Deep Nonlinear Metric Learning for 3-D Shape Retrieval.

Effective 3-D shape retrieval is an important problem in 3-D shape analysis. Recently, feature learning-based shape retrieval methods have been widely studied, where the distance metrics between 3-D shape descriptors are usually hand-crafted. In this paper, motivated by the fact that deep neural network has the good ability to model nonlinearity, we propose to learn an effective nonlinear distance metric between 3-D shape descriptors for retrieval. First, the locality-constrained linear coding method is employed to encode each vertex on the shape and the encoding coefficient histogram is formed as the global 3-D shape descriptor to represent the shape. Then, a novel deep metric network is proposed to learn a nonlinear transformation to map the 3-D shape descriptors to a nonlinear feature space. The proposed deep metric network minimizes a discriminative loss function that can enforce the similarity between a pair of samples from the same class to be small and the similarity between a pair of samples from different classes to be large. Finally, the distance between the outputs of the metric network is used as the similarity for shape retrieval. The proposed method is evaluated on the McGill, SHREC'10 ShapeGoogle, and SHREC'14 Human shape datasets. Experimental results on the three datasets validate the effectiveness of the proposed method.