Distance Transform for Images Represented by Quadtrees

The concept of distance used in binary array representations of images is adapted to a quadtree representation. The chessboard distance metric is shown to be particularly suitable for the quadtree. A chessboard distance transform for a quadtree is defined as the minimum distance in the plane from each BLACK node to the border of a WHiTE node. An algorithm is presented which computes this transform by only examining the BLACK node´s adjacent and abutting neighbors and their progeny. However, unlike prior work with quadtrees, computation of the distance transform requires a capability of finding neighbors in the diagonal direction rather than merely in the horizontal and vertical directions. The algorithm´s average execution time is proportional to the number of leaf nodes in the quadtree.