Concept

Curvature of Riemannian manifolds

Related publications (167)

Internal dynamics of Newtonian and viscoplastic fluid avalanches down a sloping bed

Christophe Ancey, Nicolas Andreini, Gaël Epely Chauvin

We experimentally investigated the spreading of fluid avalanches (i.e., fixed volumes of fluid) down an inclined flume. Emphasis was given to the velocity field within the head. Using specific imaging techniques, we were able to measure velocity profiles w ...

2012

Invariant Higher-Order Variational Problems II

Tudor Ratiu, François Gay-Balmaz

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as ...

Springer Verlag2012

How to Measure Cortical Folding from MR Images: a Step-by-Step Tutorial to Compute Local Gyrification Index

Jean-Philippe Thiran, Meritxell Bach Cuadra, Marie Schaer

Cortical folding (gyrification) is determined during the first months of life, so that adverse events occurring during this period leave traces that will be identifiable at any age. As recently reviewed by Mangin and colleagues2, several methods exist to q ...

2012

Scale Invariant Features and Polar Descriptors in Omnidirectional Imaging

Pascal Frossard, Zafer Arican

We propose a method to compute scale invariant features in omnidirectional images. We present a formulation based on Riemannian geometry for the definition of differential operators on non-Euclidian manifolds that describe the mirror and lens structure in ...

Institute of Electrical and Electronics Engineers2012

Local Sampling Analysis for Quadratic Embeddings of Riemannian Manifolds

Hemant Tyagi

In this work we do a theoretical analysis of the local sampling conditions for points lying on a quadratic embedding of a Riemannian manifold in a Euclidean space. The embedding is assumed to be quadratic at a reference point

P

. Our analysis is based on ...

2011

Déformations conformes des variétés de Finsler-Ehresmann

Ratiba Djelid

An intrinsic approach to Finsler geometry is proposed. A concept of Finsler- Ehresmann manifold, denoted by (M,F,H), is introduced and a generalized Chern connection is built for this manifold. Conformal deformations on this manifold are considered. First, ...

EPFL2011

Discretization of Parametrizable Signal Manifolds

Pascal Frossard, Elif Vural

Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several transformation manif ...

Institute of Electrical and Electronics Engineers2011

Learning pattern transformation manifolds with parametric atom selection

Pascal Frossard, Elif Vural

We address the problem of building a manifold in order to represent a set of geometrically transformed images by selecting a good common sparse approximation of them with parametric atoms. We propose a greedy method to construct a representative pattern su ...

2011

Harmonic Active Contours for multichannel image segmentation

Jean-Philippe Thiran, Xavier Bresson, Dominique Zosso, Virginia Estellers Casas

We propose a segmentation method based on the geometric representation of images as surfaces embedded in a higher dimensional space, handling naturally multichannel images. The segmentation is based on an active contour embedded in the image manifold, alon ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Optimal image alignment with random projections of manifolds: algorithm and geometric analysis

Pascal Frossard, Daniel Kressner, Effrosyni Kokiopoulou

This paper addresses the problem of image alignment based on random measurements. Image alignment consists of estimating the relative transformation between a query image and a reference image. We consider the specific problem where the query image is prov ...

2011

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Local Sampling Analysis for Quadratic Embeddings of Riemannian Manifolds

Hemant Tyagi

P

. Our analysis is based on ...

2011