  Point cloud is an important type of 3D representation. However, directly
applying convolutions on point clouds is challenging due to the sparse,
irregular and unordered data structure. In this paper, we propose a novel
Interpolated Convolution operation, InterpConv, to tackle the point cloud
feature learning and understanding problem. The key idea is to utilize a set of
discrete kernel weights and interpolate point features to neighboring
kernel-weight coordinates by an interpolation function for convolution. A
normalization term is introduced to handle neighborhoods of different sparsity
levels. Our InterpConv is shown to be permutation and sparsity invariant, and
can directly handle irregular inputs. We further design Interpolated
Convolutional Neural Networks (InterpCNNs) based on InterpConv layers to handle
point cloud recognition tasks including shape classification, object part
segmentation and indoor scene semantic parsing. Experiments show that the
networks can capture both fine-grained local structures and global shape
context information effectively. The proposed approach achieves
state-of-the-art performance on public benchmarks including ModelNet40,
ShapeNet Parts and S3DIS.
