Chapter 9
Deformable Templates

There are cases that are not easily reduced to pattern detection and classification. One such a case is the detailed estimation of the parameters of a parametric curve. Another important case is the comparison of anatomical structures, such as brain sections. Instead of modeling the variability of the patterns within a class as a static multidimensional manifold, we may focus on the constrained deformation of a parameterized model and measure similarity by the deformation stress. The chapter analyzes the Hough transform from a dynamical perspective: shapes are attracted from image feature maps acting as physical potential fields. Active shape models, integrating textural and geometrical information, are a natural and efficient extension that benefits from the usage of PCA techniques. The possibility of establishing a dense correspondence field between the pixels of different images opens the way to interesting morphing applications in medical analysis and computer graphics animation.

keywords: potential field, deformable templates, active shape models, diffeomorphic matching, optical flow.