首次从图像中学习形状变形的测地线流，实现精准对齐与比较。
Learning Geodesics of Geometric Shape Deformations From Images
- 用神经算子直接学习测地线变形映射，避免依赖初始条件。
- 在2D合成数据和3D脑MRI上实现高精度形状对齐，验证了方法有效性。
- 适合医学图像分析、三维形变建模等需要精确几何变换的研究者。
本文提出一种新方法——测地线可变形网络（GDN），首次实现了从图像中学习变形场的测地线流。测地线变形即配对图像间最优变换，由满足非线性微分方程的光滑矢量场序列参数化。现有工作多聚焦于通过配准网络学习初始条件（如初速度场），但测地线本身的定义未被网络捕捉。为此，我们设计了一种高效的神经算子，将测地线视为从潜在变形空间中学习的未知映射函数，并通过积分算子与平滑激活函数组合有效逼近该映射。与以往方法不同，GDN联合优化一种新型测地线损失，显著提升网络的正则化能力和泛化性能。我们在2D合成数据和3D真实脑部磁共振成像（MRI）数据上验证了GDN的有效性。
原文摘要 · Abstract (English)
This paper presents a novel method, named geodesic deformable networks (GDN), that for the first time enables the learning of geodesic flows of deformation fields derived from images. In particular, the capability of our proposed GDN being able to predict geodesics is important for quantifying and comparing deformable shape presented in images. The geodesic deformations, also known as optimal transformations that align pairwise images, are often parameterized by a time sequence of smooth vector fields governed by nonlinear differential equations. A bountiful literature has been focusing on learning the initial conditions (e.g., initial velocity fields) based on registration networks. However, the definition of geodesics central to deformation-based shape analysis is blind to the networks. To address this problem, we carefully develop an efficient neural operator to treat the geodesics as unknown mapping functions learned from the latent deformation spaces. A composition of integral operators and smooth activation functions is then formulated to effectively approximate such mappings. In contrast to previous works, our GDN jointly optimizes a newly defined geodesic loss, which adds additional benefits to promote the network regularizability and generalizability. We demonstrate the effectiveness of GDN on both 2D synthetic data and 3D real brain magnetic resonance imaging (MRI).
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。