用微分同胚变形+梯度场匹配，实现无需大量数据的精准图像分割
A new approach for image segmentation based on diffeomorphic registration and gradient fields
- 通过微分同胚变形模板曲线来拟合目标边界
- 利用梯度场与变体表示的损失函数提升分割精度
- 无需大规模训练数据，适合小样本场景
图像分割是计算机视觉中的基础任务，旨在精确勾勒图像中物体的边界。传统方法如边缘检测和变分法已被广泛研究，而深度学习虽取得进展，但通常依赖大量标注数据。本文提出一种基于形状分析与微分同胚变换的新型2D图像分割变分框架。该方法将分割建模为模板曲线在图像域上的微分同胚变形，采用大变形微分同胚度量映射（LDDMM）框架。曲线演化由一个损失函数驱动，该函数通过几何形状的变体表示，比较变形后的曲线与图像梯度场的差异。方法使用Python实现，并借助PyKeops库实现GPU加速。该框架具有灵活且理论严谨的特点，无需依赖大规模数据集即可实现高精度分割。
原文摘要 · Abstract (English)
Image segmentation is a fundamental task in computer vision aimed at delineating object boundaries within images. Traditional approaches, such as edge detection and variational methods, have been widely explored, while recent advances in deep learning have shown promising results but often require extensive training data. In this work, we propose a novel variational framework for 2D image segmentation that integrates concepts from shape analysis and diffeomorphic transformations. Our method models segmentation as the deformation of a template curve via a diffeomorphic transformation of the image domain, using the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. The curve evolution is guided by a loss function that compares the deformed curve to the image gradient field, formulated through the varifold representation of geometric shapes. The approach is implemented in Python with GPU acceleration using the PyKeops library. This framework allows for accurate segmentation with a flexible and theoretically grounded methodology that does not rely on large datasets.
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