Discrete techniques for 3-D digital images and patterns under transformation

Three-dimensional (3-D) digital images and patterns under transformations are facilitated by the splitting-shooting method (SSM) and the splitting-integration method (SIM). The combination (CSIM) of using both SSM and SIM and two combinations (CIIM) of using SIM only are proposed for a cycle conversion T^-1T, where T is a nonlinear transformation, and T^-1 is its inverse transformation. This paper focuses on exploitation of accuracy of obtained image greyness. In our discrete algorithms, letting a 3-D pixel be split into N³ subpixels, the convergence rates, O(1/N), O(1/N²), and O(1/N ³), of sequential error can be achieved by the three combinations respectively. High convergence rates indicate less CPU time needed. Both error bounds and computation of pixel greyness have shown the significance of the proposed new algorithms