Reconstructing shapes with guarantees by unions of convex sets (2009)
Attali, Dominique, Lieutier, André
A simple way to reconstruct a shape $A$ from a sample $P$ is to output an $r$-offset $P + r B$, where $B$ designates the unit Euclidean ball centered at the origin. Recently, it has been proved that...
Reconstructing shapes with guarantees by unions of convex sets (2009)
Attali, Dominique, Lieutier, André
A simple way to reconstruct a shape $A$ from a sample $P$ is to output an $r$-offset $P + r B$, where $B$ designates the unit Euclidean ball centered at the origin. Recently, it has been proved that...
Stability and computation of medial axes – a state-of-the-art report (2008)
Dominique Attali, Jean-daniel Boissonnat, Herbert Edelsbrunner
Summary. The medial axis of a geometric shape captures its connectivity. In spite of its inherent instability, it has found applications in a number of areas that deal with shapes. In this survey...
A Tight Bound for the Delaunay Triangulation of Points on a Polyhedron (2008)
Amenta, Nina, Attali, Dominique, Devillers, Olivier
We show that the Delaunay triangulation of a set of n points distributed nearly uniformly on a p-dimensional polyhedron (not necessarily convex) in d-dimensional Euclidean space is O(n^((d-k+1)/p)),...
A Tight Bound for the Delaunay Triangulation of Points on a Polyhedron (2008)
Amenta, Nina, Attali, Dominique, Devillers, Olivier
We show that the Delaunay triangulation of a set of n points distributed nearly uniformly on a p-dimensional polyhedron (not necessarily convex) in d-dimensional Euclidean space is O(n^((d-k+1)/p)),...
Stability and computation of medial axes – a state-of-the-art report (2008)
Dominique Attali, Jean-daniel Boissonnat, Herbert Edelsbrunner
Summary. The medial axis of a geometric shape captures its connectivity. In spite of its inherent instability, it has found applications in a number of areas that deal with shapes. In this survey...
Nonnumerical Algorithms and Problems—[Geometrical (2008)
The main result of this paper is an extension of de Silva’s Weak Delaunay Theorem to smoothly embedded curves and surfaces in Euclidean space. Assuming a sufficiently fine sampling, we prove that i...
Abstract Complexity of Delaunay triangulation for points on lower-dimensional polyhedra (2008)
We show that the Delaunay triangulation of a set of points distributed nearly uniformly on a polyhedron (not necessarily convex) of dimension p in d-dimensional space is O(n (d−1)/p). For all 2 ≤...
Sujet de stage --- Annee 2004 - 2005 (2008)
Calcul Un Axe, Dominique Attali, Jean-daniel Boissonnat
e que le #-axe median est une partie stable de l'axe median [4] (voir Figure 2). Cependant, il n'est pas clair de savoir quelle valeur de # convient le mieux et parfois, il n'existe...
A Tight Bound for the Delaunay Triangulation of Points on a Polyhedron (2008)
Amenta, Nina, Attali, Dominique, Devillers, Olivier
We show that the Delaunay triangulation of a set of n points distributed nearly uniformly on a p-dimensional polyhedron (not necessarily convex) in d-dimensional Euclidean space is O(n^((d-k+1)/p)),...
A Tight Bound for the Delaunay Triangulation of Points on a Polyhedron (2008)
Amenta, Nina, Attali, Dominique, Devillers, Olivier
We show that the Delaunay triangulation of a set of n points distributed nearly uniformly on a p-dimensional polyhedron (not necessarily convex) in d-dimensional Euclidean space is O(n^((d-k+1)/p)),...
Volume xxx, (1997) number yyy pp. 000--000 Skeletal Reconstruction of Branching Shapes (2007)
We present a new method to reconstruct an implicit representation of a branching object from a set of data points scattered on its surface. The method is based on the computation of a geometric...
