Discrete Geometry for Computer Imagery

Discrete Objects and Shapes.- Multiresolution Representation of Shapes Based on Cell Complexes.- Decomposing Digital 3D Shapes Using a Multiresolution Structure.- Optimal Time Computation of the Tangent of a Discrete Curve: Application to the Curvature.- The Discrete Moments of the Circles.- Planes.- Graceful Planes and Thin Tunnel-Free Meshes.- Local Configurations of Digital Hyperplanes.- (n, m)-Cubes and Farey Nets for Naive Planes Understanding.- Surfaces.- A Digital Lighting Function for Strong 26-Surfaces.- Intersection Number of Paths Lying on a Digital Surface and a New Jordan Theorem.- A Topological Method of Surface Representation.- Presentation of the Fundamental Group in Digital Surfaces.- Reconstruction.- Reconstruction in Different Classes of 2D Discrete Sets.- Curve Reconstruction in Arbitrary Dimension and the Traveling Salesman Problem.- Shape-from-Silhouette/Stereo and Its Application to 3-D Digitizer.- Topology.- Set Connections and Discrete Filtering.- Topological Operators on the Topological Graph of Frontiers.- New Notions for Discrete Topology.- A Model for Digital Topology.- Border Map: A Topological Representation for nD Image Analysis.- A Discrete Homotopic Deformable Model Dealing with Objects with Different Local Dimensions.- Distance and Object Recognition.- Unraveling the Thrill of Metric Image Spaces.- Measuring Resemblance of Complex Patterns.- Tree Representation for Image Matching and Object Recognition.- Thinning.- Ultra-Fast Skeleton Based on an Isotropic Fully Parallel Algorithm.- Directional 3D Thinning Using 8 Subiterations.- Order Independent Homotopic Thinning.- Discretization.- Computable Partial Solids and Voxels Sets.- Convex Hull of Grid Points below a Line or a Convex Curve.- Rounding Voronoi Diagram.- Digitization of Bézier Curves and Patches using Discrete Geometry.- Hausdorff Discretization and Its Comparison to Other Discretization Schemes.- Visualization.- The Discrete Tube: A Spatial Acceleration Technique for Efficient Diffraction Computation.- Polyhedrization of the Boundary of a Voxel Object.- Discrete Ray-Casting.- 3D Discrete Normal Vectors.