Medial Representations

1. Front Matter

   Pages i-xvii

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2. Mathematics

   1. Introduction

      • Stephen Pizer, Kaleem Siddiqi, Paul Yushkevich

      Pages 1-34

   2. Local Forms and Transitions of the Medial Axis

      • Peter J. Giblin, Benjamin B. Kimia

      Pages 37-68

   3. Geometry and Medial Structure

      • James Damon

      Pages 69-123

3. Algorithms

   1. Skeletons via Shocks of Boundary Evolution

      • Kaleem Siddiqi, Sylvain Bouix, Jayant Shah

      Pages 127-154

   2. Discrete Skeletons from Distance Transforms in 2D and 3D

      • Gunilla Borgefors, Ingela Nyström, Gabriella Sanniti di Baja

      Pages 155-190

   3. Voronoi Skeletons

      • Gábor Székely

      Pages 191-221

   4. Voronoi Methods for 3D Medial Axis Approximation

      • Nina Amenta, Sunghee Choi

      Pages 223-239

   5. Synthesis, Deformation, and Statistics of 3D Objects via M-Reps

      • Stephen Pizer, Qiong Han, Sarang Joshi, P. Thomas Fletcher, Paul A. Yushkevich, Andrew Thall

      Pages 241-266

4. Applications

   1. Statistical Applications with Deformable M-Reps

      • Stephen Pizer, Martin Styner, Timothy Terriberry, Robert Broadhurst, Sarang Joshi, Edward Chaney et al.

      Pages 269-308

   2. 3D Model Retrieval Using Medial Surfaces

      • Kaleem Siddiqi, Juan Zhang, Diego Macrini, Sven Dickinson, Ali Shokoufandeh

      Pages 309-326

   3. From the Infinitely Large to the Infinitely Small

      • Frederic F. Leymarie, Benjamin B. Kimia

      Pages 327-351

5. Back Matter

   Pages 353-439

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The last half century has seen the development of many biological or physical t- ories 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. We bring this kno- edge and experience together into this book in order to make medial technology more widely understood and used. The book consists of an introductory chapter, two chapters on the major mat- matical results on medial representations, ?ve 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. We hope that this book will serve the science and engineering communities using medial models and will provide learning material for students entering this ?eld. We are fortunate to have recruited many of the world leaders in medial theory, algorithms, and applications to write chapters in this book. We thank them for their signi?cant effort in preparing their contributions. We have edited these chapters and have combined them with the ?ve chapters that we have written to produce an integrated whole.

• 3D
• Area
• Computer Vision
• Moment
• algorithms
• complexity
• image analysis
• learning
• medial algorithms
• medial applications
• medial representations
• model
• object geometry
• skeletons
• statistics

• School of Computer Science, McGill University, Montreal, Canada

  Kaleem Siddiqi

• Department of Computer Science, University of North Carolina, Chapel Hill, USA

  Stephen M. Pizer

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