Three dimensional moment invariants under rigid transformation

Abstract

In the area of Computer Vision, the recognition and understanding of three-dimensional (3D) objects depend on their characteristics. The use of 3D moments presents a good method to compute such charateristics. They can characterize the surfaces of objects effectively and independent of size, position and orientation. In this paper, 3D moment invariants under rigid transformation, relative and absolute moment invariants of the rotation subgroups of SO(3) are presented. Some of the 3D absolute moment invariants were already given by Sadjadi and Hall, but the fundamental theorem of moment invariants that was presented by Hu and used by them to prove their results have been proved that it has to be corrected. Here a direct proof is given for this theorem by Sadjadi and Hall (Theorem 1 in this paper). Together with other moment invariants, the results proposed in this paper are significant in further segmentation and matching of 3D objects.