On robust estimation of the location parameter

A fully probabilistic framework is presented for estimating local probability density functions on parameters of interest in a model of diffusion. This technique is applied to the estimation of parameters in the diffusion tensor model, and also to a simple partial volume model of diffusion. In both cases the parameters of interest include parameters defining local fiber direction. A technique is then presented for using these density functions to estimate global connectivity (i.e., the probability of the existence of a connection through the data field, between any two distant points), allowing for the quantification of belief in tractography results. This technique is then applied to the estimation of the cortical connectivity of the human thalamus. The resulting connectivity distributions correspond well with predictions from invasive tracer methods in nonhuman primate.

/pdf/characterization-and-propagation-of-uncertainty-in-diffusion-22y3bpncsw.pdf

Characterization and propagation of uncertainty in diffusion-weighted MR imaging.

In recent years, a variety of nonlinear dimensionality reduction techniques have been proposed that aim to address the limitations of traditional techniques such as PCA and classical scaling. The paper presents a review and systematic comparison of these techniques. The performances of the nonlinear techniques are investigated on artificial and natural tasks. The results of the experiments reveal that nonlinear techniques perform well on selected artificial tasks, but that this strong performance does not necessarily extend to real-world tasks. The paper explains these results by identifying weaknesses of current nonlinear techniques, and suggests how the performance of nonlinear dimensionality reduction techniques may be improved.

/pdf/dimensionality-reduction-a-comparative-review-4vhn8oy7jr.pdf

Dimensionality Reduction: A Comparative Review

Unbiased Average Age-Appropriate Atlases for Pediatric Studies

How rich functionality emerges from the invariant structural architecture of the brain remains a major mystery in neuroscience. Recent applications of network theory and theoretical neuroscience to large-scale brain networks have started to dissolve this mystery. Network analyses suggest that hierarchical modular brain networks are particularly suited to facilitate local (segregated) neuronal operations and the global integration of segregated functions. Although functional networks are constrained by structural connections, context-sensitive integration during cognition tasks necessarily entails a divergence between structural and functional networks. This degenerate (many-to-one) function-structure mapping is crucial for understanding the nature of brain networks. The emergence of dynamic functional networks from static structural connections calls for a formal (computational) approach to neuronal information processing that may resolve this dialectic between structure and function.

https://science.sciencemag.org/content/sci/342/6158/1238411.full.pdf

Structural and functional brain networks: from connections to cognition.

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2004

In this paper we present a framework for unsupervised segmentation of white matter fiber traces obtained from diffusion weighted MRI data. Fiber traces are compared pairwise to create a weighted undirected graph which is partitioned into coherent sets using the normalized cut (Ncut) criterion. A simple and yet effective method for pairwise comparison of fiber traces is presented which in combination with the Ncut criterion is shown to produce plausible segmentations of both synthetic and real fiber trace data. Segmentations are visualized as colored stream-tubes or transformed to a segmentation of voxel space, revealing structures in a way that looks promising for future explorative studies of diffusion weighted MRI data.

/pdf/clustering-fiber-traces-using-normalized-cuts-1tbzf6e4l9.pdf

Clustering Fiber Traces Using Normalized Cuts.

We propose a novel post processing method for visualization of fiber traces from DT-MRI data. Using a recently proposed non-linear dimensionality reduction technique, Laplacian eigenmaps [3], we create a mapping from a set of fiber traces to a low dimensional Euclidean space. Laplacian eigenmaps constructs this mapping so that similar traces are mapped to similar points, given a custom made pairwise similarity measure for fiber traces. We demonstrate that when the low-dimensional space is the RGB color space, this can be used to visualize fiber traces in a way which enhances the perception of fiber bundles and connectivity in the human brain.

Coloring of DT-MRI Fiber Traces Using Laplacian Eigenmaps

The development of Diffusion Tensor MRI has raised hopes in the neuro-science community for in vivo methods to track fiber paths in the white matter. A number of approaches have been presented, but there are still several essential problems that need to be solved. In this paper a novel fiber propagation model is proposed, based on stochastics and regularization, allowing paths originating in one point to branch and return a probability distribution of possible paths. The proposed method utilizes the principles of a statistical Monte Carlo method called Sequential Importance Sampling and Resampling (SISR).

/pdf/regularized-stochastic-white-matter-tractography-using-3nak7az4if.pdf

Regularized Stochastic White Matter Tractography Using Diffusion Tensor MRI

This paper investigates the use of a total least squares approach in a generalization of the iterative closest point (ICP) algorithm for shape registration. A new Generalized Total Least Squares (GTLS) formulation of the minimization process is presented opposed to the traditional Least Squares (LS) technique. Accounting for uncertainty both in the target and in the source models will lead to a more robust estimation of the transformation. Robustness against outliers is guaranteed by an iterative scheme to update the noise covariances. Experimental results show that this generalization is superior to the least squares counterpart.

/pdf/robust-generalized-total-least-squares-iterative-closest-33opfq1cu1.pdf

Anders Brun

Papers

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2004

Clustering Fiber Traces Using Normalized Cuts.

Coloring of DT-MRI Fiber Traces Using Laplacian Eigenmaps

Regularized Stochastic White Matter Tractography Using Diffusion Tensor MRI

Robust Generalized Total Least Squares Iterative Closest Point Registration