Unified interpretation of projection method, linear interpolation, and the inductive introduction of improved reduction and enlargement methods
Eiji Atsumi, Masayuki Yoshida, Fumitaka Ono · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1997
This paper clarifies two traditional image size reduction and enlargement methods, projection-method (PM) and linear- interpolation (LI), in terms of multi-rate signal processing. We have proved that both size conversion methods of scaling ratio of N/M can be implemented with the same structure, i.e., zero-hold enlargement by 1:n, average filtering of M-taps for PM or N-taps for LI, and M:1 down- sampling for both methods. Such implementation enables objective evaluations of PM and LI under the same manner that evaluates other size conversion methods originally developed with digital filtering. The empirical matter that PM provides better image quality in reduction than LI and the opposite behavior in enlargement is confirmed under multi-rate signal processing. We have developed a unified method of PM and LI by introducing selective filter-length. N-taps for enlargement and M-taps for reduction are used to produce better or equal image quality at any scaling ratio of N/M than PM or LI alone does. We also show that minute filter-length adjustment of the unified method can control image quality more delicately; a slight decrease of the filter-length provides sharper images and a slight increase provides smoother images.