  Auto-encoder is an important architecture to understand point clouds in an
encoding and decoding procedure of self reconstruction. Current auto-encoder
mainly focuses on the learning of global structure by global shape
reconstruction, while ignoring the learning of local structures. To resolve
this issue, we propose Local-to-Global auto-encoder (L2G-AE) to simultaneously
learn the local and global structure of point clouds by local to global
reconstruction. Specifically, L2G-AE employs an encoder to encode the geometry
information of multiple scales in a local region at the same time. In addition,
we introduce a novel hierarchical self-attention mechanism to highlight the
important points, scales and regions at different levels in the information
aggregation of the encoder. Simultaneously, L2G-AE employs a recurrent neural
network (RNN) as decoder to reconstruct a sequence of scales in a local region,
based on which the global point cloud is incrementally reconstructed. Our
outperforming results in shape classification, retrieval and upsampling show
that L2G-AE can understand point clouds better than state-of-the-art methods.
