A Unified Feature Representation and Learning Framework for 3D Shape

In conventional 3D shape retrieval and classification, they differentiate each other in their final stages. We propose a unified feature representation and learning framework for the instance-based shape retrieval and classification. Firstly, we render every 3D model in several directions and use the produced view-sets to represent the 3D models. In this way, both tasks can be tackled by measuring the distances between rendered views of 3D models. Secondly, we construct the viewsets as Symmetric positive definite matrices (SPDMs), which are points on a Riemannian manifold. Thus, the shape retrieval and classification tasks are reduced to a problem of measuring the distances between projected views and SPDMs. To solve this heterogeneous problem, we map them to a Hilbert space using a method of point-to-set matching. In this Hilbert space, the distances are surprisingly easy to calculate. Finally, we use a robust nearest-neighbor approach to unify the instancebased shape retrieval and classification. Our framework combines the state-of-the-art deep learning approaches with traditional mathematical optimization method, makes full use of both advantages, which is much more flexible than pure deep learning methods. Experimental results show the efficiency of our approach.