A Generalized Comparison of Quadtree and Bintree Storage Requirements

The quadtree and bintree data structures are two variants on the principle of hierarchical regular decomposition applied to image representation. A comparison of the storage requirements for images represented by these two methods is presented. The relative storage efficiency of quadtrees and bintrees is determined by two factors: the relative mode size for the two representations as determined by the data structure implementation, and the number of quadtree leaf node pairs that merge to form a single leaf node after conversion to the bintree representation. The merging probability is analyzed, and found to be close to 0.5 for most images. The resulting storage efficiency for a number for representative implementations is discussed. Each of the data structures has implementations (and associated applications) for which it is more space efficient.