3D Bessel moments for 3D model retrieval

Three-dimensional (3D) model retrieval and shape recognition are focus of research with the development of big data technology and the increasing application of 3D model in practical application recently. However, there still exist some challenges, such as the diculties of designing more accurate and efficient description with low dimension, geometric invariance and strong robustness in feature extraction. In virtue of this, we propose 3D Bessel moments based on polar representation by the first-class Bessel polynomial. The 3D Bessel moments inherit the properties of and geometric invariance of Bessel polynomial and possess strong capability of shape describing for 3D models. Firstly, the derivation of 3D Bessel moments are constructed and its geometric invariance proofs are given theoretically. Secondly the standardized coordinate system is calculated and the principal component analysis transform is performed to eliminate the position and scale dierences between 3D models. Thereafter, 3D models in the test sets are voxelized. Finally, 3D Bessel moments are calculated to extract rotation, scaling, and translation invariance descriptors for model retrieval. The effectiveness of the proposed method is verified on the McGill 3D shape benchmark and ModelNet10 datasets. Experimental results show that the proposed method has strong robust to different simplification rates of 3D models, is invariant to rotation, scaling and translation, and performs better for model retrieval than state-of-the-art methods on test datasets.