There are a number of techniques for representing pictorial information, among them are borders, arrays, and skeletons. Quadtrees are often used to store black and white picture information. A variety of techniques have been suggested for improving quadtrees, including linear quadtrees, QMATs (quadtree medial axis transform), forests of quadtrees, etc. The major purpose of these improvements is to reduce the storage required without greatly increasing the processing costs. All of these methods suffer from the fact that the structure of the underlying quadtree can be very sensitive to the placement of the origin.
In this paper we discuss a translation invariant data structure (which we name TID) for storing and processing images based on the medial axis transform of the image that consists of all the maximal black squares contained in the image. We also discuss the performance of TID with other existing structures such as QMATs, forests of quadtrees, and normalized quadtrees. Some discussion on the union and intersection of images using TID is included.
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