Complexity of Delaunay Triangulation for Points on Lower-dimensional~Polyhedra (2007)
Amenta, Nina, Attali, Dominique, Devillers, Olivier
We show that the Delaunay triangulation of a set of points distributed nearly uniformly on a polyhedron (not necessarily convex) of dimension p in d-dimensional space is O(n^(d-1)/p))$. For all p...
Complexity of Delaunay Triangulation for Points on Lower-dimensional~Polyhedra (2007)
Amenta, Nina, Attali, Dominique, Devillers, Olivier
We show that the Delaunay triangulation of a set of points distributed nearly uniformly on a polyhedron (not necessarily convex) of dimension p in d-dimensional space is O(n^(d-1)/p))$. For all p...
FRANÇOISE PEYRIN, ZSOLT PETER, AYMERIC LARRUE, ALEXANDRA BONNASSIE, DOMINIQUE ATTALI
This paper proposes a new method for local evaluation the geometry of complex 3D porous networks such as bone micro-architecture. The method described here allows local quantification of the geometry...
Weak Witnesses for Delaunay triangulations of Submanifold (2007)
Attali, Dominique, Edelsbrunner, Herbert, Mileyko, Yuriy
The main result of this paper is an extension of de Silva’s Weak Delaunay Theorem to smoothly embedded curves and surfaces in Euclidean space. Assuming a sufficiently fine sampling, we...
Alpha-Beta Witness Complexes (2007)
Attali, Dominique, Edelsbrunner, Herbert, Harer, John, Mileyko, Yuriy
Building on the work of Martinetz, Schulten and de Silva, Carlsson, we introduce a 2-parameter family of witness complexes and algorithms for constructing them. This family can be used to determine...
Inclusion-exclusion formulas for independent complexes (2007)
Attali, Dominique, Edelsbrunner, Herbert
Using inclusion-exclusion, we can write the indicator function of a union of finitely many balls as an alternating sum of indicator functions of common intersections of balls. We exhibit abstract...
Weak Witnesses for Delaunay triangulations of Submanifold (2007)
Attali, Dominique, Edelsbrunner, Herbert, Mileyko, Yuriy
The main result of this paper is an extension of de Silvas Weak Delaunay Theorem to smoothly embedded curves and surfaces in Euclidean space. Assuming a sufficiently fine sampling, we...
Alpha-Beta Witness Complexes (2007)
Attali, Dominique, Edelsbrunner, Herbert, Harer, John, Mileyko, Yuriy
Building on the work of Martinetz, Schulten and de Silva, Carlsson, we introduce a 2-parameter family of witness complexes and algorithms for constructing them. This family can be used to determine...
Inclusion-exclusion formulas for independent complexes (2007)
Attali, Dominique, Edelsbrunner, Herbert
Using inclusion-exclusion, we can write the indicator function of a union of finitely many balls as an alternating sum of indicator functions of common intersections of balls. We exhibit abstract...
Complexity of Delaunay triangulation for points on lower-dimensional polyhedra (2007)
Thème Sym, Nina Amenta, Nina Amenta, Dominique Attali, Dominique Attali, Olivier Devillers, ...
apport de recherche ISSN 0249-6399 ISRN INRIA/RR--5986--FR+ENG Complexity of Delaunay triangulation for points on lower-dimensional polyhedra
Alpha-beta witness complexes (2007)
Dominique Attali, Herbert Edelsbrunner, John Harer, Yuriy Mileyko
Carlsson, we introduce a 2-parameter family of witness complexes and algorithms for constructing them. This family can be used to determine the gross topology of point cloud data in R d or other...
Complexity of Delaunay triangulation for points on lower-dimensional~polyhedra (2006)
Amenta, Nina, Attali, Dominique, Devillers, Olivier
We show that the Delaunay triangulation of a set of points distributed nearly uniformly on a polyhedron (not necessarily convex) of dimension p in d-dimensional space is of order n to the power...
Complexity of Delaunay triangulation for points on lower-dimensional~polyhedra (2006)
Amenta, Nina, Attali, Dominique, Devillers, Olivier
We show that the Delaunay triangulation of a set of points distributed nearly uniformly on a polyhedron (not necessarily convex) of dimension p in d-dimensional space is of order n to the power...
