Threaded Linear Hierarchical Quadtree for Computation of Geometric Properties of Binary Images

A modification of the linear quadtree [3], the threaded linear hierarchical quadtree (TLHQT), is proposed for the computation of geometric properties of binary images. Since most of the algorithms used in connection with computation of geometric properties require frequent exploration of adjacencies, a structure which keeps permanently in memory some adjacency links is introduced. In this paper, we present some results obtained by using the TLHQT for labeling connected components, evaluating perimeter and Euler’s number in a quadtree environment. The algorithms for computing perimeter and Euler number and the first phase of the labeling algorithm are shown to have time complexity O ( B ) , where B is the number of black nodes of the quadtree. The authors determine the adjacency links at the very beginning-namely, when the binary image is mapped from raster scan to the quadtree. Pixel adjacency is, in fact, available during row scanning, and node’s adjacency is easy to evaluate locally when performing condensation of nodes into larger quadrants and also while merging partial quadtrees. Although the structure requires space nearly four times as much as the linear quadtfee, the requirement is roughly half that for the pointer-based quadtree. Also it appears that for computing geometric properties, the TLHQT offers execution timings better than those obtained by both the linear and pointer-based quadtrees and the graph structure reported in [16].