Fast 3D image reconstruction by cuboids and 3D Charlier's moments

In this article, we propose a novel approach to accelerate the processing of 3D images by the discrete orthogonal moments of Charlier. The proposed approach is based on two fundamental notions: The first is the acceleration of the computing time of Charlier discrete orthogonal polynomials and moments in the case of the 3D image using digital filters. The second is the description of the 3D image by a set of cuboids of fixed size instead of individual voxels by decomposing the image by cuboids of small sizes to ensure numerical stability. By applying this method, the 3D Charlier moments are calculated from the cuboids instead of the whole image, as the image processing will be locally in each cuboid. This method allows us to speed up the computation time of the moments and to avoid the problem of propagation of digital errors encountered as well when using of digital filters for 3D images of large sizes. The simulation results show the effectiveness of the proposed method in terms of the computation time of the 3D moments of Charlier and in terms of quality of 3D image.