Topological Quadrangulations of Closed Triangulated Surfaces using the Reeb Graph (2003)
Hétroy, Franck, Attali, Dominique
Although surfaces are more and more often represented by dense triangulations, it can be useful to convert them to B-spline surface patches, lying on quadrangles. This paper presents a method for the...
Detection of Constrictions on Closed Polyhedral Surfaces (2003)
Hétroy, Franck, Attali, Dominique
We define constrictions on a surface as simple closed geodesic curves, i.e. curves whose length is locally minimal. They can be of great interests in order to cut the surface in smaller parts. In...
From a Closed Piecewise Geodesic to a Constriction on a Closed Triangulated Surface (2003)
Hétroy, Franck, Attali, Dominique
Constrictions on a surface are defined as simple closed curves whose length is locally minimal. In particular, constrictions are periodic geodesics. We use constrictions in order to segment objects....
Detection of Constrictions on Closed Polyhedral Surfaces (2003)
Hétroy, Franck, Attali, Dominique
We define constrictions on a surface as simple closed geodesic curves, i.e. curves whose length is locally minimal. They can be of great interests in order to cut the surface in smaller parts. In...
From a Closed Piecewise Geodesic to a Constriction on a Closed Triangulated Surface (2003)
Hétroy, Franck, Attali, Dominique
Constrictions on a surface are defined as simple closed curves whose length is locally minimal. In particular, constrictions are periodic geodesics. We use constrictions in order to segment objects....
Topological Quadrangulations of Closed Triangulated Surfaces using the Reeb Graph (2003)
Hétroy, Franck, Attali, Dominique
Although surfaces are more and more often represented by dense triangulations, it can be useful to convert them to B-spline surface patches, lying on quadrangles. This paper presents a method for the...
Topological Quadrangulations of Closed Triangulated Surfaces using the Reeb Graph (2003)
Hétroy, Franck, Attali, Dominique
Although surfaces are more and more often represented by dense triangulations, it can be useful to convert them to B-spline surface patches, lying on quadrangles. This paper presents a method for the...
Detection of Constrictions on Closed Polyhedral Surfaces (2003)
Hétroy, Franck, Attali, Dominique
We define constrictions on a surface as simple closed geodesic curves, i.e. curves whose length is locally minimal. They can be of great interests in order to cut the surface in smaller parts. In...
From a Closed Piecewise Geodesic to a Constriction on a Closed Triangulated Surface (2003)
Hétroy, Franck, Attali, Dominique
Constrictions on a surface are defined as simple closed curves whose length is locally minimal. In particular, constrictions are periodic geodesics. We use constrictions in order to segment objects....
Attali, Dominique, Boissonnat, Jean-Daniel
Delaunay triangulations and Voronoi diagrams have found numerous applications in surface modeling, surface mesh generation, deformable surface modeling and surface reconstruction. Many algorithms in...
Attali, Dominique, Boissonnat, Jean-Daniel
Delaunay triangulations and Voronoi diagrams have found numerous applications in surface modeling, surface mesh generation, deformable surface modeling and surface reconstruction. Many algorithms in...
Attali, Dominique, Boissonnat, Jean-Daniel
Delaunay triangulations and Voronoi diagrams have found numerous applications in surface modeling, surface mesh generation, deformable surface modeling and surface reconstruction. Many algorithms in...
From Local Approximation to a G1 Global Representation (2002)
Gerot, Cedric, Attali, Dominique, Montanvert, Annick
To represent a complex surface, it is useful to describe it as a set of simple parametric primitives such as quadrics. But if one wants to use few primitives, these have to be smoothly blended. To...
Abstract Topological quadrangulations of closed triangulated surfaces using the Reeb graph (2002)
Franck Hetroy, Dominique Attali
Although surfaces are more and more often represented by dense triangulations, it can be useful to convert them to B-spline surface patches, lying on quadrangles. This paper presents a method for the...
