Abstract: Representation of two and three-dimensional objects by tree structures has been used extensively in solid modeling, computer graphics, computer vision and image processing. (See for example [Mantyla] [Chen] [Hunter] [Rosenfeld] [Leonardi].) Quadtrees, which are used to represent objects in 2-D space, and octrees, which are the extension of quadtrees in 3-D space, have been studied thoroughly for applications in graphics and image processing.
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