This paper presents a motion estimation algorithm based on a new multiresolution representation, the quadtree spline. This representation describes the motion field as a collection of smoothly connected patches of varying size, where the patch size is automatically adapted to the complexity of the underlying motion. The topology of the patches is determined by a quadtree data structure, and both split and merge techniques are developed for estimating this spatial subdivision. The quadtree spline is implemented using another novel representation, the adaptive hierarchical basis spline, and combines the advantages of adaptively-sized correlation windows with the speedups obtained with hierarchical basis preconditioners. Results are presented on some standard motion sequences.