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This book constitutes the proceedings of the Second IAPR International Conference on Discrete Geometry and Mathematical Morphology, DGMM 2022, which was held during October 24-27, 2022, in Strasbourg, France.The 33 papers included in this volume were carefully reviewed and selected from 45 submissions. They were organized in topical sections as follows: discrete and combinatorial topology; discrete tomography and inverse problems; multivariate and PDE-based mathematical morphology, morphological filtering; hierarchical and Graph-Based Models, Analysis and Segmentation; discrete geometry - models, transforms, and visualization; learning based morphology to Mathematical Morphology; and distance transform.
The book also contains 3 invited keynote papers.
List of contents
Invited papers.- Reflections on a Scientific Career and its Possible Legacy.- Hybrid Artificial Intelligence for Knowledge Representation and Model-based Medical Image Understanding - Towards Explainability.- Digital Geometry, Mathematical Morphology, and Discrete Optimization: a survey.- Discrete and combinatorial topology.- Gradient Vector Fields of Discrete Morse Functions and Watershed-cuts.- Towards topological analysis of non-symmetric tensor fields via complexification.- A Heuristic for Short Homology Basis of Digital Objects.- Completions and ramifications.- Algorithms for pixelwise shape deformations preserving digital convexity.- Full convexity for polyhedral models in digital spaces.- Implicit Encoding and Simplification/Reduction of nGmaps.- Topological analysis of simple segmentation maps.- Discrete tomography and inverse problems.- On the Decomposability of Homogeneous Binary Planar Configurations with respect to a given Exact Polyomino.- Properties of SAT formulas characterizing convex sets with given projections.- Multivariate and PDE-based mathematical morphology, morphological filtering.- Morphological counterpart of Ornstein-Uhlenbeck semigroups and PDEs.- A novel approach for computation of morphological operations using the number theoretic transform.- Equivariance-Based Analysis of PDE Evolutions Related to Multivariate Medians.- Differential Oriented Image Foresting Transform Segmentation by Seed Competition.- Hierarchical and Graph-Based Models, Analysis and Segmentation.- A Topological Tree of Shapes.- Component-Tree Simplification through Fast Alpha Cuts.- Approximation of Digital Surfaces by a Hierarchical Set of Planar Patches.- Component Tree Loss Function: Definition and Optimization.- Fast and Effective Superpixel Segmentation using Accurate Saliency Estimation.- Join, select, and insert: efficient out-of-core algorithms for hierarchical segmentation trees.- Graph-Based Image Segmentation With Shape Priors and Band Constraints.- Discrete geometry - models, transforms, and visualization.- Tangential cover for 3D irregular noisy digital curves.- A Curious Invariance Property of Certain Perfect Legendre Arrays: Stirring Without Mixing.- A Simple Discrete Calculus for Digital Surfaces.- Distance-Driven Curve-Thinning on the Face-Centered Cubic Grid.- A new lattice-based plane-probing algorithm.- Exact and Optimal Conversion of a Hole-free 2D Digital Object into a Union of Balls in Polynomial Time.- Density functions of periodic sequences.- Learning based morphology to Mathematical Morphology.- Morphological adjunctions represented by matrices in max-plus algebra for signal and image processing.- MorphoActivations: Generalizing ReLU activations by mathematical morphology.- Logarithmic Morphological Neural Nets robust to lighting variations.- Distance transform.- Introduction to Discrete Soft Transforms.- On the Validity of the Two Raster Sequences Distance TransformAlgorithm.
