Discrete Geometry for Computer Imagery

1. Front Matter

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2. Models for Discrete Geometry

   1. Optimal Covering of a Straight Line Applied to Discrete Convexity

      • Jean-Marc Chassery, Isabelle Sivignon

      Pages 1-10

   2. On Dimension Partitions in Discrete Metric Spaces

      • Fabien Rebatel, Édouard Thiel

      Pages 11-22

   3. Walking in the Farey Fan to Compute the Characteristics of a Discrete Straight Line Subsegment

      • Isabelle Sivignon

      Pages 23-34

   4. Persistent Patterns in Integer Discrete Circles

      • André Hoarau, Thierry Monteil

      Pages 35-46

   5. Comparison of Point Clouds Acquired by 3D Scanner

      • Natalia Dyshkant

      Pages 47-58

   6. Generalized Simple Surface Points

      • J. C. Ciria, E. Domínguez, A. R. Francés, A. Quintero

      Pages 59-70

3. Discrete and Combinatorial Topology

   1. A Parallel Thinning Algorithm for Grayscale Images

      • Michel Couprie, Nivando Bezerra, Gilles Bertrand

      Pages 71-82

   2. New Structures Based on Completions

      • Gilles Bertrand

      Pages 83-94

   3. Asymptotic Analysis and Random Sampling of Digitally Convex Polyominoes

      • O. Bodini, Ph. Duchon, A. Jacquot, L. Mutafchiev

      Pages 95-106

   4. Critical Connectedness of Thin Arithmetical Discrete Planes

      • Valérie Berthé, Damien Jamet, Timo Jolivet, Xavier Provençal

      Pages 107-118

   5. A 3D Curvilinear Skeletonization Algorithm with Application to Path Tracing

      • John Chaussard, Laurent Noël, Venceslas Biri, Michel Couprie

      Pages 119-130

4. Geometric Transforms

   1. From the Zones of Influence of Skeleton Branch Points to Meaningful Object Parts

      • L. Serino, C. Arcelli, G. Sanniti di Baja

      Pages 131-142

   2. Merging Faces: A New Orthogonal Simplification of Solid Models

      • Irving Cruz-Matías, Dolors Ayala

      Pages 143-154

   3. Sufficient Conditions for Topological Invariance of 2D Images under Rigid Transformations

      • Phuc Ngo, Yukiko Kenmochi, Nicolas Passat, Hugues Talbot

      Pages 155-168

   4. Digital Distances and Integer Sequences

      • Nicolas Normand, Robin Strand, Pierre Evenou

      Pages 169-179

5. Discrete Shape Representation, Recognition and Analysis

   1. The Persistence Space in Multidimensional Persistent Homology

      • Andrea Cerri, Claudia Landi

      Pages 180-191

   2. A Study of Monodromy in the Computation of Multidimensional Persistence

      • Andrea Cerri, Marc Ethier, Patrizio Frosini

      Pages 192-202

   3. Skeleton Extraction of Vertex Sets Lying on Arbitrary Triangulated 3D Meshes

      • Dimitri Kudelski, Sophie Viseur, Jean-Luc Mari

      Pages 203-214

   4. Integral Based Curvature Estimators in Digital Geometry

      • David Coeurjolly, Jacques-Olivier Lachaud, Jérémy Levallois

      Pages 215-227

This book constitutes the thoroughly refereed proceedings of the 17th International Conference on Discrete Geometry for Computer Imagery, DGCI 2013, held in Seville, Spain, in March 2013. The 34 revised full papers presented were carefully selected from 56 submissions and focus on geometric transforms, discrete and combinatorial tools for image segmentation and analysis, discrete and combinatorial topology, discrete shape representation, recognition and analysis, models for discrete geometry, morphological analysis and discrete tomography.

• computational geometry
• digital imaging
• geometric modeling
• simplification
• topology
• algorithm analysis and problem complexity

• Applied Math I, University of Seville, Seville, Spain

  Rocio Gonzalez-Diaz, Maria-Jose Jimenez, Belen Medrano

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