Diffeomorphic Image Registration of Diffusion MRI Using Spherical Harmonics

Intramural Res. Program, Nat. Institutes of Health, Baltimore, MD, USA
IEEE Transactions on Medical Imaging (Impact Factor: 3.39). 04/2011; 30(3):747 - 758. DOI: 10.1109/TMI.2010.2095027
Source: IEEE Xplore


Nonrigid registration of diffusion magnetic resonance imaging (MRI) is crucial for group analyses and building white matter and fiber tract atlases. Most current diffusion MRI registration techniques are limited to the alignment of diffusion tensor imaging (DTI) data. We propose a novel diffeomorphic registration method for high angular resolution diffusion images by mapping their orientation distribution functions (ODFs). ODFs can be reconstructed using q-ball imaging (QBI) techniques and represented by spherical harmonics (SHs) to resolve intra-voxel fiber crossings. The registration is based on optimizing a diffeomorphic demons cost function. Unlike scalar images, deforming ODF maps requires ODF reorientation to maintain its consistency with the local fiber orientations. Our method simultaneously reorients the ODFs by computing a Wigner rotation matrix at each voxel, and applies it to the SH coefficients during registration. Rotation of the coefficients avoids the estimation of principal directions, which has no analytical solution and is time consuming. The proposed method was validated on both simulated and real data sets with various metrics, which include the distance between the estimated and simulated transformation fields, the standard deviation of the general fractional anisotropy and the directional consistency of the deformed and reference images. The registration performance using SHs with different maximum orders were compared using these metrics. Results show that the diffeomorphic registration improved the affine alignment, and registration using SHs with higher order SHs further improved the registration accuracy by reducing the shape difference and improving the directional consistency of the registered and reference ODF maps.

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    • "If not degenerated, the affine transformations are also diffeomorphic. Examples of registration algorithms that include diffeomorphic transformations can be found in (Ashburner, 2007; Auzias et al., 2011; Beg et al., 2005; Geng et al., 2011; Joshi and Miller, 2000; Marsland and Twining, 2004; Rao et al., 2004; Vercauteren et al., 2007; 2009; Yeo et al., 2010a; Yeo et al., 2009). "
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    ABSTRACT: This paper presents a review of automated image registration methodologies that have been used in the medical field. The aim of this paper is to be an introduction to the field, provide knowledge on the work that has been developed and to be a suitable reference for those who are looking for registration methods for a specific application. The registration methodologies under review are classified into intensity or feature based. The main steps of these methodologies, the common geometric transformations, the similarity measures and accuracy assessment techniques are introduced and described.
    Computer Methods in Biomechanics and Biomedical Engineering 01/2014; 17(2):73-93. DOI:10.1080/10255842.2012.670855 · 1.77 Impact Factor
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    • "In order to overcome known limitations of the diffusion tensor model (Skare et al., 2000; Descoteaux et al., 2006; Zhang et al., 2006; Barmpoutis et al., 2007; Hess and Mukherjee, 2007; Koay et al., 2009), higher order models have been proposed (Barmpoutis et al., 2007; Cheng et al., 2009; Dhollander et al., 2010; Verma and Bloy, 2010; Yap et al., 2010; Du et al., 2011; Geng et al., 2011; Raffelt et al., 2011). Nevertheless, relying on such diffusion models might not completely capture the information contained in the raw data and could therefore affect the registration accuracy. "
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    ABSTRACT: Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis.
    Frontiers in Neuroscience 04/2013; 7:41. DOI:10.3389/fnins.2013.00041 · 3.66 Impact Factor
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    • "[4] performs registration of ODF images by using the SH band energies as rotationally invariant features in a multi-channel diffeomorphic demons algorithm. [5] [6] use the SH coefficients of the ODFs as features to find the diffeomorphism between the source and target images. [7] incorporates the Riemannian metric of ODFs for quantifying the similarity between the two images into a variational problem defined under the large deformation diffeomorphic metric mapping (LDDMM) framework. "
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    ABSTRACT: We consider the problem of aligning high angular resolution diffusion images characterized by orientation distribution functions (ODFs). We cast this problem as an optimization problem where we seek the rotation that aligns the source and target ODFs. This rotation induces a linear transformation of the spherical harmonic coefficients of the ODFs, which can be parametrized by the rotation Euler angles. We propose an algebraic approach to estimate this transformation from a number of ODF correspondences. We evaluate the proposed method on synthetic ODFs as well as on a diffusion MR phantom dataset.
    IEEE International Symposium on Biomedical Imaging, Barcelona, Spain; 03/2012
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