The quadtree and the bintree data structures are two variants on the p
rinciple of hierarchical regular decomposition applied to image repres
entation. A comparison of the storage requirements for images represen
ted by these two methods is presented. The relative storage efficiency
of quad- and bintrees is determined by two factors: the relative node
sizes 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 representa
tion. A probablistic model for images is developed to analyse the merg
ing probability of quadtree leaf node pairs. The analysis reveals that
exactly half of such pairs are expected to merge. Empirical results c
losely match these calculations. The resulting storage efficiency for
a number of representative implementations is discussed. Each of the d
ata structures has implementations (and associated applications) for w
hich it is more space efficient.