An improvement of rotation invariant 3D-shape based on functions on concentric spheres

In this paper, we consider 3D-shape descriptors generated by using functions on a sphere. The descriptors are engaged for retrieving polygonal mesh models. Invariance of descriptors with respect to rotation of a model can be achieved either by using the principle component analysis (PCA) or defining features in which the invariance exists. The contribution of the paper is twofold: firstly, we define a new rotation invariant feature vector based on functions on concentric spheres, which outperforms a recently proposed descriptor; secondly, we compare the two approaches for achieving rotation invariance as well as options to use a single function or several functions on concentric spheres to generate feature vectors. We conclude that descriptors, which use the PCA, outperform others, while capturing the internal structure of a 3D-model with functions on concentric spheres can improve retrieval effectiveness.