  How to obtain the desirable representation of a 3D shape, which is
discriminative across categories and polymerized within classes, is a
significant challenge in 3D shape retrieval. Most existing 3D shape retrieval
methods focus on capturing strong discriminative shape representation with
softmax loss for the classification task, while the shape feature learning with
metric loss is neglected for 3D shape retrieval. In this paper, we address this
problem based on the intuition that the cosine distance of shape embeddings
should be close enough within the same class and far away across categories.
Since most of 3D shape retrieval tasks use cosine distance of shape features
for measuring shape similarity, we propose a novel metric loss named angular
triplet-center loss, which directly optimizes the cosine distances between the
features. It inherits the triplet-center loss property to achieve larger
inter-class distance and smaller intra-class distance simultaneously. Unlike
previous metric loss utilized in 3D shape retrieval methods, where Euclidean
distance is adopted and the margin design is difficult, the proposed method is
more convenient to train feature embeddings and more suitable for 3D shape
retrieval. Moreover, the angle margin is adopted to replace the cosine margin
in order to provide more explicit discriminative constraints on an embedding
space. Extensive experimental results on two popular 3D object retrieval
benchmarks, ModelNet40 and ShapeNetCore 55, demonstrate the effectiveness of
our proposed loss, and our method has achieved state-of-the-art results on
various 3D shape datasets.
