Multiple vocabulary coding for 3D shape retrieval using Bag of Covariances

Bag of Covariance matrices (BoC) have been recently introduced as an extension of the standard Bag of Words (BoW) to the space of positive semi-definite matrices, which has a Riemannian structure. BoC descriptors can be constructed with various Riemannian metrics and using various quantization approaches. Each construction results in some quantization errors, which are often reduced by increasing the vocabulary size. This, however, results in a signature that is not compact, increasing both the storage and computation complexity. This article demonstrates that a compact signature, with minimum distortion, can be constructed by using multiple vocabulary based coding. Each vocabulary is constructed from a different quantization method of the covariance feature space. The proposed method also extracts non-linear dependencies between the different BoC signatures to compose the final compact signature. Our experiments show that the proposed approach can boost the performance of the BoC descriptors in various 3D shape classification and retrieval tasks.