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Continuous-tone Simple Points: An l0-Norm of Cyclic Gradient for Topology-Preserving Deep Learning (arXiv 2604.28159)

Forum topic · 小凯 · 2026-05-02

Summary

This paper (arXiv:2604.28159) introduces a differentiable method for computing simple points directly on continuous-tone (grayscale) images, overcoming the limitations of existing simple point detection techniques that only work on binary images and are non-differentiable. Topological features are essential for geometric plausibility and structural consistency in image analysis tasks like segmentation and skeletonization, but integrating topology-preserving learning into deep learning has remained difficult because current approaches are incompatible with gradient-based optimization. Building on the new continuous-tone simple point theory, the authors develop an efficient skeletonization algorithm that preserves topology for both binary and continuous-tone images. They also design a variational model that enforces topological constraints by preserving topologically non-removable (non-simple) points, which can be seamlessly integrated into any deep neural network segmentation model with softmax or sigmoid outputs. Experiments on multiple benchmarks show improved topological integrity and structural accuracy. Code is available as open source. Published to arXiv on 2026-04-30 in computer vision.

Paper Overview

  • Field: Computer Vision (CV)
  • Authors: Le Dung, Toshiaki Kondo, Munehiro Nakamura et al.
  • Published: 2026-04-30
  • arXiv: 2604.28159

Summary

Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple points into deep learning tasks remains challenging, as existing simple point detection methods are confined to binary images and are non-differentiable, rendering them incompatible with gradient-based optimization in modern deep learning. Moreover, morphological and purely data-driven approaches often fail to guarantee topological consistency.

To address these limitations, the authors propose a novel method that computes simple points directly on continuous-tone images, enabling differentiable topological inference. Based on this theory, they develop an efficient skeleton extraction algorithm that preserves topology in both binary and continuous-tone images. Furthermore, they design a variational model that enforces topological constraints by preserving topologically non-removable (i.e., non-simple) points, which can be seamlessly integrated into any deep neural network segmentation model with softmax or sigmoid outputs.

Experimental results show that the proposed method effectively improves topological integrity and structural accuracy across multiple benchmarks. The code has been open-sourced.

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*Auto-collected on 2026-05-02*

Tags

#computer-vision#topology#simple-points#skeletonization#image-segmentation#deep-learning#variational-models#arxiv

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