The last half century has seen the development of many biological or physical theories that
have explicitly or implicitly involved medial descriptions of objects and other spatial
entities in our world. Simultaneously mathematicians have studied the properties of these
skeletal descriptions of shape and stimulated by the many areas where medial models are
useful computer scientists and engineers have developed numerous algorithms for computing and
using these models. The book consists of an introductory chapter two chapters on the major
mathematical results on medial representations five chapters on algorithms for extracting
medial models from boundary or binary image descriptions of objects and three chapters on
applications in image analysis and other areas of study and design. This book will serve the
science and engineering communities using medial models and will provide learning material for
students entering this field. TOC:1. Introduction.- Part I Mathematics. 2. Local Forms and
Transitions of the Medial Axis. 3. Geometry and Medial Structure.- Part II Algorithms. 4.
Skeletons Via Shocks of Boundary Evolution. 5. Discrete Skeletons from Distance Transforms in
2D and 3D. 6. Voronoi Skeletons. 7. Voronoi Methods for 3D Medial Axis Approximation. 8.
Synthesis Deformation and Statistics of 3D Objects via M-reps.- Part III Applications. 9.
Statistical Applications with Deformable M-Reps. 10. 3D Model Retrieval Using Medial Surfaces.
11. From The Infinitely Large to the Infinitely Small.- A Notation.- Glossary.- References.
