Morphological operations on images represented by quadtrees

This paper presents an algorithm to directly perform morphological operations on images represented by quadtrees and produce the dilated/eroded images, also represented by quadtrees. As in many other algorithms that execute on the quadtree representation of an image, the execution time is proportional to the number of nodes in the quadtree, rather than to the number of pixels in the original image array. In our algorithm, only black nodes have to be processed for dilation, and only white nodes have to be processed for erosion. We also performed experiments to show that the execution time for binary images that can be effectively represented by quadtrees can be significantly reduced, compared to direct computation on the original image arrays