Spherical Demons: Fast Diffeomorphic Landmark-Free Surface Registration

Computer Science and Artificial Intelligence Laboratory, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
IEEE Trans Med Imaging 09/2009; 29:650-668. DOI: 10.1109/TMI.2009.2030797
Source: DBLP


We present the Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizors for the modified Demons objective function can be efficiently approximated on the sphere using iterative smoothing. Based on one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast. The Spherical Demons algorithm can also be modified to register a given spherical image to a probabilistic atlas. We demonstrate two variants of the algorithm corresponding to warping the atlas or warping the subject. Registration of a cortical surface mesh to an atlas mesh, both with more than 160 k nodes requires less than 5 min when warping the atlas and less than 3 min when warping the subject on a Xeon 3.2 GHz single processor machine. This is comparable to the fastest nondiffeomorphic landmark-free surface registration algorithms. Furthermore, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different applications that use registration to transfer segmentation labels onto a new image 1) parcellation of in vivo cortical surfaces and 2) Brodmann area localization in ex vivo cortical surfaces.

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Available from: Mert R Sabuncu, Jun 19, 2014
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    • "Surface registration is obtained by matching geometric quantities defined on each surfaces. Some commonly chosen geometric quantities are surface curvatures (Yeo et al., 2010), surface metric (Lord et al., 2007) , angular structure (Haker et al., 2000; Gu et al., 2004; Jin et al., 2008; Hurdal and Stephenson, 2009) and convexity (Fischl et al., 1999b). The third category of registration models is the hybrid surface registration algorithm, which combines both landmarkguided and geometry-guided registration together. "
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    ABSTRACT: We address the registration problem of genus-one surfaces (such as vertebrae bones) with prescribed landmark constraints. The high-genus topology of the surfaces makes it challenging to obtain a unique and bijective surface mapping that matches landmarks consistently. This work proposes to tackle this registration problem using a special class of quasi-conformal maps called Teichmüller maps (T-Maps). A landmark constrained T-Map is the unique mapping between genus-1 surfaces that minimizes the maximal conformality distortion while matching the prescribed feature landmarks. Existence and uniqueness of the landmark constrained T-Map are theoretically guaranteed. This work presents an iterative algorithm to compute the T-Map. The main idea is to represent the set of diffeomorphism using the Beltrami coefficients (BC). The BC is iteratively adjusted to an optimal one, which corresponds to our desired T-Map that matches the prescribed landmarks and satisfies the periodic boundary condition on the universal covering space. Numerical experiments demonstrate the effectiveness of our proposed algorithm. The method has also been applied to register vertebrae bones with prescribed landmark points and curves, which gives accurate surface registrations. Copyright © 2015 Elsevier B.V. All rights reserved.
    Medical Image Analysis 04/2015; 25(1). DOI:10.1016/ · 3.65 Impact Factor
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    • "A number of algorithms that enforce inverse consistency have been proposed. A representative set of such algorithms can be found in [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]. The consistency of three transformations was used by Holden et al. [12], Freeborough [24], Woods et al. [11], and Christensen [10] to compare and evaluate several similarity measures and registration algorithms. "
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    ABSTRACT: Identification of error in non-rigid registration is a critical problem in the medical image processing community. We recently proposed an algorithm that we call "Assessing Quality Using Image Registration Circuits" (AQUIRC) to identify non-rigid registration errors and have tested its performance using simulated cases. In this article, we extend our previous work to assess AQUIRC's ability to detect local non-rigid registration errors and validate it quantitatively at specific clinical landmarks, namely the Anterior Commissure (AC) and the Posterior Commissure (PC). To test our approach on a representative range of error we utilize 5 different registration methods and use 100 target images and 9 atlas images. Our results show that AQUIRC's measure of registration quality correlates with the true target registration error (TRE) at these selected landmarks with an R² = 0.542. To compare our method to a more conventional approach, we compute Local Normalized Correlation Coefficient (LNCC) and show that AQUIRC performs similarly. However, a multi-linear regression performed with both AQUIRC's measure and LNCC shows a higher correlation with TRE than correlations obtained with either measure alone, thus showing the complementarity of these quality measures. We conclude the article by showing that the AQUIRC algorithm can be used to reduce registration errors for all five algorithms.
    IEEE Transactions on Medical Imaging 07/2014; 34(1). DOI:10.1109/TMI.2014.2344911 · 3.39 Impact Factor
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    • "Anatomical measures like cortical thickness, sulcal depth, and gyrification index, which can be directly derived from this mathematical representation, have been widely used in the study of both healthy and diseased brains (Thompson et al. 2007; Nordahl et al. 2007; Schmitt et al. 2007; Im et al. 2008; Goldman et al. 2009; Thambisetty et al. 2010). Cortical reconstruction is also the first step in many neuroimaging algorithms including but not limited to cortical labeling (Bruce Fischl et al. 2004; Desikan et al. 2006; Destrieux et al. 2010), surface based registration (B Fischl et al. 1999; Tosun et al. 2004; Lyttelton et al. 2007; Tosun and Prince 2008; Yeo et al. 2010), and surface based morphometry (Chung et al. 2003; Chung, Dalton, and Davidson 2008; Fornito et al. 2008). "
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    ABSTRACT: Cortical atrophy has been reported in a number of diseases, such as multiple sclerosis and Alzheimer's disease, that are also associated with white matter (WM) lesions. However, most cortical reconstruction techniques do not account for these pathologies, thereby requiring additional processing to correct for the effect of WM lesions. In this work, we introduce CRUISE+, an automated process for cortical reconstruction from magnetic resonance brain images with WM lesions. The process extends previously well validated methods to allow for multichannel input images and to accommodate for the presence of WM lesions. We provide new validation data and tools for measuring the accuracy of cortical reconstruction methods on healthy brains as well as brains with multiple sclerosis lesions. Using this data, we validate the accuracy of CRUISE+ and compare it to another state-of-the-art cortical reconstruction tool. Our results demonstrate that CRUISE+ has superior performance in the cortical regions near WM lesions, and similar performance in other regions. Hum Brain Mapp, 2013. © 2013 Wiley Periodicals, Inc.
    Human Brain Mapping 07/2014; 35(7). DOI:10.1002/hbm.22409 · 5.97 Impact Factor
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