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This book constitutes the refereed proceedings of the Third International Joint Conference on Discrete Geometry and Mathematical Morphology, DGMM 2024, held in Florence, Italy during April 15-18, 2024.
The 34 full papers included in this book were carefully reviewed and selected from 51 submissions. They were organized in topical sections as follows: Digital Geometry - Models, Transforms, and Visualization; Computational Aspects of Discrete Structures and Tilings; Learning Based Morphology; Hierarchical and Graph-Based Models, Analysis and Segmentation; Discrete and Combinatorial Topology; and Mathematical Morphology and Digital Geometry for Applications.
List of contents
.- Digital Geometry - Models, Transforms, and Visualization.
.- Bijectivity analysis of finite rotations on Z 2 A hierarchical approach.
.- Recognition of arithmetic line segments and hyperplanes using the Stern-Brocot tree.
.- Bijective Digitized 3D Rotation Based on Beam Shears.-
.- New characterizations of full convexity.- Decomposition of Rational Discrete Planes.
.- Differential Maximum Euclidean Distance Transform Computation in Component Trees .
.- Construction of Fast and Accurate 2D Bijective Rigid Transformation .
.- Digital Calculus Frameworks and Comparative Evaluation of their Laplace-Beltrami operators .
.- Fitting egg-shapes to discretized object boundaries .
.- Computational Aspects of Discrete Structures and Tilings.
.- Construction of Tilings with Transitivity Properties on the Square Grid .
.- Some geometric and tomographic results on gray-scale images .
.- A Khalimsky-like Topology on the Triangular Grid .
.- Learning Based Morphology.
.- Group Equivariant Networks Using Morphological Operators.
.- An Algorithm to Train Unrestricted Sequential Discrete Morphological Neural Networks .
.- Discovering Repeated Patterns From the Onsets in a Multidimensional Representation of Music .
.- The Lattice Overparametrization Paradigm for the Machine Learning of Lattice Operators .
.- Convex Optimization for Binary Tree-Based Transport Networks .
.- Training morphological neural networks with gradient descent: some theoretical insights.
.- HaarNet: Large-scale Linear-Morphological Hybrid Network for RGB-D Semantic Segmentation .
.- Nonlinear representation theory of equivariant CNNs on homogeneous spaces using group morphology .
.- Hierarchical and Graph-Based Models, Analysis and Segmentation.
.- Building the Topological Tree of Shapes from the Tree of Shapes.
.- End-to-end Ultrametric Learning for Hierarchical Segmentation .
.- Out-of-core Attribute Algorithms for Binary Partition Hierarchies .
.- Multi Scale Component Tree: A Hierarchical Representation for Sparse Objects .
.- An Approach to Colour Morphological Supremum Formation using the LogSumExp Approximation .
.- Image Segmentation by Hierarchical Layered Oriented Image Foresting Transform Subject to Closeness Constraints .
.- Discrete and Combinatorial Topology.
.- Elastic Analysis of Augmented Curves and Constrained Surfaces .
.- Morse Frames .- Morse Sequences.
.- 1Attempt and Equivalent Thinning on the Hexagonal Grid.
.- A survey on 2D Euclidean curve classes in discrete geometry with new results.
.- Mathematical Morphology and Digital Geometry for applications.
.- Counting melanocytes with trainable h-maxima and connected component layers.
.- Mathematical Morphology Applied to Feature Extraction in Music Spectrograms.
.- A Discrete Geometry Method for Atom Depth Computation in Complex Molecular Systems.
