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.