Fast multiresolution image operations in the wavelet domain

A wide class of operations on images can be performed directly in the wavelet domain by operating on coefficients of the wavelet transforms of the images and other matrices defined by these operations. Operating in the wavelet domain enables one to perform these operations progressively in a coarse-to-fine fashion, operate on different resolutions, manipulate features at different scales, trade off accuracy for speed, and localize the operation in both the spatial and the frequency domains. Performing such operations in the wavelet domain and then reconstructing the result is also often more efficient than performing the same operation in the standard direct fashion. In this paper, we demonstrate the applicability and advantages of this framework to three common types of image operations: image blending, 3D warping of images and sequences, and convolution of images and image sequences.