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Laplacian Operator, Diffusion Flow and Active Contour on non-Euclidean Images

Publications associées (101)

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Graph-based representation for multiview image geometry

Pascal Frossard, Thomas Maugey

In this paper, we propose a new representation for multiview image sets. Our approach relies on graphs to describe geometry information in a compact and controllable way. The links of the graph connect pixels in different images and describe the proximity ...

Institute of Electrical and Electronics Engineers2015

Relax and Unfold: Microphone Localization with Euclidean Distance Matrices

Martin Vetterli, Ivan Dokmanic, Juri Ranieri

Recent methods for localization of microphones in a microphone array exploit sound sources at a priori unknown locations. This is convenient for ad-hoc arrays, as it requires little additional infrastructure. We propose a flexible localization algorithm by ...

2015

ShapeNet: Convolutional Neural Networks on Non-Euclidean Manifolds

Pierre Vandergheynst, Michael Bronstein

Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we propose ShapeNet, a generalization of the popular convolutional neural ...

2015

Curvature-induced symmetry breaking determines elastic surface patterns

Pedro Miguel Nunes Pereira de Almeida Reis

Symmetry-breaking transitions associated with the buckling and folding of curved multilayered surfaces—which are common to a wide range of systems and processes such as embryogenesis, tissue differentiation and structure formation in heterogeneous thin fil ...

Nature Publishing Group2015

Principal Flows

Victor Panaretos, Tung Huy Pham, Zhigang Yao

We revisit the problem of extending the notion of principal component analysis (PCA) to multivariate datasets that satisfy nonlinear constraints, therefore lying on Riemannian manifolds. Our aim is to determine curves on the manifold that retain their cano ...

American Statistical Association2014

Harmonic Active Contours

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

We propose a segmentation method based on the geometric representation of images as two-dimensional manifolds embedded in a higher dimensional space. The segmentation is formulated as a minimization problem, where the contours are described by a level set ...

Institute of Electrical and Electronics Engineers2014

State of the Art in Surface Reconstruction from Point Clouds

Andrea Tagliasacchi

The area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data ...

The Eurographics Association2014

An Exotic Deformation of the Hyperbolic Space

Nicolas Monod

Let Isom(H^n) be the group of isometries of the n-dimensional real hyperbolic space. We first classify all continuous non-elementary actions of on the infinite-dimensional real hyperbolic space. We then prove the existence of a continuous family of non-iso ...

Johns Hopkins Univ Press2014

Tangent space estimation for smooth embeddings of Riemannian manifolds

Pascal Frossard, Elif Vural, Hemant Tyagi

Numerous dimensionality reduction problems in data analysis involve the recovery of low-dimensional models or the learning of manifolds underlying sets of data. Many manifold learning methods require the estimation of the tangent space of the manifold at a ...

2013

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

Martins Bruveris, Martin Bauer

The geodesic distance vanishes on the group of compactly supported diffeomorphisms of a Riemannian manifold of bounded geometry, for the right invariant weak Riemannian metric which is induced by the Sobolev metric of order on the Lie algebra of vector fie ...

Springer Verlag2013