The study of shape is a recurring theme in computer vision. For example, shape is one of the main sources of information that can be used for object recognition. In this talk I will present techniques for characterizing two-dimensional shapes using a particular representation of objects in terms of triangulated polygons. This representation has important properties both from a perceptual and a computational point of view.

It is common to look for non-rigid objects in images by considering each object as a deformed version of an ideal template. I will describe an efficient algorithm to solve this problem in a wide range of situations, and show examples on both medical images and images of natural scenes. I will also consider the problem of learning a deformable shape model for a particular class of objects. Finally I will describe a stochastic grammar that can generate arbitrary triangulated polygons while capturing Gestalt principles of shape regularity. Intuitively the grammar tends to generate shapes that have smooth boundaries and a nice decomposition into almost symmetric parts. I will illustrate how this grammar can be used as a generic model for detecting objects in images.