ArticleIEEE transactions on pattern analysis and machine intelligence2020
Hyperbolic Wasserstein Distance for Shape Indexing.
Article in IEEE transactions on pattern analysis and machine intelligence, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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Who cites it
8 citing papers in PubMed.
- Hippocampal surface analysis using discrete Ricci flow and Riemannian metrics for the diagnosis of Alzheimer's disease.Research square · 2026Article
- Quantification of planar cortical magnification with optimal transport and topological smoothing.NeuroImage · 2026Article
- Article
- Statistical Learning Methods for Neuroimaging Data Analysis with Applications.Annual review of biomedical data science · 2023Review
- Cortical Surface Shape Analysis Based on Alexandrov Polyhedra.Proceedings. IEEE International Conference on Computer Vision · 2021Article
- Cortical Morphometry Analysis based on Worst Transportation Theory.Information processing in medical imaging : proceedings of the ... conference · 2021Article
- Predicting future cognitive decline with hyperbolic stochastic coding.Medical image analysis · 2021Article
- Computing Univariate Neurodegenerative Biomarkers with Volumetric Optimal Transportation: A Pilot Study.Neuroinformatics · 2020Article
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2 authors.
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Abstract
Shape space is an active research topic in computer vision and medical imaging fields. The distance defined in a shape space may provide a simple and refined index to represent a unique shape. This work studies the Wasserstein space and proposes a novel framework to compute the Wasserstein distance between general topological surfaces by integrating hyperbolic Ricci flow, hyperbolic harmonic map, and hyperbolic power Voronoi diagram algorithms. The resulting hyperbolic Wasserstein distance can intrinsically measure the similarity between general topological surfaces. Our proposed algorithms are theoretically rigorous and practically efficient. It has the potential to be a powerful tool for 3D shape indexing research. We tested our algorithm with human face classification and Alzheimer's disease (AD) progression tracking studies. Experimental results demonstrated that our work may provide a succinct and effective shape index.
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