mlsanityData to 7 Oct 2026

A Multi-parameter Persistence Framework for Mathematical Morphology

arXiv 2103.13013 ↗First posted 24 Mar 2021cs.CG cs.CV math.ATcited by 2

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Abstract (arXiv)

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.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 12 of its 74 references that are in the map. First posted on arXiv 24 Mar 2021.

Builds on

12 of 74 references.

References · 12

  1. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
  2. 2017Skin Lesion Analysis Toward Melanoma Detection: A Challenge at the 2017 International Symposium on Biomedical Imaging (ISBI), Hosted by the International Skin Imaging Collaboration (ISIC)cited by 549
  3. 2019A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homologycited by 134
  4. 2015A roadmap for the computation of persistent homologycited by 126
  5. 2019A Topology Layer for Machine Learningcited by 79
  6. 2018Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topologycited by 73
  7. 2019A Topological "Reading" Lesson: Classification of MNIST using TDAcited by 21
  8. 2018A Kernel for Multi-Parameter Persistent Homologycited by 12
  9. 2021TDA-Net: Fusion of Persistent Homology and Deep Learning Features for COVID-19 Detection in Chest X-Ray Imagescited by 12
  10. 2017Persistence Diagrams with Linear Machine Learning Modelscited by 7
  11. 2018A salt and pepper noise image denoising method based on the generative classificationcited by 1
  12. 2019Convolutional Neural Network with Median Layers for Denoising Salt-and-Pepper Contaminationscited by 1

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Cited by year

Citing papers per year: 2022: 1; 2023: 0; 2024: 0; 2025: 1.

2 papers.

  1. 2025CuMPerLay: Learning Cubical Multiparameter Persistence Vectorizationscited by 1
  2. 2022Convolutional Persistence Transformscited by 0