Efficient axis-translation of binary digital pictures by blocks in linear quadtree representation

Abstract

For binary digital pictures with large all-black fragments, the linear quadtree representation is a space-efficient data structure on which many time-efficient algorithms, such border-determination and filling, have been implemented. Translation—moving the picture bodily in a fixed direction—was originally done by converting each pixel into bit-map form. More recently, a recursive translation-rotation algorithm has appeared which makes better use of the hierarchical nature of the data structure, together with a time-complexity bound expressed in terms of the output. We present a nonrecursive translation algorithm with the same asymptotic worst-case time-complexity bound as the recursive algorithm, but which turns out to execute significantly faster than either of the previous algorithms. We generalize this algorithm to higher dimensional pictures, and we express the time-complexity in terms of the input data.