Discrete techniques for 3D digital images and patterns under transformations

摘要

Three dimensional (3-D) digital images and patterns under transformations are facilitated by the splitting-shooting method (SSM) and the splitting- integrating method (SIM). The combination (CSIM) of SSM and SIM and the combination (CIIM) of SIM and SIM are proposed for a cycle conversion T$+$MIN@1$/T, where T is a nonlinear transformation, and T$+$MIN@1$/ is its inverse transformation. This paper focuses on exploitation of accuracy of the obtained image greyness. In our discrete algorithms, let a 3-D pixel be split into N$+3$/ subpixels. The convergence rates of sequential errors can be denoted by O(1/N$+k$/), k $GREQ 1. High convergence rates indicate less CPU time needed. Both error bounds and computation of pixel greyness have shown the following important conclusions: (1) O(1/N) for CSIM; (2) O(1/N) or O(1/N$+2$/) for CIIM; (3) O(1/N$+3$/) for CIIM using quadratic B-spline functions in antialiasing images.