🍩 Database of Original & Non-Theoretical Uses of Topology

1. Topology-Based Signal Separation (2004)

   V. Robins, N. Rooney, E. Bradley

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   • Signal Processing
   • Dynamical system
   • Betti numbers
   • Noise
   • Time series
   • minimal spanning tree
   • nearest neighbor graph

2. A Multi-Parameter Persistence Framework for Mathematical Morphology (2021)

   Yu-Min Chung, Sarah Day, Chuan-Shen Hu

   Abstract

   The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis. We demonstrate that morphological operations naturally form a multiparameter filtration and that persistent homology can then be used to extract information about both topology and geometry in the images as well as to automate methods for optimizing the study and rendering of structure in images. For illustration, we apply this framework to analyze noisy binary, grayscale, and color images.

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   • Computer vision
   • Pattern recognition
   • images
   • images:binary
   • images:colour
   • images:grey scale
   • Multiparameter persistence
   • Persistent homology
   • Salt and pepper noise