@conference {13209,
	title = {Multi-level fast multipole method for thin plate spline evaluation},
	booktitle = {Image Processing, 2004. ICIP {\textquoteright}04. 2004 International Conference on},
	volume = {3},
	year = {2004},
	month = {2004/10//},
	pages = {1683 - 1686 Vol. 3 - 1683 - 1686 Vol. 3},
	abstract = {Image registration is an important problem in image processing and computer vision. Much recent work in image registration is on matching non-rigid deformations. Thin plate splines are an effective image registration method when the deformation between two images can be modeled as the bending of a thin metal plate on point constraints such that the topology is preserved (non-rigid deformation). However, because evaluating the computed TPS model at all the image pixels is computationally expensive, we need to speed it up. We introduce the use of multi-level fast muitipole method (MLFMM) for this purpose. Our contribution lies in the presentation of a clear and concise MLFMM framework for TPS, which will be useful for future application developments. The achieved speedup using MLFMM is an improvement from O(N<sup>2</sup>) to O(N log N). We show that the fast evaluation outperforms the brute force method while maintaining acceptable error bound.},
	keywords = {(mathematics);, Computer, deformation;, evaluation;, fast, image, MATCHING, matching;, metal, method;, multilevel, multipole, nonrigid, pixel;, plate, plate;, processing;, registration;, resolution;, spline, splines, thin, vision;},
	doi = {10.1109/ICIP.2004.1421395},
	author = {Zandifar,A. and Lim,S. and Duraiswami, Ramani and Gumerov, Nail A. and Davis, Larry S.}
}
