Rectangular convolution for fast filtering of characters

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Abstract
While the race towards higher-resolution bitmap displays is still on, many grayscale displays have appeared on the scene. To fully utilize their capabilities, grayscale fonts are needed, and these can be produced by filtering bi-level masters. Most of the efficient filtering techniques cannot directly be applied. For example, prefiltering is impractical, due to the number of character masters and the requirement of sub-pixel positioning. Furthermore, we would like to impose as few restrictions as possible on the characteristics of the filter, in order to facilitate exploration into the quality of various filters.We describe a fast filtering technique especially adapted to this task. The characters are decomposed into rectangles, and a summed-area representation of the filter is efficiently convolved with each individual rectangle to construct the grayscale character. For a given filter, the number of operations is O (linear size of the grayscale character) , which is optimal.We give an analysis of the efficiency of this technique, and examples of its implementation applied to various families of fonts and point sizes. The performance of the implementation is such that filtering characters for grayscale displays is feasible in realtime on personal workstations.

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