Multiresolution moment filters

We define multiscale moments that are estimated locally by analyzing an image through a sliding window at multiple scales. When the analysis window satisfies a two-scale relation, we prove that these moments can be computed very efficiently using a multiresolution wavelet-like algorithm. We also show that B-spline windows are best suited for this kind of analysis because, in addition to being refinable, they are positive, symmetric and very nearly isotropic. We present two applications of our method. The first is a feature extraction method for detecting strands of DNA in noisy cryoelectron-micrographs. The second is an extension of the Lucas-Kanade optical flow algorithm (see Lucas, B. and Kanade, T., Proc. DARPA IU Workshop, p.121-30, 1981) that assumes a local affine model of the motion field. The results obtained in both cases are very promising.