Thinning algorithms based on quadtree and octree representations

Thinning is a critical pre-processing step to obtain skeletons for pattern analysis. Quadtree and octree are hierarchical data representations in image processing and computer graphics. In this paper, we present new 2-D area-based and 3-D surface-based thinning algorithms for directly converting quadtree and octree representations to skeletons. The computational complexity of our thinning algorithm for a 2-D or a 3-D image with each length N is respectively O(N2) or O(N3), which is more efficient than the existing algorithms of O(N3) or O(N4). Furthermore, our thinning algorithms can lessen boundary noise spurs and are suited for parallel implementation.