Feature descriptors play a crucial role in a wide range of geometry analysis
and processing applications, including shape correspondence, retrieval, and
segmentation. In this paper, we introduce Geodesic Convolutional Neural
Networks (GCNN), a generalization of the convolutional networks (CNN) paradigm
to non-Euclidean manifolds. Our construction is based on a local geodesic
system of polar coordinates to extract "patches", which are then passed through
a cascade of filters and linear and non-linear operators. The coefficients of
the filters and linear combination weights are optimization variables that are
learned to minimize a task-specific cost function. We use GCNN to learn
invariant shape features, allowing to achieve state-of-the-art performance in
problems such as shape description, retrieval, and correspondence.

本文提出了一种称为 “测地线卷积神经网络”（GCNN）的新型神经网络，可用于处理形状相关的任务，例如形状描述，检索以及匹配。GCNN 使用局部极坐标系中的局部测地线系统提取 “补丁”，通过一系列过滤器和线性非线性算子，来学习不变的形状特征，从而获得最先进的性能。