B-spline registration of 3D images with Levenberg-Marquardt optimization

Sven Kabus; Thomas Netsch; Bernd Fischer; Jan Modersitzki

doi:10.1117/12.533976

12 May 2004 B-spline registration of 3D images with Levenberg-Marquardt optimization

Sven Kabus, Thomas Netsch, Bernd Fischer, Jan Modersitzki

Proceedings Volume 5370, Medical Imaging 2004: Image Processing; (2004) https://doi.org/10.1117/12.533976
Event: Medical Imaging 2004, 2004, San Diego, California, United States

Abstract

B-splines are a well-known approach for non-rigid image registration. Though successfully applied to various medical applications they exhibit a high computational complexity mainly because of the lack of dedicated optimization methods. In this work we focus on a Levenberg-Marquardt type optimization routine. As a similarity measure we use least-squares functionals such as the sum of squared differences, the cross-correlation and the local correlation measure, respectively. The latter is used for multi-modality registration tasks. The proposed registration algorithm consists of three main parts. In each iteration step one has to (a) build a linear system of equations, (b) solve this system and compute an update, (c) determine the step length for the following iteration step. Appropriate stopping criteria ensure the termination of the registration task. A standard approach for (c) and several modifications are investigated. Using a quadratic model we are able to avoid additional execution of (b) during the step length adaption. Several solvers (Cholesky, CG, pre-conditioning) for (b) have been evaluated. Also, modifications on the most time consuming task (a) are investigated, leading to a speed-up by a factor up to 30. Finally, the algorithm is embedded in a multi-scale framework (both on image and on parameter level) providing additional regularization, an increased capture range and speed-up. Convergence tests have been successfully applied for a priori known transformations. Feasibility of the proposed approach is also shown for clinical applications including PET-CT registrations (19 data sets) and MR mammography.

Citation Download Citation

Sven Kabus, Thomas Netsch, Bernd Fischer, and Jan Modersitzki "B-spline registration of 3D images with Levenberg-Marquardt optimization", Proc. SPIE 5370, Medical Imaging 2004: Image Processing, (12 May 2004); https://doi.org/10.1117/12.533976

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