A Stable Algorithm computing high-order 3D Zernike Moments and Shape Reconstructions

3D Zernike moments are used as the 3D object shape descriptors. In this paper, we introduce a series of stable algorithms for calculating high-order the 3D Zernike moments. A kind of recurrence formula among 3D Zernike radial polynomials is presented. A voxel-based algorithm is hereby developed. The proposed method provides an accurate reconstruction image. When our algorithms are applied to the 3D object 'Einstein bust' with 100x100x100 voxels, the error rate for the shape reconstruction attains its value 0.000012 and 0 for computing all moments up to order 350 (390 respectively).