This chapter concerns models for 2D and 3D shape. The motivation for shape models is twofold. First, we may wish to identify exactly which pixels in the scene belong to a given object. One approach to this segmentation problem, is to model the outer contour of the object (i.e., the shape) explicitly. Second, the shape may provide information about the identity or other characteristics of the object: it can be used as an intermediate representation for inferring higher-level properties.

Unfortunately, modeling the shape of an object is challenging; we must account for deformations of the object, the possible absence of some parts of the object and even changes in the object topology. Furthermore, the object may be partially occluded, making it difficult to relate the shape model to the observed data.

One possible approach to establishing 2D object shape is to use a bottom-up approach; here, a set of boundary fragments are identified using an edge detector (Section 13.2.1) and the goal is to connect these fragments to form a coherent object contour. Unfortunately, achieving this goal has proved surprisingly elusive. In practice, the edge detector finds extraneous edge fragments that are not part of the object contour and misses others that are part of the true contour. Hence it is difficult to connect the edge fragments in a way that correctly reconstructs the contour of an object.