Quadtree traversal algorithms for pointer-based and depth-first representations

Simple top-down pointer-based quadtree traversal algorithms for four-neighbor traversal, eight-neighbor traversal, and connected-component labeling are proposed. It is shown that for this class of algorithms there exist efficient pointer-based representations that can require as little as 2N bytes, where N is total number of nodes in the tree. The algorithms can also be implemented using a depth-first quadtree representation, at the cost of additional nonrecursive walks over the data structure to locate the arbitrary sons of interior nodes.>