Diffusion tensor imaging provides structural information in medical images in the form of a symmetric positive
matrix that provides, at each point, the covariance of water diffusion in the tissue. We here describe a new
approach designed for smoothing this tensor by directly acting on the field of frames provided by the eigenvectors
of this matrix. Using a representation of fields of frames as linear forms acting on smooth tensor fields, we use
the theory of reproducing kernel Hilbert spaces to design a measure of smoothness based on kernels which is
then used in a denoising algorithm. We illustrate this with brain images and show the impact of the procedure
on the output of fiber tracking in white matter.
Diffusion tensor MR image data gives at each voxel in the image a symmetric, positive definite matrix that is
denoted as the diffusion tensor at that voxel location. The eigenvectors of the tensor represent the principal
directions of anisotopy in water diffusion. The eigenvector with the largest eigenvalue indicates the local orientation
of tissue fibers in 3D as water is expected to diffuse preferentially up and down along the fiber tracts.
Although there is no anatomically valid positive or negative direction to these fiber tracts, for many applications,
it is of interest to assign an artificial direction to the fiber tract by choosing one of the two signs of the principal
eigenvector in such a way that in local neighborhoods the assigned directions are consistent and vary smoothly
We demonstrate here an algorithm for realigning the principal eigenvectors by flipping their sign such that it
assigns a locally consistent and spatially smooth fiber direction to the eigenvector field based on a Monte-Carlo
algorithm adapted from updating clusters of spin systems. We present results that show the success of this
algorithm on 11 available unsegmented canine cardiac volumes of both healthy and failing hearts.
This paper analyzes the performance of ATR algorithms in clutter. The variability of target type and pose is accommodated by introducing a deformable template for every target type, with low-dimensional groups of geometric transformations representing position and pose. Signature variation of targets is taken into account by expanding deformable templates into robust deformable templates generated from the template and a linear combination of PCA elements, spanning signature intensities. Detection and classification performance is characterized using ROC analysis. Asymptotic expressions for probabilities of recognition errors are derived, yielding asymptotic error rates. The results indicate that the asymptotic error probabilities depend upon a parameter, which characterizes the separation between the true target and the most similar but incorrect one. It is shown that the asymptotic expressions derived almost accurately predict performance of detection and identification of targets occluded by natural clutter.
This communication presents new results about convergence of stochastic gradient algorithms for maximum likelihood estimation of Markov random fields. We first present theoretical results dealing with the convergence of a generalized Robbins-Montro procedure. These results provide rigorous justifications for simple numerical strategies which can be employed in practice; they are illustrated by numerical experiments.
This study presents and compares two models for estimating motion in meteorological images sequences. The first method makes use of the grey level pixel conservation hypothesis. It produces a dense vector field through a variational formulation, and authorizes discontinuities in the resulting field. A second method use a model taking affine motion as ground hypothesis. Motion parameters are then estimated with an incremental least-square procedure. One of its principal advantages results in a modeling of the variation of the grey level values. The two methods are complementary: the second computes a global estimation of the motion, which is locally enhanced by the first.