  Graph convolutional networks are a new promising learning approach to deal
with data on irregular domains. They are predestined to overcome certain
limitations of conventional grid-based architectures and will enable efficient
handling of point clouds or related graphical data representations, e.g.
superpixel graphs. Learning feature extractors and classifiers on 3D point
clouds is still an underdeveloped area and has potential restrictions to equal
graph topologies. In this work, we derive a new architectural design that
combines rotationally and topologically invariant graph diffusion operators and
node-wise feature learning through 1x1 convolutions. By combining multiple
isotropic diffusion operations based on the Laplace-Beltrami operator, we can
learn an optimal linear combination of diffusion kernels for effective feature
propagation across nodes on an irregular graph. We validated our approach for
learning point descriptors as well as semantic classification on real 3D point
clouds of human poses and demonstrate an improvement from 85% to 95% in Dice
overlap with our multi-kernel approach.
