Quad-Trees, Oct-Trees, and K-Trees: A Generalized Approach to Recursive Decomposition of Euclidean Space
Issue No.05 - May (1983 vol.5)
Chris L. Jackins , 1943 7th Avenue West, Seattle, WA 98119.
Steven L. Tanimoto , Department of Computer Science, University of Washington, Seattle, WA 98105.
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  for the perimeter problem. Our method has been implemented in Pascal, and a computational example is given.
Chris L. Jackins, Steven L. Tanimoto, "Quad-Trees, Oct-Trees, and K-Trees: A Generalized Approach to Recursive Decomposition of Euclidean Space", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.5, no. 5, pp. 533-539, May 1983, doi:10.1109/TPAMI.1983.4767433