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This book constitutes the thoroughly refereed proceedings of the 21st IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2019, held in Marne-la-Vallée, France, in March 2019.

The 38 full papers were carefully selected from 50 submissions. The papers are organized in topical sections on discrete geometric models and transforms; discrete topology; graph-based models, analysis and segmentation; mathematical morphology; shape representation, recognition and analysis; and geometric computation.

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Discrete Geometric Models and Transforms.- Digital Two-dimensional Bijective Reflection and Associated Rotation.- Digital Curvature Evolution Model for Image Segmentation.- Rhombic Dodecahedron Grid { Coordinate System and 3D Digital Object Definitions.- Facet Connectedness of Arithmetic Discrete Hyperplanes with Non Zero Shift.- Local Turn-boundedness: a Curvature Control for a Good Digitization.- Distance Transform based on Weight Sequences.- Stochastic Distance Transform.- Discrete Topology.- Filtration Simplification for Persistent Homology via Edge Contraction.- One More Step towards Well-composedness of Cell Complexes over nD Pictures.- On the Space between Critical Points.- Rigid Motions in the Cubic Grid: A Discussion on Topological Issues.- Graph-based Models, Analysis and Segmentation.- A New Entropy for Hypergraphs.- Graph-based Segmentation with Local Band Constraints.- A Study of Observation Scales based on Felzenswalb-Huttenlocher Dissimilarity Measure for Hierarchical Segmentation.- The Role of Optimum Connectivity in Image Segmentation: Can the algorithm learn object information during the process?.- On the Degree Sequence of 3-uniform Hypergraph: A New Sufficient Condition.- Optimization of Max-Norm Objective Functions in Image Processing and Computer Vision.- Common Object Discovery as Local Search for Maximum Weight Cliques in a Global Object Similarity Graph.- Reconstruction of the Crossing Type of a Point Set from the Compatible Exchange Graph of Noncrossing Spanning Trees.- Mathematical Morphology.- Vector-based Mathematical Morphology Operations on Polygons Using Straight Skeletons for Digital Pathology.- Morphological Networks for Image De-raining.- Minimal Component-Hypertrees.- Single Scan Granulometry Estimation from an Asymmetric Distance Map.- Recognizing Hierarchical Watersheds.- Shape Representation, Recognition and Analysis.- Straight Line Reconstruction for Fully Materialized Table Extraction in Degraded Document Images.- A Spatial Convexity Descriptor for Object Enlacement.- The Propagating Skeleton: A Robust Detail-preserving Approach.- Non-Centered Voronoi Skeletons.- Dual Approaches for Elliptic Hough Transform: Eccentricity/Orientation vs Center based.- Digital Plane Recognition with Fewer Probes.- Geometric Computation.- Convex and Concave Vertices on a Simple Closed Curve in the Triangular Grid.- Efficient Algorithms to Test Digital Convexity.- Compact Packings of the Plane with Three Sizes of Discs.- Convex Aggregation Problems in 2 .- Polygon Approximations of the Euclidean Circles on the Square Grid by Broadcasting Sequences.- Unfolding Level 1 Menger Polycubes of Arbitrary Size with Help of Outer Faces.- A Discrete Bisector Function Based on Annulus.- Average Curve of n Digital Curves.

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