用神经网络高效计算形状签名，提升图像分割的几何精度。
Harmonic Beltrami Signature Network: a Shape Prior Module in Deep Learning Framework
- 通过预/后空间变换网络与UNet结构，实现形状归一化与角度正则化。
- 在复杂形状上准确提取哈密顿贝尔特拉米签名，保持平移旋转缩放不变性。
- 可嵌入现有分割模型，适合需要几何先验的医学图像分析场景。
本文提出一种名为调和贝尔特拉米签名网络（HBSN）的新颖深度学习架构，用于从二值图像中计算调和贝尔特拉米签名（HBS）。HBS是一种形状表示方法，能与二维单连通形状建立一一对应关系，并具备平移、缩放和旋转不变性。利用神经网络的函数逼近能力，HBSN实现了形状先验信息的高效提取与应用。该网络包含一个预空间变换网络（pre-STN）用于形状归一化，一个基于UNet的主干网络用于预测HBS，以及一个后空间变换网络（post-STN）进行角度正则化。实验表明，即使对于复杂形状，HBSN也能准确计算出HBS表示。此外，我们展示了如何将HBSN直接集成到现有的深度学习分割模型中，通过引入形状先验显著提升性能。结果证实，HBSN可作为通用模块嵌入计算机视觉流程，有效融入几何形状信息。
原文摘要 · Abstract (English)
This paper presents the Harmonic Beltrami Signature Network (HBSN), a novel deep learning architecture for computing the Harmonic Beltrami Signature (HBS) from binary-like images. HBS is a shape representation that provides a one-to-one correspondence with 2D simply connected shapes, with invariance to translation, scaling, and rotation. By exploiting the function approximation capacity of neural networks, HBSN enables efficient extraction and utilization of shape prior information. The proposed network architecture incorporates a pre-Spatial Transformer Network (pre-STN) for shape normalization, a UNet-based backbone for HBS prediction, and a post-STN for angle regularization. Experiments show that HBSN accurately computes HBS representations, even for complex shapes. Furthermore, we demonstrate how HBSN can be directly incorporated into existing deep learning segmentation models, improving their performance through the use of shape priors. The results confirm the utility of HBSN as a general-purpose module for embedding geometric shape information into computer vision pipelines.
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