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Harmonic Active Contours for multichannel image segmentation

Publications associées (42)

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$L_{q,p}$-cohomology of Riemannian Manifolds with Negative Curvature

Marc Troyanov

We consider the L_{q,p}-cohomology of a complete simply connected Riemannian manifold (M,g) with pinched negative curvature. The connection between the L_{q,p}-cohomology of (M,g) and Sobolev inequalities for differential forms on (M,g) was established by ...

Springer2009

Optimal control of geodesics in Riemannian manifolds

Roland Rozsnyo

The aim of this dissertation is to solve numerically the following problem, denoted by P : given a Riemannian manifold and two points a and b belonging to that manifold, find a tangent vector T at a, such that expa(T) = b, assuming that T exists. This prob ...

EPFL2007

Sobolev inequalities for differential forms and $L_{q,p}$-cohomology

Marc Troyanov

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold

(M,g)

and the

L_{q,p}

-cohomology of that manifold. The

L_{q,p}

-cohomology of

(M,g)

is defined to be the quotient of the space of closed differential ...

2006

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

Jean-Philippe Thiran, Pierre Vandergheynst, Xavier Bresson, Iva Bogdanova Vandergheynst

We propose here some basic approaches to direct processing of the

360^o

-images as we take into consideration the geometry of each one. Obviously, the geometry of each of these images is a consequence of the geometry of the sensor's mirror used. This tech ...

2005

Image segmentation with variational active contours

Xavier Bresson

An important branch of computer vision is image segmentation. Image segmentation aims at extracting meaningful objects lying in images either by dividing images into contiguous semantic regions, or by extracting one or more specific objects in images such ...

EPFL2005

Multiscale Active Contours

Jean-Philippe Thiran, Pierre Vandergheynst, Xavier Bresson

In this paper, we propose an evolution equation for the active contours in scale spaces. This evolution equation is based on the Polyakov functional that has been first introduced in physics and has been then used in image processing in ...

SPIE2005

Optimal control of geodesics in Riemannian manifolds

Klaus-Dieter Semmler, Roland Rozsnyo

Summary: We present a method based on an optimal control technique for numerical computations of geodesic paths between two fixed points of a Riemannian manifold under the assumption of existence. In this method, the control variable is the tangent vector ...

2004

Multiscale Active Contours

Jean-Philippe Thiran, Pierre Vandergheynst, Xavier Bresson

In this paper, we propose two approaches to define an evolution equation for the active contours in scale spaces. The evolution equation is based on the Polyakov functional that has been first introduced in physics and has been then used in image processin ...

2004

Liouville type theorems for mappings with bounded (co)-distortion

Marc Troyanov

We obtain Liouville type theorems for mappings with bounded

s

-distorsion between Riemannian manifolds. Besides these mappings, we introduce and study a new class, which we call mappings with bounded

q

-codistorsion. ...

2002

Segmentation of Natural Images by Non-linear Scale-Space linking

Pierre Vandergheynst

A new method of image segmentation based on building up a hierarchical tree through non-linear scale-space is proposed. Non-linear scale space creates from the original image the whole family of blurred images but keeps sharp region boundaries. This charac ...

2001

Sobolev inequalities for differential forms and $L_{q,p}$-cohomology

Marc Troyanov

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold

(M,g)

and the

L_{q,p}

-cohomology of that manifold. The

L_{q,p}

-cohomology of

(M,g)

is defined to be the quotient of the space of closed differential ...

2006

Liouville type theorems for mappings with bounded (co)-distortion

Marc Troyanov

We obtain Liouville type theorems for mappings with bounded

s

-distorsion between Riemannian manifolds. Besides these mappings, we introduce and study a new class, which we call mappings with bounded

q

-codistorsion. ...

2002

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

Jean-Philippe Thiran, Pierre Vandergheynst, Xavier Bresson, Iva Bogdanova Vandergheynst

We propose here some basic approaches to direct processing of the

360^o

-images as we take into consideration the geometry of each one. Obviously, the geometry of each of these images is a consequence of the geometry of the sensor's mirror used. This tech ...

2005