Proceedings PaperFast correlation techniques for wavelet representations
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This paper describes methods for using wavelets to perform image registration at high speed. The basic idea of Le Moigne is to do fast registration on low-resolution images, and then improve the registration by progressively sharpening the resolution. Reduction in resolution by a factor of N reduces the number of operations by a factor of N2, while requiring only a small number of subsequent operations to refine the registration to full-resolution accuracy. The operation count can be reduced further by performing the wavelet correlations in the Fourier-wavelet domain with no additional reduction in accuracy. For examples in the paper, this yielded another order of magnitude reduction in complexity. The Fourier techniques are most appropriate for image mappings that are rigid translations, but they also can be applied to more general image mappings. We show how to discover small rotations by selecting several distinct subimages and registering them individually as pure translations. The translation data re then used to recover both an angular and a translation displacement of the full image. For a test involving an image with a half-million pixels these techniques yielded a speed-up of about 34,000 to 1 when compared to a full- resolution search in the pixel domain. Example registrations for two different image sets required 13 operations per full-resolution pixel at 1/64th resolution and 46 resolution and 46 operations per pixel at 1/16th resolution.