introduction: appropriate definition of the distance measure between diffusion tensors has a deep impact on diffusion tensor image (dti) segmentation results. the geodesic metric is the best distance measure since it yields high-quality segmentation results. however, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. the main goal of this ...

Introduction: Appropriate definition of the distance measure between diffusion tensors has a deep impact on Diffusion Tensor Image (DTI) segmentation results. The geodesic metric is the best distance measure since it yields high-quality segmentation results. However, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. The main goal of this ...

We show that every n-point metric of negative type (in particular, every n-point subset of L1) admits a Fréchet embedding into Euclidean space with distortion O (√ log n · log log n), a result which is tight up to the O(log log n) factor, even for Euclidean metrics. This strengthens our recent work on the Euclidean distortion of metrics of negative into Euclidean space.

Introduction In many diffusion tensor imaging (DTI) analysis methods, including registration, realignment and re-slicing, averaging or interpolating tensors is required. Defining how distance is measured between tensors, through a metric, determines the interpolation results. It was demonstrated that when using a conventional Euclidean metric, the resulted tensor might have a larger volume (det...

It is shown in DS] that the Sierpi nski gasket S IR N can be represented as the Martin boundary of a certain Markov chain and hence carries a canonical metric M induced by the embedding into an associated Martin space M. It is a natural question to compare this metric M with the Euclidean metric. We show rst that the harmonic measure coincides with the normalized H = (log(N + 1)= log 2)-dimensi...

Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...

A classical result in metric geometry asserts that any n-point metric admits a linear-size spanner of dilation O(log n) [PS89]. More generally, for any c > 1, any metric space admits a spanner of size O(n), and dilation at most c. This bound is tight assuming the well-known girth conjecture of Erdős [Erd63]. We show that for a metric induced by a set of n points in high-dimensional Euclidean sp...

This paper introduces a novel mathematical and computational framework, namely Log-Hilbert-Schmidt metric between positive definite operators on a Hilbert space. This is a generalization of the Log-Euclidean metric on the Riemannian manifold of positive definite matrices to the infinite-dimensional setting. The general framework is applied in particular to compute distances between covariance o...

This paper presents a new action recognition approach based on local spatio-temporal features. The main contributions of our approach are twofold. First, a new local spatio-temporal feature is proposed to represent the cuboids detected in video sequences. Specifically, the descriptor utilizes the covariance matrix to capture the self-correlation information of the low-level features within each...

Consider an n-point metric space M = (V, δ), and a transmission range assignment r : V → R that maps each point v ∈ V to the disk of radius r(v) around it. The symmetric disk graph (henceforth, SDG) that corresponds to M and r is the undirected graph over V whose edge set includes an edge (u, v) if both r(u) and r(v) are no smaller than δ(u, v). SDGs are often used to model wireless communicati...