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In this paper, we present a novel algorithm for non-rigidly registering two high angular resolution diffusion weighted MRIs (HARDI), each represented by a Gaussian mixture field (GMF). We model the non-rigid warp by a thin-plate spline and formulate the registration problem as the minimization of the L2 distance between the two given GMFs. The key… (More)

In this paper, we address the problem of video tracking using covariance descriptors constructed from simple features extracted from the given image sequence. Theoretically, this can be posed as a tracking problem in the space of (n, n) symmetric positive definite (SPD) matrices denoted by Pn. A novel probabilistic dynamic model in Pn based on Riemannian… (More)

Computation of the mean of a collection of symmetric positive definite (SPD) matrices is a fundamental ingredient of many algorithms in diffusion tensor image (DTI) processing. For instance, in DTI segmentation, clustering, etc. In this paper, we present novel recursive algorithms for computing the mean of a set of diffusion tensors using several… (More)

In this paper we present a form of law of large numbers on P n , the space of n × n symmetric positive-definite (SPD) matrices equipped with Fisher-Rao metric. Specifically, we propose a recursive algorithm for estimating the Karcher expectation of an arbitrary distribution defined on P n , and we show that the estimates computed by the recursive algorithm… (More)

The unscented Kalman filter (UKF) was recently introduced in literature for simultaneous multi-tensor estimation and tractography. This UKF however was not intrinsic to the space of diffusion tensors. Lack of this key property leads to inaccuracies in the multi-tensor estimation as well as in tractography. In this paper, we propose an novel intrinsic… (More)

Groupwise image registration is an essential part of atlas construction which is a very import and challenging task in medical image analysis. In this paper, we present a novel atlas construction technique using a groupwise registration of high angular resolution diffusion (MR) imaging datasets each of which is represented by a Gaussian Mixture field. To… (More)

Symmetric positive-definite (SPD) matrices are ubiquitous in Computer Vision, Machine Learning and Medical Image Analysis. Finding the center/average of a population of such matrices is a common theme in many algorithms such as clustering, segmentation, principal geodesic analysis, etc. The center of a population of such matrices can be defined using a… (More)

Tractography refers to the process of tracing out the nerve fiber bundles from diffusion Magnetic Resonance Images (dMRI) data acquired either in vivo or ex-vivo. Tractography is a mature research topic within the field of diffusion MRI analysis, nevertheless, several new methods are being proposed on a regular basis thereby justifying the need, as the… (More)

A novel adaptation of the unscented Kalman filter (UKF) was recently introduced in literature for simultaneous multitensor estimation and fiber tractography from diffusion MRI. This technique has the advantage over other tractography methods in terms of computational efficiency, due to the fact that the UKF simultaneously estimates the diffusion tensors and… (More)

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