Curve shortening and its applications

Abstract

This thesis primarily deals with the curve evolution andshortening process and its applications to image processing.In Chapter 2, there will an indepth discussion about themathematical framework of curve evolution. Curve evolution followsa Partial Differential Equation such that the shape of the closedcurve changes over time. In the second section of this chapter,the concept of curve shortening will be introduced. The lastsection will link the curve shortening process with non-linearheat diffusion. In this section there will be a brief discussionon the preservation of the area and perimeter of a closed curve.The last chapter in this thesis will give an application ofthe curve shortening process called anisotropic diffusion