The ground-breaking performance obtained by deep convolutional neural networks (CNNs) for image processing tasks is inspiring research efforts attempting to extend it for 3D geometric tasks. One of the main challenge in applying CNNs to 3D shape analysis is how to define a natural convolution operator on noneuclidean surfaces. In this paper, we present a method for applying deep learning to 3D surfaces using their spherical descriptors and alt-az anisotropic convolution on 2-sphere. A cascade set of geodesic disk filters rotate on the 2-sphere and collect spherical patterns and so to extract geometric features for various 3D shape analysis tasks. We demonstrate theoretically and experimentally that our proposed method has the possibility to bridge the gap between 2D images and 3D shapes with the desired rotation equivariance/invariance, and its effectiveness is evaluated in applications of non-rigid/ rigid shape classification and shape retrieval.
Deep Learning 3D Shapes Using ALT-AZ Anisotropic 2-Sphere Convolution
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Min Liu is an assistant professor working in the department of Mechanical Engineering at Tsinghua University. Currently, she is also a visiting assistant professor in the School of Mechanical Engineering at Purdue, working with Prof. Ramani. She received her Ph.D. in the School of Mechanical Engineering at Purdue University in 2008. She earned her MS in manufacturing and automation from Tsinghua University in 2001 and a BS in Mechatronics from Central South University of China in 1998. Her current research interests are in geometric processing of 3D shapes for manufacturing applications, pattern recognition and feature analysis in 2D/3D images.