3D Shape Descriptor by Principal Component Analysis Embedding for Non-rigid 3D Shape Retrieval in A Learning Framework

In the paper, we propose a 3D shape descriptor which can be applied to areas such as non-rigid 3D shape analysis and retrieval. We start with the calculation of the Wave Kernel Signature (WKS) and the scale-invariant Heat Kernel Signature (siHKS) of surface points belong to a 3D shape. Then we combine them together and obtain their principle components by PCA (principle component analysis), which are employed as our own point signatures. We take a weighted average of all the point signatures over a 3D surface to obtain our own shape descriptor. Different from other approaches, we employ shape curvature as the element of weight in the construction of the shape descriptor. Moreover, our shape descriptor is also trained in a machine learning framework and then used to a non-rigid 3D shape retrieval application. The results of the experiments in the end of the paper show that our 3D shape descriptor is efficient and feasible for applications such as analysis of non-rigid 3D shape, non-rigid 3D shape matching and 3D shape retrieval, etc..