Comparative Evaluation of Voxel Similarity Measures for Affine Registration of Diffusion Tensor MR Images

Abstract-In this paper we present a robust approach to the registration of white matter tractographies extracted from DT-MRI scans. The fibers are projected into a high dimensional feature space based on the sequence of their 3D coordinates. Adaptive mean-shift (AMS) clustering is applied to extract a compact set of representative fiber-modes (FM). Each FM is assigned to a multivariate Gaussian distribution according to its population thereby leading to a Gaussian Mixture model (GMM) representation for the entire set of fibers. The registration between two fiber sets is treated as the alignment of two GMMs and is performed by maximizing their correlation ratio. A 9 parameters affine transform is recovered and eventually refined to a 12 parameters affine transform using an innovative meanshift (MS) based registration refinement scheme presented in this paper. The validation of the algorithm on synthetic intra-subject data demonstrates its robustness to interrupted and deviating fiber artifacts as well as outliers. Using real intra-subject data, a comparison is conducted to other intensity based and fiber-based registration algorithms, demonstrating competitive results. An option for tracking-in-time, on specific white matter fiber tracts, is also demonstrated on the real data.

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“…2) Pure rotational transformation Formally, y = Rx (25) R is a rotation matrix. Since the rotation matrix R represents a linear transformation:…”

Section: Discussionmentioning

confidence: 99%

“…Directional and magnitude information are weighted differently depending on the type of diffusion. A few of these tensor based metrics were evaluated and compared in [25].…”

Section: Introductionmentioning

confidence: 99%

Co-registration of White Matter Tractographies by Adaptive-Mean-Shift and Gaussian Mixture Modeling

Zvitia

Mayer

Shadmi

et al. 2010

IEEE Trans. Med. Imaging

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“…Inspired by [14], we model the diffusivity function as a probability density function (pdf), by normalizing its integral over the spherical angle Ω to 1: (2) where gtr is the generalized trace of D [14]. For two diffusivity functions D p and D q , we define the symmetric KL-divergence based on the corresponding pdfs p(θ, φ) and q(θ, φ): (3) Applying Eq (2) to the integrals in Eq (3), for example, (4) we then have (5) Direct estimation of sKL in Eq (5) is computationally expensive, but is faster if we expand the diffusivity functions D(θ, φ) as a spherical harmonic (SH) series [9,10]: (6) here are the associated Legendre polynomials. D(θ, φ) is real and radially symmetric, so it is sufficient to adopt a real basis function set Y lm while retaining the orthonormality of [10]:…”

Section: Kullback-leibler Divergence Of Two Diffusivity Functionsmentioning

confidence: 99%

“…Diffusivity profiles can be resolved more clearly in brain regions where fiber tracts cross, providing more accurate information for fiber-tracking (tractography), disease detection, and analysis of anatomical connectivity. differences (SSD) [5]. Here we evaluate a new information-theoretic metric, the symmetric Kullback-Leibler divergence (sKL-divergence), for measuring differences between diffusivity profiles in HARDI.…”

Section: Introductionmentioning

confidence: 99%

Information-Theoretic Analysis of Brain White Matter Fiber Orientation Distribution Functions

Chiang

Klunder

McMahon

et al. 2007

Lecture Notes in Computer Science

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We propose a new information-theoretic metric, the symmetric Kullback-Leibler divergence (sKLdivergence), to measure the difference between two water diffusivity profiles in high angular resolution diffusion imaging (HARDI). Water diffusivity profiles are modeled as probability density functions on the unit sphere, and the sKL-divergence is computed from a spherical harmonic series, which greatly reduces computational complexity. Adjustment of the orientation of diffusivity functions is essential when the image is being warped, so we propose a fast algorithm to determine the principal direction of diffusivity functions using principal component analysis (PCA). We compare sKL-divergence with other inner-product based cost functions using synthetic samples and real HARDI data, and show that the sKL-divergence is highly sensitive in detecting small differences between two diffusivity profiles and therefore shows promise for applications in the nonlinear registration and multi-subject statistical analysis of HARDI data.

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“…The distance or similarity between a native image and a template can be represented by the Euclidean difference [ 15 ]. The Euclidean difference would arise with increasing differences of images.…”

Section: Introductionmentioning

confidence: 99%

Reducing Individual Variation for fMRI Studies in Children by Minimizing Template Related Errors

Weng

Dong

et al. 2015

PLoS ONE

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Spatial normalization is an essential process for group comparisons in functional MRI studies. In practice, there is a risk of normalization errors particularly in studies involving children, seniors or diseased populations and in regions with high individual variation. One way to minimize normalization errors is to create a study-specific template based on a large sample size. However, studies with a large sample size are not always feasible, particularly for children studies. The performance of templates with a small sample size has not been evaluated in fMRI studies in children. In the current study, this issue was encountered in a working memory task with 29 children in two groups. We compared the performance of different templates: a study-specific template created by the experimental population, a Chinese children template and the widely used adult MNI template. We observed distinct differences in the right orbitofrontal region among the three templates in between-group comparisons. The study-specific template and the Chinese children template were more sensitive for the detection of between-group differences in the orbitofrontal cortex than the MNI template. Proper templates could effectively reduce individual variation. Further analysis revealed a correlation between the BOLD contrast size and the norm index of the affine transformation matrix, i.e., the SFN, which characterizes the difference between a template and a native image and differs significantly across subjects. Thereby, we proposed and tested another method to reduce individual variation that included the SFN as a covariate in group-wise statistics. This correction exhibits outstanding performance in enhancing detection power in group-level tests. A training effect of abacus-based mental calculation was also demonstrated, with significantly elevated activation in the right orbitofrontal region that correlated with behavioral response time across subjects in the trained group.

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Comparative Evaluation of Voxel Similarity Measures for Affine Registration of Diffusion Tensor MR Images

Cited by 4 publications

References 11 publications

Co-registration of White Matter Tractographies by Adaptive-Mean-Shift and Gaussian Mixture Modeling

Co-registration of White Matter Tractographies by Adaptive-Mean-Shift and Gaussian Mixture Modeling

Information-Theoretic Analysis of Brain White Matter Fiber Orientation Distribution Functions

Reducing Individual Variation for fMRI Studies in Children by Minimizing Template Related Errors

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