论文标题
差异组的深度神经网络，用于最佳形状重新聚集
Deep neural networks on diffeomorphism groups for optimal shape reparameterization
论文作者
论文摘要
形状分析中的基本问题之一是在计算其形状之间的大地距离之前对齐曲线或表面。找到实现这种对齐的最佳修复化是一项计算要求的任务，通常是通过在差异组上解决优化问题来完成的。在本文中，我们提出了一种算法，用于通过基本差异性的组成来构建定向差异的近似。该算法是使用Pytorch实施的，并且适用于未参数化的曲线和表面。此外，我们显示了构造体系结构的通用近似特性，并获得了所得差异性的Lipschitz常数的边界。
One of the fundamental problems in shape analysis is to align curves or surfaces before computing geodesic distances between their shapes. Finding the optimal reparametrization realizing this alignment is a computationally demanding task, typically done by solving an optimization problem on the diffeomorphism group. In this paper, we propose an algorithm for constructing approximations of orientation-preserving diffeomorphisms by composition of elementary diffeomorphisms. The algorithm is implemented using PyTorch, and is applicable for both unparametrized curves and surfaces. Moreover, we show universal approximation properties for the constructed architectures, and obtain bounds for the Lipschitz constants of the resulting diffeomorphisms.