Delaunay triangulations and Voronoi diagrams have found numerous applications in surface modeling, surface mesh generation, deformable surface modeling and surface reconstruction. Many algorithms in...
Complexity of the Delaunay triangulation of points on polyhedral surfaces (2001)
Attali, Dominique, Boissonnat, Jean-Daniel
It is well known that the complexity of the Delaunay triangulation of $n$ points in $R ^d$, i.e. the number of its simplices, can be $\Omega (n^\lceil \frac{d{2}\rceil })$. In particular, in $R ^3$,...
Complexity of the Delaunay triangulation of points on polyhedral surfaces (2001)
Attali, Dominique, Boissonnat, Jean-Daniel
It is well known that the complexity of the Delaunay triangulation of $n$ points in $R ^d$, i.e. the number of its simplices, can be $\Omega (n^\lceil \frac{d{2}\rceil })$. In particular, in $R ^3$,...
Complexity of the Delaunay triangulation of points on polyhedral surfaces (2001)
Attali, Dominique, Boissonnat, Jean-Daniel
It is well known that the complexity of the Delaunay triangulation of $n$ points in $R ^d$, i.e. the number of its simplices, can be $\Omega (n^\lceil \frac{d{2}\rceil })$. In particular, in $R ^3$,...
Classification topologique locale d'images 3D (2001)
BONNASSIE, Alexandra, PEYRIN, Francoise, ATTALI, Dominique
L'objectif de ce travail est de proposer une méthode d'analyse locale des formes des objets contenus dans une image 3D. Nous nous intéressons plus particulièrement aux formes de type cylindre ou...
Construction d'iso-surfaces sous contraintes de delaunay, codage par squelettes et filtrage (1999)
ATTALI, Dominique, LACHAUD, Jacques-Olivier
Les iso-surfaces calculées à l'aide de l'algorithme de marching-cubes fournissent une triangulation des objets présents dans une image volumétrique. Dans cet article, nous construisons un nouveau...
r-regular shape reconstruction from unorganized points (1997)
In this paper, the problem of reconstructing a surface, given a set of scattered data points is addressed. First, a precise formulation of the reconstruction problem is proposed. The solution is...
Skeletal Reconstruction of Branching Shapes (1997)
We present a new method for the implicit reconstruction of branching shapes from a set of scattered data points. The method is based on the computation of a geometric skeleton inside the data set....
Skeletal Reconstruction of Branching Shapes (1997)
We present a new method to reconstruct an implicit representation of a branching object from a set of data points scattered on its surface. The method is based on the computation of a geometric...
Modeling Noise For a Better Simplification of Skeletons (1996)
Dominique Attali, Annick Montanvert
The skeleton of an object is the locus of the centers of maximal discs included in the shape. The skeleton provides a compact representation of objects, useful for shape description and recognition....
Skeletal reconstruction of branching shapes (1996)
We present a new method for the implicit reconstruction of branching shapes from a set of scattered data points. The method is based on the computation of a geometric skeleton inside the data set....
Squelettes et graphes de Voronoï 2D et 3D (1995)
Notre travail concerne l'étude, le calcul et la simplification des squelettes d'objets 2D et 3D. Le squelette d'un objet est une figure mince, centrée dans la forme et qui en résume l'aspect. Il...
Squelettes et graphes de Voronoï 2D et 3D (1995)
Notre travail concerne l'étude, le calcul et la simplification des squelettes d'objets 2D et 3D. Le squelette d'un objet est une figure mince, centrée dans la forme et qui en résume l'aspect. Il...
Squelettes et graphes de Voronoï 2D et 3D (1995)
Notre travail concerne l'étude, le calcul et la simplification des squelettes d'objets 2D et 3D. Le squelette d'un objet est une figure mince, centrée dans la forme et qui en résume l'aspect. Il...
Squelettes et graphes de Voronoï 2D et 3D (1995)
Notre travail concerne l'étude, le calcul et la simplification des squelettes d'objets 2D et 3D. Le squelette d'un objet est une figure mince, centrée dans la forme et qui en résume l'aspect. Il...