θ(1) time quadtree algorithm and its application for image geometric properties on a mesh connected computer (MCC)

Quadtree and octree decomposition of multicolored images is often used to solve problems of image processing. This paper describes a θ(1) time algorithm for the decomposition of the images into quadtree and octree on a mesh connected computer. Images will be stored in the MCC of the same size, at one pixel per processing element (PE). Certain applications of the algorithm are also described namely, the computation of such geometric properties as the area and perimeter. The complexity of these algorithms depends on the hierarchical data structure. They are carried out in O(log
²
m + log m) times on an n × n MCC, where m = n/k, and k is the size of the smallest homogeneous quadrant in the image.