDEs in image processing

In this thesis we study some applications of partial differential equations in image processing. Specifically we look at three well known problems: Determination of Optical flow, Stereo disparity and Computation of Active Contours.; For determination of Optical Flow from a sequence of images a novel approach based on total variation is presented. It is shown that the approach has inherent advantages since it does not smooth the flow-velocity across the edges and hence preserves edge information. A numerical approach based on computation of evolving curves is proposed for computing the optical flow field. Computations are carried out on a number of real and synthetic image sequences in order to illustrate the theory as well as the numerical approach. A comparison is made with existing techniques as to the accuracy of the computed flow fields using synthetic test image sequences.; A pixel matching approach to the stereo-disparity problem is presented. The problem is cast in a framework similar to the optical flow problem. Two evolution equations can be simultaneously solved to get two disparity functions, one for each left and right image. The advantage is that the disparity functions are not excessively smooth and therefore preserve depth information in the images much better.; We sketch some aspects of a project on active contours in which I participated. Some interesting aspects of a new approach to active contours that make it highly desirable over the conventional approach to snakes via direct minimization of an energy functional are observed in the simulations that are presented.