  We present a novel 3D shape completion method that operates directly on
unstructured point clouds, thus avoiding resource-intensive data structures
like voxel grids. To this end, we introduce KAPLAN, a 3D point descriptor that
aggregates local shape information via a series of 2D convolutions. The key
idea is to project the points in a local neighborhood onto multiple planes with
different orientations. In each of those planes, point properties like normals
or point-to-plane distances are aggregated into a 2D grid and abstracted into a
feature representation with an efficient 2D convolutional encoder. Since all
planes are encoded jointly, the resulting representation nevertheless can
capture their correlations and retains knowledge about the underlying 3D shape,
without expensive 3D convolutions. Experiments on public datasets show that
KAPLAN achieves state-of-the-art performance for 3D shape completion.
