  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.
