Deep Multimetric Learning for Shape-Based 3D Model Retrieval

Recently, feature-learning-based 3D shape retrieval methods have been receiving more and more attention in the 3D shape analysis community. In these methods, the hand-crafted metrics or the learned linear metrics are usually used to compute the distances between shape features. Since there are complex geometric structural variations with 3D shapes, the single hand-crafted metric or learned linear metric cannot characterize the manifold, where 3D shapes lie well. In this paper, by exploring the nonlinearity of the deep neural network and the complementarity among multiple shape features, we propose a novel deep multimetric network for 3D shape retrieval. The developed multimetric network minimizes a discriminative loss function that, for each type of shape feature, the outputs of the network from the same class are encouraged to be as similar as possible and the outputs from different classes are encouraged to be as dissimilar as possible. Meanwhile, the Hilbert-Schmidt independence criterion is employed to enforce the outputs of different types of shape features to be as complementary as possible. Furthermore, the weights of the learned multiple distance metrics can be adaptively determined in our developed deep metric network. The weighted distance metric is then used as the similarity for shape retrieval. We conduct experiments with the proposed method on the four benchmark shape datasets. Experimental results demonstrate that the proposed method can obtain better performance than the learned deep single metric and outperform the state-of-the-art 3D shape retrieval methods.