Summary of Scalar Function Topology Divergence: Comparing Topology Of 3d Objects, by Ilya Trofimov et al.
Scalar Function Topology Divergence: Comparing Topology of 3D Objects
by Ilya Trofimov, Daria Voronkova, Eduard Tulchinskii, Evgeny Burnaev, Serguei Barannikov
First submitted to arxiv on: 11 Jul 2024
Categories
- Main: Computer Vision and Pattern Recognition (cs.CV)
- Secondary: Machine Learning (cs.LG); Algebraic Topology (math.AT); Metric Geometry (math.MG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed Scalar Function Topology Divergence (SFTD) is a novel tool for computer vision that measures the dissimilarity of multi-scale topology between sublevel sets of two functions sharing a common domain. This method differs from existing approaches, which rely on Wasserstein distance and neglect the localization of topological features. SFTD minimizes the divergence to ensure corresponding topological features are situated in similar areas. The tool provides visualizations highlighting regions where function topologies diverge. Applications include 3D computer vision, where SFTD improves cellular shape reconstruction from 2D microscopy images and identifies topological errors in 3D segmentation. SFTD also outperforms Betti matching loss in 2D segmentation tasks. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Scalar Function Topology Divergence (SFTD) is a new way to compare pictures or shapes in computer vision. It helps us understand how different two functions are, not just at a single point, but across many scales and locations. This is useful for tasks like reconstructing 3D shapes from 2D images or identifying errors in shape recognition. SFTD provides visual tools that show where the differences are most significant. |
