Scalar Function Topology Divergence: Comparing Topology of 3D Objects
cs.CV, cs.LG, math.AT, math.CO, math.MG
Submitted: 2024-07-11
Updated: 2024-11-12
Journal ref: ECCV 2024
DOI: 10.1007/978-3-031-73223-2_16
Code: https://github.com/IlyaTrofimov/SFTD
License: http://creativecommons.org/licenses/by/4.0/
The gist: We propose a new topological tool for computer vision - Scalar Function Topology Divergence (SFTD), which measures the dissimilarity of multi-scale topology between sublevel sets of two functions
Terminology
Abstract
We propose a new topological tool for computer vision - Scalar Function Topology Divergence (SFTD), which measures the dissimilarity of multi-scale topology between sublevel sets of two functions having a common domain. Functions can be defined on an undirected graph or Euclidean space of any dimensionality. Most of the existing methods for comparing topology are based on Wasserstein distance between persistence barcodes and they don't take into account the localization of topological features. The minimization of SFTD ensures that the corresponding topological features of scalar functions are located in the same places. The proposed tool provides useful visualizations depicting areas where functions have topological dissimilarities. We provide applications of the proposed method to 3D computer vision. In particular, experiments demonstrate that SFTD as an additional loss improves the reconstruction of cellular 3D shapes from 2D fluorescence microscopy images, and helps to identify topological errors in 3D segmentation. Additionally, we show that SFTD outperforms Betti matching loss in 2D segmentation problems.
Sources
- The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic Classification
- Representation Topology Divergence: A Method for Comparing Neural Network Representations
- Loss Barcode: A Topological Measure of Escapability in Loss Landscapes
- An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists
- Swin UNETR: Swin Transformers for Semantic Segmentation of Brain Tumors in MRI Images
- Topological Graph Neural Networks
- Topology-Aware Segmentation Using Discrete Morse Theory
- Improving Self-supervised Molecular Representation Learning using Persistent Homology
- Learning Topology-Preserving Data Representations
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