Shape approximation using quadtrees

The quadtree representation encodes a 2″ by 2″ binary image as a set of maximal blocks of 1's or 0's whose sizes and positions are powers of 2. With the aid of the quadtree, a hierarchy of approximations to the image can be defined. Several ways of doing this are described. The accuracy of these approximations is empirically evaluated by studying how fast estimates of the first few moments of the image, computed from the approximations, converge to the true values, using a database of 112 airplane silhouettes. Approaches to the problem of fast shape matching using these approximations are also discussed.