Digital Geometry Algorithms

1. Front Matter

   Pages I-X

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2. General

   1. Front Matter

      Pages 1-1

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   2. Digital Geometry in Image-Based Metrology

      • Alfred M. Bruckstein

      Pages 3-26

   3. Provably Robust Simplification of Component Trees of Multidimensional Images

      • Gabor T. Herman, T. Yung Kong, Lucas M. Oliveira

      Pages 27-69

3. Topology, Transformations

   1. Front Matter

      Pages 71-71

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   2. Discrete Topological Transformations for Image Processing

      • Michel Couprie, Gilles Bertrand

      Pages 73-107

   3. Modeling and Manipulating Cell Complexes in Two, Three and Higher Dimensions

      • Lidija Čomić, Leila De Floriani

      Pages 109-144

   4. Binarization of Gray-Level Images Based on Skeleton Region Growing

      • Xiang Bai, Quannan Li, Tianyang Ma, Wenyu Liu, Longin Jan Latecki

      Pages 145-164

   5. Topology Preserving Parallel 3D Thinning Algorithms

      • Kálmán Palágyi, Gábor Németh, Péter Kardos

      Pages 165-188

   6. Separable Distance Transformation and Its Applications

      • David Coeurjolly, Antoine Vacavant

      Pages 189-214

   7. Separability and Tight Enclosure of Point Sets

      • Peter Veelaert

      Pages 215-243

4. Image and Shape Analysis

   1. Front Matter

      Pages 245-245

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   2. Digital Straightness, Circularity, and Their Applications to Image Analysis

      • Partha Bhowmick, Bhargab B. Bhattacharya

      Pages 247-299

   3. Shape Analysis with Geometric Primitives

      • Fabien Feschet

      Pages 301-321

   4. Shape from Silhouettes in Discrete Space

      • Atsushi Imiya, Kosuke Sato

      Pages 323-358

   5. Combinatorial Maps for 2D and 3D Image Segmentation

      • Guillaume Damiand, Alexandre Dupas

      Pages 359-393

   6. Multigrid Convergence of Discrete Geometric Estimators

      • David Coeurjolly, Jacques-Olivier Lachaud, Tristan Roussillon

      Pages 395-424

5. Back Matter

   Pages 425-428

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Digital geometry emerged as an independent discipline in the second half of the last century. It deals with geometric properties of digital objects and is developed with the unambiguous goal to provide rigorous theoretical foundations for devising new advanced approaches and algorithms for various problems of visual computing. Different aspects of digital geometry have been addressed in the literature. This book is the first one that explicitly focuses on the presentation of the most important digital geometry algorithms. Each chapter provides a brief survey on a major research area related to the general volume theme, description and analysis of related fundamental algorithms, as well as new original contributions by the authors. Every chapter contains a section in which interesting open problems are addressed.

• computational imaging
• digital geometry algorithms
• visual computing

• Buffalo State College, Department of Mathematics, State University of New York, Buffalo, USA

  Valentin E. Brimkov

• Department of Computer Science, State University of New York at Fredonia, Fredonia, USA

  Reneta P. Barneva

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