Rotation Scaling and Translation Invariants of 3D Radial Shifted Legendre Moments

This paper proposes a new set of 3 D rotation scaling and translation invariants of 3 D radially shifted Legendre moments.We aim to develop two kinds of transformed shifted Legendre moments: a 3 D substituted radial shifted Legendre moments(3 DSRSLMs) and a 3 D weighted radial one(3 DWRSLMs). Both are centered on two types of polynomials. In the first case, a new 3 D radial complex moment is proposed. In the second case, new 3 D substituted/weighted radial shifted Legendre moments(3 DSRSLMs/3 DWRSLMs) are introduced using a spherical representation of volumetric image. 3 D invariants as derived from the suggested 3 D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three issues. To confirm the proposed approach, we have resolved three issues: rotation, scaling and translation invariants. The result of experiments shows that the 3 DSRSLMs and 3 DWRSLMs have done better than the 3 D radial complex moments with and without noise. Simultaneously, the reconstruction converges rapidly to the original image using 3 D radial 3 DSRSLMs and 3 DWRSLMs, and the test of 3 D images are clearly recognized from a set of images that are available in Princeton shape benchmark(PSB) database for 3 D image.