Unsupervised Learning of 3-D Local Features From Raw Voxels Based on a Novel Permutation Voxelization Strategy

Effective 3-D local features are significant elements for 3-D shape analysis. Existing hand-crafted 3-D local descriptors are effective but usually involve intensive human intervention and prior knowledge, which burdens the subsequent processing procedures. An alternative resorts to the unsupervised learning of features from raw 3-D representations via popular deep learning models. However, this alternative suffers from several significant unresolved issues, such as irregular vertex topology, arbitrary mesh resolution, orientation ambiguity on the 3-D surface, and rigid and slightly nonrigid transformation invariance. To tackle these issues, we propose an unsupervised 3-D local feature learning framework based on a novel permutation voxelization strategy to learn high-level and hierarchical 3-D local features from raw 3-D voxels. Specifically, the proposed strategy first applies a novel voxelization which discretizes each 3-D local region with irregular vertex topology and arbitrary mesh resolution into regular voxels, and then, a novel permutation is applied to permute the voxels to simultaneously eliminate the effect of rotation transformation and orientation ambiguity on the surface. Based on the proposed strategy, the permuted voxels can fully encode the geometry and structure of each local region in regular, sparse, and binary vectors. These voxel vectors are highly suitable for the learning of hierarchical common surface patterns by stacked sparse autoencoder with hierarchical abstraction and sparse constraint. Experiments are conducted on three aspects for evaluating the learned local features: (1) global shape retrieval; (2) partial shape retrieval; and (3) shape correspondence. The experimental results show that the learned local features outperform the other state-of-the-art 3-D shape descriptors.