Translation, rotation and superposition of linear quadtrees

Abstract

In Gargantini (1982 a) it has been shown that storing black nodes of a quadtree is sufficient to retrieve any basic property associated with quadtrees. To achieve this, each black node must be represented as a quaternary integer whose digits (from left to right) describe the path from the root to that node. The sorted sequence of quaternary integers representing a given region is called the linear quadtree associated with that region. Such a structure has been shown to save more than two-thirds of the memory locations used by regular quadtrees. In this paper we present procedures for translating and rotating a region and consider the superposition of binary images with different characteristics (such as different resolution parameter, different pixel size and/or different center). Translation, rotation, and superposition are shown to be O(N log N) operations; for translation N is the number of black pixels; for rotation N is the number of black nodes; for superposition N is the sum of black nodes or black pixels of the two images, depending on whether or not the two regions are centered on the same raster.