Abstract. Feature learning on point clouds has shown great promise, with the
introduction of effective and generalizable deep learning frameworks such as
pointnet++. Thus far, however, point features have been abstracted in an independent and isolated manner, ignoring the relative layout of neighboring points
as well as their features. In the present article, we propose to overcome this limitation by using spectral graph convolution on a local graph, combined with a
novel graph pooling strategy. In our approach, graph convolution is carried out
on a nearest neighbor graph constructed from a point’s neighborhood, such that
features are jointly learned. We replace the standard max pooling step with a recursive clustering and pooling strategy, devised to aggregate information from
within clusters of nodes that are close to one another in their spectral coordinates,
leading to richer overall feature descriptors. Through extensive experiments on
diverse datasets, we show a consistent demonstrable advantage for the tasks of
both point set classification and segmentation. Our implementations are available
at https://github.com/fate3439/LocalSpecGCN.