A quadtree medial axis transform

Abstract

As printed Quadtree skeletons are exact representations of the image and are used because they are observed to yield space efficiently and a decreased sensitivity to shifts in contrast with the quadtree. The QMAT can be used as the underlying representation when solving most problems that can be solved by using a quadtree. An algorithm is presented for the computation of the QMAT of a given quadtree by only examining each BLACK node's adjacent and abutting neighbors. Corrected Abstract (published as corrigendum in CACM 27, 2 (February 1984) p. 151) The skeletal and medial axis transform concepts used in traditional image processing representations are adapted to the quadtree representation. The result is the definition of of a new data structure termed the Quadtree Medial Axis Transform (QMAT). A QMAT results in a partition of the image into a set of nondisjoint squares having sides whose lengths are sums of powers of 2 rather than, as is the case with quadtrees, a set of disjoint squares having sides of lengths which are powers of 2. The motivation is not to study skeletons for the usual purpose of obtainings approximations of the image. Instead, quadtree skeletons are exact representations of the image and are used because they are observed to yield space efficiency and a decreased sensitvity to shifts in contrast with the quadtree. The QMAT can be used as the underlying representation when solving most problems that can be solved by using a quadtree. An algorithm is presented for the computation of the QMAT of a given quadtree by only examining each BLACK node's adjacent and abutting neighbors. Analysis of the algorithm reveals an average execution time proportional to the complexity of the image, i.e., the number of BLACK blocks.