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2008, 5(1): 125-144. doi: 10.3934/mbe.2008.5.125

## Multiscale deformable registration of noisy medical images

 1 Department of Mathematics, Kenyon College, Gambier, OH 43022-9623, United States 2 Department of Mathematics and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, MD 20742 3 Department of Radiation Oncology, Stanford University, Stanford, CA 94305-5947

Received  July 2007 Revised  November 2007 Published  January 2008

Multiscale image registration techniques are presented for the reg- istration of medical images using deformable registration models. The tech- niques are particularly effective for registration problems in which one or both of the images to be registered contains significant levels of noise. A brief overview of existing deformable registration techniques is presented, and exper- iments using B-spline free-form deformation registration models demonstrate that ordinary deformable registration techniques fail to produce accurate re- sults in the presence of significant levels of noise. The hierarchical multiscale image decomposition described in E. Tadmor, S. Nezzar, and L. Vese's, ''A multiscale image representation using hierarchical (BV,L2) decompositions'' (Multiscale Modeling and Simulations, 2 (2004): 4, pp. 554-579) is reviewed, and multiscale image registration algorithms are developed based on the mul- tiscale decomposition. Accurate registration of noisy images is achieved by obtaining a hierarchical multiscale decomposition of the images and iteratively registering the resulting components. This approach enables a successful reg- istration of images that contain noise levels well beyond the level at which ordinary deformable registration fails. Numerous image registration experi- ments demonstrate the accuracy and efficiency of the multiscale registration techniques.
Citation: Dana Paquin, Doron Levy, Lei Xing. Multiscale deformable registration of noisy medical images. Mathematical Biosciences & Engineering, 2008, 5 (1) : 125-144. doi: 10.3934/mbe.2008.5.125
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