The different lengths and conduction velocities of axons connecting cortical regions of the brain yield information transmission delays which are believed to be fundamental to brain dynamics. A critical step in the estimation of axon conduction speed in vivo is the estimation of the inter hemispheric transfer time (IHTT). The IHTT is estimated using electroencephalography (EEG) by measuring the latency between the peaks of specific electrodes or by computing the lag to maximum correlation on contra lateral electrodes. These approaches do not take the subject’s anatomy into account and, due to the limited number of electrodes used, only partially leverage the information provided by EEG. Using the previous published Connectivity Informed Maximum Entropy on the Mean (CIMEM) method, we propose a new approach to estimate the IHTT. In CIMEM, a Bayesian network is built using the structural connectivity information between cortical regions. EEG signals are then used as evidence into this network to compute the posterior probability of a connection being active at a particular time. Here, we propose a new quantity which measures how much of the EEG signals are supported by connections, which is maximized when the correct conduction delays are used. Using simulations, we show that CIMEM provides a more accurate estimation of the IHTT compared to the peak latency and lag to maximum correlation methods.
Extracting information about axon diameter distributions in the brain is a challenging task which provides
useful information for medical purposes; for example, the ability to characterize and monitor axon diameters
would be useful in diagnosing and investigating diseases like amyotrophic lateral sclerosis (ALS)1 or autism.2
Three families of operators are defined by Ozarslan,3 whose action upon an NMR attenuation signal extracts
the moments of the pore size distribution of the ensemble under consideration; also a numerical method is
proposed to continuously reconstruct a discretely sampled attenuation profile using the eigenfunctions of the
simple harmonic oscillator Hamiltonian: the SHORE basis. The work presented here extends Ozarlan's method
to other bases that can offer a better description of attenuation signal behaviour; in particular, we propose the use
of the radial Spherical Polar Fourier (SPF) basis. Testing is performed to contrast the efficacy of the radial SPF
basis and SHORE basis in practical attenuation signal reconstruction. The robustness of the method to additive
noise is tested and analysed. We demonstrate that a low-order attenuation signal reconstruction outperforms a
higher-order reconstruction in subsequent moment estimation under noisy conditions. We propose the simulated
annealing algorithm for basis function scale parameter estimation. Finally, analytic expressions are derived and
presented for the action of the operators on the radial SPF basis (obviating the need for numerical integration,
thus avoiding a spectrum of possible sources of error).
Diffusion MRI has become an established research tool for the investigation of tissue structure and orientation from which
has stemmed a number of variations, such as Diffusion Tensor Imaging (DTI) Diffusion Spectrum Imaging (DSI) and QBall
Imaging (QBI). The acquisition and analysis of such data is very challenging due to its complexity. Recently, an
exciting new Kalman filtering framework has been proposed for DTI and QBI reconstructions in real time during the repetition
time (TR) of the acquisition sequence. In this article, we first revisit and thoroughly analyze this approach and show
it is actually sub-optimal and not recursively minimizing the intended criterion due to the Laplace-Beltrami regularization
term. Then, we propose a new approach that implements the QBI reconstruction algorithm in real-time using a fast and
robust Laplace-Beltrami regularization without sacrificing the optimality of the Kalman filter. We demonstrate that our
method solves the correct minimization problem at each iteration and recursively provides the optimal QBI solution. We
validate with real QBI data that our proposed real-time method is equivalent in terms of QBI estimation accuracy to the
standard off-line processing techniques and outperforms the existing solution. This opens new and interesting opportunities
for real-time feedback for clinicians during an acquisition and also for researchers investigating into optimal diffusion
orientation sets and, real-time fiber tracking and connectivity mapping.
Diffusion Tensor Imaging (DTI) is currently a widespread technique to infer white matter architecture in the
human brain. An important application of DTI is to understand the anatomical coupling between functional
cortical regions of the brain. To solve this problem, anisotropy maps are insufficient and fiber tracking methods
are used to obtain the main fibers. While the diffusion tensor (DT) is important to obtain anisotropy maps
and apparent diffusivity of the underlying tissue, fiber tractography using the full DT may result in diffusive
tracking that leaks into unexpected regions. Sharpening is thus of utmost importance to obtain complete and
accurate tracts. In the tracking literature, only heuristic methods have been proposed to deal with this problem.
We propose a new tensor sharpening transform. Analogously to the general issue with the diffusion and fiberOrientation Distribution Function (ODF) encountered when working with High Angular Resolution Diffusion
Imaging (HARDI), we show how to transform the diffusion tensors into so-called fiber tensors. We demonstrate
that this tensor transform is a natural pre-processing task when one is interested in fiber tracking. It also leads
to a dramatic improvement of the tractography results obtained by front propagation techniques on the full
diffusion tensor. We compare and validate sharpening and tracking results on synthetic data and on known fiber
bundles in the human brain.
