Deep learning with geodesic moments for 3D shape classification

In this paper, we present a deep learning framework for efficient 3D shape classification using geodesic moments. Our approach inherits many useful properties from the geodesic distance, most notably the capture of the intrinsic geometric structure of 3D shapes and the invariance to isometric deformations. Moreover, we show the similarity between the convergent series of the geodesic moments and the inverse-square eigenvalues of the Laplace-Beltrami operator in the continuous setting. The proposed algorithm uses a two-layer stacked sparse autoencoder to learn deep features from geodesic moments by training the hidden layers individually in an unsupervised fashion, followed by a softmax classifier. Experimental results on three standard 3D shape benchmarks demonstrate superior performance of the proposed approach compared to existing methods.