基于曲率能量的变分法自动提取图像中1D结构
A variational method for curve extraction with curvature-dependent energies
- 用能量泛函离散化与向量场分解设计曲线提取方法
- 无需标注即可自动识别图像中的1D结构，效果优于传统方法
- 适用于医学图像、神经纤维等曲率敏感场景
我们提出一种基于能量离散化和Smirnov向量场分解定理的变分方法，用于在预设端点间提取曲线。该方法被扩展至曲率依赖能量形式，通过将曲线提升到位置与方向空间，并采用适当的子黎曼或芬斯勒度量，实现对图像中1D结构的自动提取，主要为无监督学习。该框架能有效捕捉具有复杂曲率特征的细长结构。
原文摘要 · Abstract (English)
We introduce a variational approach for extracting curves between a list of possible endpoints, based on the discretization of an energy and Smirnov's decomposition theorem for vector fields. It is used to design a bi-level minimization approach to automatically extract curves and 1D structures from an image, which is mostly unsupervised. We extend then the method to curvature-dependent energies, using a now classical lifting of the curves in the space of positions and orientations equipped with an appropriate sub-Riemanian or Finslerian metric.
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