A spectral graph wavelet approach for nonrigid 3D shape retrieval

In this paper, we propose a spectral graph wavelet approach for 3D shape retrieval using the bag-of-features paradigm. In an effort to capture both local and global characteristics of a 3D shape, we present a three-step feature description framework. Local descriptors are first extracted via the spectral graph wavelet transform having the Mexican hat wavelet as a generating kernel. Then, mid-level features are obtained by embedding local descriptors into the visual vocabulary space using the soft-assignment coding step of the bag-of-features model. A global descriptor is subsequently constructed by aggregating mid-level features weighted by a geodesic exponential kernel, resulting in a matrix representation that describes the frequency of appearance of nearby codewords in the vocabulary. Then, we compare the global descriptor of a query to all global descriptors of the shapes in the dataset using a dissimilarity measure and find the closest shape. Experimental results on two standard 3D shape benchmarks demonstrate the effectiveness of the proposed shape retrieval approach in comparison with state-of-the-art methods.