Deep learning for 3D data processing

Extracting local features from raw 3D data is a nontrivial and challenging task that requires carefully designed 3D shape descriptors. In conventional methods, these descriptors are handcrafted and require intensive human intervention and prior knowledge. To tackle this issue, we propose a novel deep learning model, namely, Circle Convolutional Restricted Boltzmann Machine (CCRBM), for unsupervised 3D local feature learning. CCRBM is specially designed for 3D shapes which effectively resolves the obstacles in the hierarchical learning process that existing deep learning models cannot resolve, such as irregular topology of vertices, orientation ambiguity on the 3D surface, and rigid or slightly nonrigid transformation invariance. Specially, by introducing the novel circle convolution, CCRBM holds a novel ring-like multilayer structure to learn 3D local features in a manner of structure preservation. Circle convolution convolves across 3D local regions with a novel circular sector convolution window by rotating itself along a xed circle direction. In the process of circle convolution, extra points are sampled on each 3D local region and projected onto the tangent plane of the center of the region. By this way, the projection distances in each sector window are employed to constitute the raw 3D feature called projection distance distribution (PDD). In addition, to eliminate the ambiguity of the initial location of a sector window, Fourier Transform Modulus (FTM) is used to transform the PDD into Fourier domain which is then conveyed to CCRBM. Experiments using the learned local features are conducted on three aspects: global shape retrieval, partial shape retrieval, and shape correspondence. The experimental results show that the learned local features outperform other state-of-the-art 3D shape descriptors.