Regularized topological data analysis for extraction of coherent brain regions

Ishaan Batta, Nicolas Honnorat, Christos Davatzikos

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Clustering is widely used in medical imaging to reduce data dimension and discover subgroups in patient populations. However, most of the current clustering algorithms depend on scale parameters which are especially difficult to select. Persistence homology has been introduced to address this issue. This topological data analysis framework analyses a dataset at multiple scales by generating clusters of increasing sizes, similar to single-linkage hierarchical clustering. Because of this approach, however, the results are sensitive to the presence of noise and outliers. Several strategies have been suggested to fix this issue. In this paper, we support this research effort by demonstrating how gradient preserving data smoothings, such as total variation regularization, can improve the stability of persistence homology results, and we derive analytical confidence regions for the significance of the persistence measured for clusters based on Pearson distances. We demonstrate the advantages of our methods by analysing structural and functional MRI data released by the Human Connectome Project.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2019
Subtitle of host publicationImage Processing
EditorsElsa D. Angelini, Elsa D. Angelini, Elsa D. Angelini, Bennett A. Landman
ISBN (Electronic)9781510625457
StatePublished - 2019
Externally publishedYes
EventMedical Imaging 2019: Image Processing - San Diego, United States
Duration: Feb 19 2019Feb 21 2019

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
ISSN (Print)1605-7422


ConferenceMedical Imaging 2019: Image Processing
Country/TerritoryUnited States
CitySan Diego


  • brain parcellation
  • hierarchical clustering
  • neuroimaging
  • persistent homology
  • topological data analysis
  • total variation de-noising

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Biomaterials
  • Radiology Nuclear Medicine and imaging


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