This paper presents recent advances in the use of diffeomorphic active shapes which incorporate the conservation laws of large deformation diffeomorphic metric mapping. The equations of evolution satisfying the conservation law are geodesics under the diffeomorphism metric and therefore termed geodesically controlled diffeomorphic active shapes (GDAS). Our principal application in this paper is...

This thesis will investigate computer algorithms and user interfaces which assist the process of deforming raster images, vector graphics, geometric models and animated characters in real time. Many recent works have focused on deformation quality, but often at the sacrifice of interactive performance. A goal of this thesis is to approach such high quality but at a fraction of the cost. This wi...

Size functions are functions from the real plane to the natural numbers useful for describing shapes of objects. They allow to translate the problem of comparing shapes to the problem of comparing functions, that is a much simpler task. In order to perform the comparison between size functions we present a method to measure the energy necessary to deform size functions into each other. Minimizi...