  We propose a novel convolutional operator for the task of point cloud
completion. One striking characteristic of our approach is that, conversely to
related work it does not require any max-pooling or voxelization operation.
Instead, the proposed operator used to learn the point cloud embedding in the
encoder extracts permutation-invariant features from the point cloud via a
soft-pooling of feature activations, which are able to preserve fine-grained
geometric details. These features are then passed on to a decoder architecture.
Due to the compression in the encoder, a typical limitation of this type of
architectures is that they tend to lose parts of the input shape structure. We
propose to overcome this limitation by using skip connections specifically
devised for point clouds, where links between corresponding layers in the
encoder and the decoder are established. As part of these connections, we
introduce a transformation matrix that projects the features from the encoder
to the decoder and vice-versa. The quantitative and qualitative results on the
task of object completion from partial scans on the ShapeNet dataset show that
incorporating our approach achieves state-of-the-art performance in shape
completion both at low and high resolutions.
