## Discrete Geometry for Computer Imagery: 7th International Workshop, DGCI '97, Montpellier, France, December 3-5, 1997, ProceedingsEhoud Ahronovitz, Christophe Fiorio This book constitutes the refereed proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery, DGCI '97, held in Montpellier, France, in December 1997. The volume presents 17 revised full papers together with three invited full papers. The contributions are organized in sections on 2D recognition, discrete shapes and planes, surfaces, topology, features, and from principles to applications. |

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### Contents

TopologyPreserving Deletion of 1s from 2 3 and 4Dimensional Binary Images | 3 |

On the Reconstruction of Finite Lattice Sets from Their XRays | 19 |

Aspects in TopologyBased Geometric Modeling | 33 |

Applications of Digital Straight Segments to Economical Image Encoding | 51 |

Maximal Superpositions of Grids and an Application | 63 |

Volume Images | 75 |

Coplanar Tricubes | 87 |

Coexistence of Tricubes in Digital Naive Plane | 99 |

An Approach Based on the Topological PointNeighbourhood | 151 |

The Euler Characteristic of Discrete Object | 163 |

Fast Estimation of Mean Curvature on the Surface of a 3D Discrete Object | 175 |

Ellipses Estimation from Their Digitization | 187 |

Topological Errors and Optimal Chamfer Distance Coefficients | 199 |

Homotopy in 2dimensional Digital Images | 213 |

Set Manipulations of Fractal Objects Using Matrices of IFS | 223 |

RayTracing and 3D Objects Representation in the BCC and FCC Grids | 235 |

Some Structural Properties of Discrete Surfaces | 113 |

A Linear Algorithm for Constructing the Polygon Adjacency Relation in IsoSurfaces of 3D Images | 125 |

Digital Lighting Functions | 139 |

Supercover of Straight Lines Planes and Triangles | 243 |

Author Index | 255 |

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### Common terms and phrases

3-edges A. W. Roscoe adjacency relation binary images boundary Boundary(g combinatorial components configurations connected connectedness consider construction contains coordinates corresponding curvature indexes defined definition denote digital object digital space digital topology dima discrete distance value Discrete Geometry discrete object discrete plane discrete surfaces DT coefficients edge ellipse encoding Euclidean distance Euclidean distance limit Euler characteristic Figure finite fractal Geometric Modeling given graph grid Image Processing integer Lemma lighting function linear Main Theorem Malgouyres manifolds matrix maximal mean curvature method n-adjacent n-cells n-connected n-homotopic n-path n-xel n—path naive plane neighbourhood normal vector notion operations pair of DT parameters pixels points the vertex polyominoes problem Proof properties pyramid reconstruction resp Schlegel diagram Schlegel(P semi-simplicial sets sequence simple simplicial simplicial sets slice contours solution subdivisions subset Supercover supp(O surfel triangle tricubes Type 2 error Universite Louis Pasteur vertex angles vertices voxels X-rays