Linear intensity-based image registration by Markov random fields and discrete optimization |
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| Authors: | Darko Zikic Ben Glocker Oliver Kutter Martin Groher Nikos Komodakis Ali Kamen Nikos Paragios Nassir Navab |
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| Affiliation: | 1. Brainnetome Center, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China;2. National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China;3. Department of Mathematics, Zhejiang University, Hangzhou 310027, China;4. School of Information and Communication Engineering, North University of China, Taiyuan 030051, China;1. Department of Clinical and Experimental Medicine, Neurology Unit, University of Pisa, Via Savi 10, 56126 Pisa, Italy;2. Azienda ULSS 12 “Veneziana”, dell''Angelo Hospital, Neurology Unit, Via Paccagnella 11, 30174 Mestre (Venice), Italy;1. Department of Radiology and BRIC, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA;2. Institute for Medical Imaging Technology, School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, China;3. Department of Brain and Cognitive Engineering, Korea University, Seoul 02841, Republic of Korea;1. Department of Radiology, University of Pennsylvania, Philadelphia, PA 19104, USA;2. Department of Electrical and Computer Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA;3. Department of Computer Science, The Johns Hopkins University, Baltimore, MD 21218 USA;4. Radiation Oncology and Molecular Radiation Sciences, The Johns Hopkins School of Medicine, Baltimore, MD 21287, USA;5. CNRM, The Henry M. Jackson Foundation for the Advancement of Military Medicine, Bethesda, MD 20892, USA |
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| Abstract: | We propose a framework for intensity-based registration of images by linear transformations, based on a discrete Markov random field (MRF) formulation. Here, the challenge arises from the fact that optimizing the energy associated with this problem requires a high-order MRF model. Currently, methods for optimizing such high-order models are less general, easy to use, and efficient, than methods for the popular second-order models.Therefore, we propose an approximation to the original energy by an MRF with tractable second-order terms. The approximation at a certain point p in the parameter space is the normalized sum of evaluations of the original energy at projections of p to two-dimensional subspaces. We demonstrate the quality of the proposed approximation by computing the correlation with the original energy, and show that registration can be performed by discrete optimization of the approximated energy in an iteration loop. A search space refinement strategy is employed over iterations to achieve sub-pixel accuracy, while keeping the number of labels small for efficiency. The proposed framework can encode any similarity measure is robust to the settings of the internal parameters, and allows an intuitive control of the parameter ranges. We demonstrate the applicability of the framework by intensity-based registration, and 2D–3D registration of medical images. The evaluation is performed by random studies and real registration tasks. The tests indicate increased robustness and precision compared to corresponding standard optimization of the original energy, and demonstrate robustness to noise. Finally, the proposed framework allows the transfer of advances in MRF optimization to linear registration problems. |
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