  We present an Adaptive Octree-based Convolutional Neural Network (Adaptive
O-CNN) for efficient 3D shape encoding and decoding. Different from
volumetric-based or octree-based CNN methods that represent a 3D shape with
voxels in the same resolution, our method represents a 3D shape adaptively with
octants at different levels and models the 3D shape within each octant with a
planar patch. Based on this adaptive patch-based representation, we propose an
Adaptive O-CNN encoder and decoder for encoding and decoding 3D shapes. The
Adaptive O-CNN encoder takes the planar patch normal and displacement as input
and performs 3D convolutions only at the octants at each level, while the
Adaptive O-CNN decoder infers the shape occupancy and subdivision status of
octants at each level and estimates the best plane normal and displacement for
each leaf octant. As a general framework for 3D shape analysis and generation,
the Adaptive O-CNN not only reduces the memory and computational cost, but also
offers better shape generation capability than the existing 3D-CNN approaches.
We validate Adaptive O-CNN in terms of efficiency and effectiveness on
different shape analysis and generation tasks, including shape classification,
3D autoencoding, shape prediction from a single image, and shape completion for
noisy and incomplete point clouds.
