Discrete signal matching using coarse-to-fine wavelet basis functions

In this paper, we propose a matching algorithm to estimate accurate and dense displacements between two signals. The displacements are characterized by a coarse-to-fine wavelet representation, which is a linear combination of hierarchical basis functions developed by Cai and Wang (SIAM Numer. Anal. 33(3) (1996) 937). The coarser-scale basis function has larger support while the finer-scale basis function has smaller support. During the iterative minimization process, the basis functions are utilized as large-to-small windows in selecting global-to-local regions for signal matching. The estimated wavelet coefficients are then used to reconstruct the signal in a coarse-to-fine manner. Two sets of synthetic examples, one with small displacement and the other with large displacements, have been employed to illustrate the advantages of the wavelet-based method. This method has been applied to estimate the dense disparity between stereo images in several real examples and the results demonstrate its effectiveness.