Tractography allows us to explore white matter connectivity in diffusion MR images of the brain. However, noise, artifacts and limited resolution introduce uncertainty into the results. We propose a statistical model that allows us to quantify and visualize the uncertainty of a neuronal pathway between any two fixed anatomical regions. Given a sample set of tract curves obtained via tractograph...

Fundamental matrix estimation is difficult since it is often based on correspondences that are spoilt by noise and outliers. Outliers must be thrown out via robust statistics, and noise gives uncertainty. In this article we provide a closed-form formula for the uncertainty of the so-called 8 point algorithm, which is a basic tool for fundamental matrix estimation via robust methods. As an appli...

Approaches to wavelet-based denoising (or signal enhancement) have so far relied on the assumption of normally distributed perturbations. To relax this assumption, which is often violated in practice, we derive a robust wavelet thresholding technique based on theMinimax Description Length principle. We rst determine the least favorable distribution in the "-contaminated normal family as the mem...

Structure from motion (SfM) comprises techniques for estimating 3D structures from uncalibrated 2D image sequences. This work focuses on two contributions: Firstly, a stability analysis is performed and the error propagation of image noise is studied. Secondly, to stabilize SfM, we present two optimization schemes by using a priori knowledge about collinearity or coplanarity of feature points i...

We prove a stability of weakly almost conformal mappings in W 1,p(Ω;Rn) for p not too far below the dimension n by studying the W 1,pquasiconvex hull of the set Cn of conformal matrices. The study is based on coercivity estimates from the nonlinear Hodge decompositions and reverse Hölder inequalities from the Ekeland variational principle.

The uncertainty is proportional to the noise level, is dependent on the geology and is influenced by the acquisition geometry. Because of the nonlinearity of the inversion problem, azimuthal AVO inversion will always produce a positive estimate of the anisotropy gradient even if the media is isotropic; thus it is important that this attribute be examined along with its uncertainty. The interpre...

—To improve the problems of noise amplification and error propagation of the fixed cooperation schemes in cooperative communications, a relay selection strategy is proposed based on the hybrid decode-amplify-forward protocol. It can adaptively determine cooperation schemes according to the Channel Status Information (CSI) of the source-relay. Then it selects the best relay from the candidate r...

The intent in robust design is to improve the quality of products and processes by reducing their sensitivity to variations, thereby reducing the effects of variability without removing its sources. Robust design is especially useful for integrating information from designers working at multiple length and time scales. Inevitably this involves the integration of uncertain information. This unce...

In this paper, we derive an EM algorithm for nonlinear state space models. We use it to estimate jointly the neural network weights, the model uncertainty and the noise in the data. In the E-step we apply a forward-backward Rauch-Tung-Striebel smoother to compute the network weights. For the M-step, we derive expressions to compute the model uncertainty and the measurement noise. We nd that the...