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Quad-Trees, Oct-Trees, and K-Trees: A Generalized Approach to Recursive Decomposition of Euclidean Space

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2 Author(s)
Chris L. Jackins ; 1943 7th Avenue West, Seattle, WA 98119. ; Steven L. Tanimoto

K-trees are developed as a K-dimensional analog of quad-trees and oct-trees. K-trees can be used for modeling K-dimensional data. A fast algorithm is given for finding the boundary size of a K-dimensional object represented by a K-tree. For K considered as con-stant; the algorithm provides a method for computing the perimeter of a quad-tree encoded image or the surface area of an oct-tree encoded object in worst case time proportional to the number of nodes in the tree. This improves upon the expected-case linear-time method of Samet [10] for the perimeter problem. Our method has been implemented in Pascal, and a computational example is given.

Published in:

IEEE Transactions on Pattern Analysis and Machine Intelligence  (Volume:PAMI-5 ,  Issue: 5 )