Discrete techniques for 3D digital images and patterns under transformations

Zi Cai Li

doi:10.1117/12.138483

18 January 1993 Discrete techniques for 3D digital images and patterns under transformations

Zi Cai Li

Proceedings Volume 1713, International Conference on Manufacturing Automation; (1993) https://doi.org/10.1117/12.138483
Event: International Conference on Manufacturing Automation, 1992, Hong Kong, Hong Kong

Abstract

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^-1T, where T is a nonlinear transformation, and T^-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 N³ subpixels. The convergence rates of sequential errors can be denoted by O(1/N^k), k >= 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/N²) for CIIM; (3) O(1/N³) for CIIM using quadratic B-spline functions in antialiasing images.

Citation Download Citation

Zi Cai Li "Discrete techniques for 3D digital images and patterns under transformations", Proc. SPIE 1713, International Conference on Manufacturing Automation, (18 January 1993); https://doi.org/10.1117/12.138483

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