Morphological Perceptrons: Geometry and Training Algorithms

DOI10.1007/978-3-319-57240-6_1zbMath1428.94018OpenAlexW2607150727MaRDI QIDQ5270528

Petros Maragos, Vasileios Charisopoulos

Publication date: 23 June 2017

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-57240-6_1

zbMATH Keywords

optimizationneural networksmachine learningmathematical morphologytropical geometry

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08)

Related Items (12)

Toward a sparsity theory on weighted lattices ⋮ Learning grayscale mathematical morphology with smooth morphological layers ⋮ MorphoActivation: generalizing ReLU activation function by mathematical morphology ⋮ Logarithmic morphological neural nets robust to lighting variations ⋮ Generalized morphological components based on interval descriptors and \(n\)-ary aggregation functions ⋮ Approximating morphological operators with part-based representations learned by asymmetric auto-encoders ⋮ Dynamical systems on weighted lattices: general theory ⋮ Some open questions on morphological operators and representations in the deep learning era. A personal vision ⋮ On some associations between mathematical morphology and artificial intelligence ⋮ Going beyond p-convolutions to learn grayscale morphological operators ⋮ Sparse approximate solutions to max-plus equations ⋮ Learnable Empirical Mode Decomposition based on Mathematical Morphology

Uses Software

• MNIST
• CVXPY
• DCCP

Cites Work

• Morphological perceptrons with competitive learning: lattice-theoretical framework and constructive learning algorithm
• Minimal half-spaces and external representation of tropical polyhedra
• Morphology neural networks: An introduction with applications
• Minimax algebra
• Graphs, dioids and semirings. New models and algorithms.
• CVXPY: A Python-Embedded Modeling Language for Convex Optimization
• Tropicalizing the Simplex Algorithm
• Multisurface method of pattern separation for medical diagnosis applied to breast cytology.
• Max-linear Systems: Theory and Algorithms
• Lectures on Polytopes
• The Concave-Convex Procedure
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