-- 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.

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.