Samuel Gerber

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This paper describes a method for building efficient representations of large sets of brain images. Our hypothesis is that the space spanned by a set of brain images can be captured, to a close approximation, by a low-dimensional, nonlinear manifold. This paper presents a method to learn such a low-dimensional manifold from a given data set. The manifold(More)
Non-linear dimensionality reduction of noisy data is a challenging problem encountered in a variety of data analysis applications. Recent results in the literature show that spectral decomposition, as used for example by the Laplacian Eigenmaps algorithm, provides a powerful tool for non-linear dimensionality reduction and manifold learning. In this paper,(More)
This paper presents a method for correcting the geometric and greyscale distortions in diffusion-weighted MRI that result from inhomogeneities in the static magnetic field. These inhomogeneities may due to imperfections in the magnet or to spatial variations in the magnetic susceptibility of the object being imaged--so called susceptibility artifacts.(More)
An important goal of scientific data analysis is to understand the behavior of a system or process based on a sample of the system. In many instances it is possible to observe both input parameters and system outputs, and characterize the system as a high-dimensional function. Such data sets arise, for instance, in large numerical simulations, as energy(More)
This paper investigates an approach to model the space of brain images through a low-dimensional manifold. A data driven method to learn a manifold from a collections of brain images is proposed. We hypothesize that the space spanned by a set of brain images can be captured, to some approximation, by a low-dimensional manifold, i.e. a parametrization of the(More)
We present a manifold learning approach to dimensionality reduction that explicitly models the manifold as a mapping from low to high dimensional space. The manifold is represented as a parametrized surface represented by a set of parameters that are defined on the input samples. The representation also provides a natural mapping from high to low(More)
As dataset size and complexity steadily increase, uncertainty is becoming an important data aspect. So, today's visualizations need to incorporate indications of uncertainty. However, characterizing uncertainty for visualization isn't always straightforward. Entropy, in the information-theoretic sense, can be a measure for uncertainty in categorical(More)
This paper presents a fast method for quantifying shape differences/similarities between pairs of magnetic resonance (MR) brain images. Most shape comparisons in the literature require some kind of deformable registration or identification of exact correspondences. The proposed approach relies on an optimal matching of a large collection of features, using(More)
This paper introduces a novel partition-based regression approach that incorporates topological information. Partition-based regression typically introduce a quality-of-fit-driven decomposition of the domain. The emphasis in this work is on a topologically meaningful segmentation. Thus, the proposed regression approach is based on a segmentation induced by(More)