High angular resolution diffusion imaging (HARDI) has recently been of great interest to characterize non-Gaussian diffusion process. In the white matter of the brain, this occurs when fiber bundles cross, kiss or diverge within the same voxel. One of the important goal is to better describe the apparent diffusion process in these multiple fiber regions, thus overcoming the limitations of classical diffusion tensor imaging (DTI). In this paper, we design the appropriate mathematical tools to describe noisy HARDI data. Using a meaningful modified spherical harmonics basis to capture the physical constraints of the problem, we propose a new regularization algorithm to estimate a smoother and closer diffusivity profile to the true diffusivities without noise. We exploit properties of the spherical harmonics to define a smoothing term based on the Laplace-Beltrami for functions defined on the unit sphere. An additional contribution of the paper is the derivation of the general transformation taking the spherical harmonics coefficients to the high order tensor independent elements. This allows the careful study of the state of the art high order anisotropy measures computed from either spherical harmonics or tensor coefficients. We analyze their ability to characterize the underlying diffusion process. We are able to recover voxels with isotropic, single fiber anisotropic and multiple fiber anisotropic diffusion. We test and validate the approach on diffusion profiles from synthetic data and from a biological rat phantom.
A large number of algorithms based on partial differential equations (PDE) have recently been proposed to tackle the problems of noise removal, image enhancement and image restoration in real images. Starting with a noisy original image, the algorithms remove noise and enhance the original image by iterating the image using various schemes that are controlled by mean curvature, min/max flow, etc. We first present a variational approach such that during image restoration, edges detected in the original image are being preserved, and then we compare in a second part, the mathematical foundation of this method with respect to some of the well known methods recently proposed in the literature within the class of PDE based algorithms. The performance of our approach will be carefully examined and compared to some of the most recent algorithms proposed in the literature within the class of PDE based algorithms. Experimental results on synthetic and real images will illustrate the capabilities of all the studied approaches.
In this paper, an original approach to deal with the important problem of stereovision using a weakly calibrated pair of images is presented. Given two different views of some 3D objects, and a virtual 3D plan set by an external operator, the method we propose allows to recover the 2D projections, in the two images, of the 3D planar curves corresponding to the intersection of the virtual plan with the different objects in the scene. To this end, an arbitrary curve is first initialized in one of the two images. This curve, and its associated homographic curve in the second image are then designed to move under the influence of internal and external image dependent forces while minimizing an energy functional. Following the work on geodesic active contours by Caselles et al and Malladi et al, we then transform the problem of minimizing this functional into a problem of geodesic computation in a Riemannian space, according to a new metric. The Euler- Lagrange equation of this new functional is derived and its associated PDE is then solved using the level set formulation scheme of Osher and Sethian by viewing it as a front propagating with internal and external image correlation dependent speed. The curves to be matched are therefore modelized as geodesic active contours evolving toward the minimum of the designed functional. Using this level set based approach, complex curves can be matched and topological changes for the evolving curves are naturally managed. The final result is also relatively independent of the curve initialization. Promising experimental results have been obtained on real images and some of these results are illustrated in the experimental section of this paper.
MOVE is one of the ESPRIT III OMI feasibility studies projects is Vision/Robotics for industrial applications. The objective of MOVE is to study a modular environment specifically designed for the field of Computer Vision, which permits the integration of heterogeneous processors and of specific software. This environment is open -- it allows integration of existing and future processors, actuators and visual sensors -- and it facilitates communication with the external world. It is used directly in the design of a set of industrial vision applications which correspond to real requirements and therefore it facilitates product development and make it cost effective. There are many areas of industry and commerce where application of machine vision would make an important impact on productivity and product quality, but the progress has been slow because of the lack of a suitable high-performance low-cost hardware. This paper gives some elements on how MOVE intends to provide the needed solution.
Deformable contours, based on energy minimization, have been widely used for tracking purposes. This paper proposes a novel type of constraint for the energy minimization problem: the use of motion models. Such an approach greatly reduces the sliding effects occurring during tracking: thus tracking provides point-to-point correspondence between the tracked B- spline based curves and reliably estimates their apparent motion. For a calibrated camera system, the stereo correspondences provided by this matching method can be used to reconstruct a 3-D curve point by point. This set of 3-D points is then approximated and refined by a 3-D deformable curve, in order to improve consistency with image observations. Furthermore, the bases of this tracking approach, i.e., B-splines and the estimation of 2-D motion models, provide an efficient way of estimating time-to-collision, and recovering the spatio-temporal surface of a moving contour, which has been proven to supply valuable information about its 3-D structure and motion. A large set of experimental results illustrates the different parts of this work.
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