  Deep neural networks have enjoyed remarkable success for various vision
tasks, however it remains challenging to apply CNNs to domains lacking a
regular underlying structures such as 3D point clouds. Towards this we propose
a novel convolutional architecture, termed SpiderCNN, to efficiently extract
geometric features from point clouds. SpiderCNN is comprised of units called
SpiderConv, which extend convolutional operations from regular grids to
irregular point sets that can be embedded in R^n, by parametrizing a family of
convolutional filters. We design the filter as a product of a simple step
function that captures local geodesic information and a Taylor polynomial that
ensures the expressiveness. SpiderCNN inherits the multi-scale hierarchical
architecture from classical CNNs, which allows it to extract semantic deep
features. Experiments on ModelNet40 demonstrate that SpiderCNN achieves
state-of-the-art accuracy 92.4% on standard benchmarks, and shows competitive
performance on segmentation task.
