Topology-Guaranteed Image Segmentation: Enforcing Connectivity, Genus, and Width Constraints
Wenxiao Li, Xue-Cheng Tai, Jun Liu

TL;DR
This paper introduces a novel mathematical framework that integrates width information into topological features for image segmentation, ensuring preservation of connectivity, genus, and width constraints through variational models and neural networks.
Contribution
It proposes a new approach combining persistent homology and PDE smoothing to incorporate width into topological analysis for segmentation.
Findings
Successfully preserves topological invariants like connectivity and genus.
Effectively embeds width properties such as thickness and length into segmentation.
Demonstrates improved topological fidelity in numerical experiments.
Abstract
Existing research highlights the crucial role of topological priors in image segmentation, particularly in preserving essential structures such as connectivity and genus. Accurately capturing these topological features often requires incorporating width-related information, including the thickness and length inherent to the image structures. However, traditional mathematical definitions of topological structures lack this dimensional width information, limiting methods like persistent homology from fully addressing practical segmentation needs. To overcome this limitation, we propose a novel mathematical framework that explicitly integrates width information into the characterization of topological structures. This method leverages persistent homology, complemented by smoothing concepts from partial differential equations (PDEs), to modify local extrema of upper-level sets. This…
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Taxonomy
TopicsTopological and Geometric Data Analysis · Advanced Graph Neural Networks · Digital Image Processing Techniques
