6 - High-level feature extraction: deformable shape analysis

Abstract

The previous chapter covered finding shapes by matching. This implies knowledge of a model (mathematical or template) of the target shape (feature). The shape is fixed in that it is flexible only in terms of the parameters that define the shape, or the parameters that define a template's appearance. Sometimes, however, it is not possible to model a shape with sufficient accuracy, or to provide a template of the target. It might be that the exact shape is unknown or it might be that the perturbation of that shape is impossible to parameterise. In this case, we seek techniques that can evolve to the target solution, or adapt their result to the data. This implies the use of flexible shape formulations. This chapter presents four techniques that can be used to find flexible shapes in images. If the shape is flexible or deformable, so as to match the image data, we have a deformable template. This is where we shall start. Later, we shall move to techniques that are called snakes because of their movement. We shall explain two different implementations of the snake model. The first one is based on discrete minimisation, and the second one on finite element analysis. We shall also look at determining a shape's skeleton, by distance analysis and by the symmetry of their appearance. This technique finds any symmetric shape by gathering evidence by considering features between pairs of points. Finally, we shall consider approaches that use the statistics of a shape's possible appearance to control selection of the final shape, called active shape models.