# American Institute of Mathematical Sciences

2007, 4(4): 711-737. doi: 10.3934/mbe.2007.4.711

## Hybrid multiscale landmark and deformable image registration

 1 Department of Mathematics, Stanford University, Stanford, CA 94305-2125, United States 2 Department of Radiation Oncology, Stanford University, Stanford, CA 94305-5947

Received  March 2007 Revised  April 2007 Published  August 2007

An image registration technique is presented for the registration of medical images using a hybrid combination of coarse-scale landmark and B-splines deformable registration techniques. The technique is particularly effective for registration problems in which the images to be registered contain large localized deformations. A brief overview of landmark and deformable registration techniques is presented. The hierarchical multiscale image decomposition of E. Tadmor, S. Nezzar, and L. Vese, A multiscale image representation using hierarchical $(BV,L^2)$ decompositions, Multiscale Modeling and Simulations, vol. 2, no. 4, pp. 554--579, 2004, is reviewed, and an image registration algorithm is developed based on combining the multiscale decomposition with landmark and deformable techniques. Successful registration of medical images is achieved by first obtaining a hierarchical multiscale decomposition of the images and then using landmark-based registration to register the resulting coarse scales. Corresponding bony structure landmarks are easily identified in the coarse scales, which contain only the large shapes and main features of the image. This registration is then fine tuned by using the resulting transformation as the starting point to deformably register the original images with each other using an iterated multiscale B-splines deformable registration technique. The accuracy and efficiency of the hybrid technique is demonstrated with several image registration case studies in two and three dimensions. Additionally, the hybrid technique is shown to be very robust with respect to the location of landmarks and presence of noise.
Citation: Dana Paquin, Doron Levy, Lei Xing. Hybrid multiscale landmark and deformable image registration. Mathematical Biosciences & Engineering, 2007, 4 (4) : 711-737. doi: 10.3934/mbe.2007.4.711
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