Selected publications

[HOME PAGE] [PREPRINTS] [JOURNALS] [CONFERENCES]

Preprints

Flat Delaunay complexes for homeomorphic manifold reconstruction.
Dominique Attali and André Lieutier.
Research Report, March 2022, arXiv:2203.05943.
[arXiv]

Delaunay-like triangulation of smooth orientable submanifolds by L1-norm minimization.
Dominique Attali and André Lieutier.
Research Report, March 2022, arXiv:2203.06008.
[arXiv]

Tight Bounds for the Learning of Homotopy à la Niyogi, Smale, and Weinberger for Subsets of Euclidean Spaces and of Riemannian Manifolds.
Dominique Attali, Hana Dal Poz Kouřimská, Christopher Fillmore, Ishika Ghosh, André Lieutier, Elizabeth Stephenson, and Mathijs Wintraecken.
Research Report, June 2022, arXiv:2206.10485.
[arXiv] [HAL]

A short version of the paper has been accepted to SoCG 2024!
A video is available on YouTube.

Journals

(δ,ε)-ball approximation of a shape: definition and complexity.
Dominique Attali, Tuong-Bach Nguyen, and Isabelle Sivignon.
Discrete and Computationa Geometry, 61:595–625, 2019.
[pdf] [hal]

Recognizing shrinkable complexes is NP-complete.
Dominique Attali, Olivier Devillers, Marc Glisse, and Sylvain Lazard.
Journal of Computational Geometry (JoCG), 7(1):430–443, 2016.
[Doi] [pdf]

Far-field reflector problem under design constraints.
Julien André, Dominique Attali, Quentin Mérigot and Boris Thibert.
International Journal of Computational Geometry & Applications (IJCGA), 25(2), June 2015.
[Doi] [pdf]

Geometry driven collapses for converting a Čech complex into a triangulation of a nicely triangulable shape.
Dominique Attali and André Lieutier.
Discrete and Computational Geometry, 54(4):798–825, 2015.
[Doi] [pdf] [arXiv]

Homological Reconstruction and Simplification in R3.
Dominique Attali, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier.
Computational Geometry: Theory and Applications (CGTA), 48(8):606–621, September 2015.
[pdf]

Optimal Reconstruction Might be Hard.
Dominique Attali and André Lieutier.
Discrete and Computational Geometry, 49(2):133–156, 2013.
[Doi] [pdf]

Efficient data structure for representing and simplifying simplicial complexes in high dimensions.
Dominique Attali, André Lieutier, and David Salinas.
International Journal of Computational Geometry and Applications (IJCGA), 22(4):279–303, 2012.
[pdf]

Vietoris-Rips complexes also provide topologically correct reconstructions of sampled shapes.
Dominique Attali, André Lieutier, and David Salinas.
Computational Geometry: Theory and Applications (CGTA), 46:448–465, 2012.
[Doi] [pdf] [Errata]

A tight bound for the Delaunay triangulation of points on a polyhedron.
Nina Amenta, Dominique Attali, and Olivier Devillers.
Discrete and Computational Geometry, 48(1):19–38, 2012.
[pdf] --- Old version:[Research Report INRIA]

Stability and Computation of the Medial Axes — A State-of-the-Art Report.
Dominique Attali, Jean-Daniel Boissonnat, and Herbert Edelsbrunner.
In T. Möller, B. Hamann, and R. Russell, editors, Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration, Mathematics and Vizualization, pages 109–125. Springer-Verlag, Berlin, Germany, 2009.
[pdf]

Représentation par axe médian.
Dominique Attali, David Coeurjolly et Eric Remy.
Chapitre 9 du livre "Géométrie discrète et images numériques" par David Coeurjolly, Annick Montanvert, and Jean-Marc Chassery. Ouvrage collectif. Traité IC2 série signal et image, Hermès, 2007.
[pdf]

Inclusion-exclusion formulas from independent complexes.
Dominique Attali and Herbert Edelsbrunner.
Discrete and Computational Geometry. Vol. 37, No. 1, January, pages 59–77, 2007.
[pdf]

A Linear Bound on the Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces.
Dominique Attali and Jean-Daniel Boissonnat.
Discrete and Computational Geometry. Vol. 31, No. 3, February, pages 369–384, 2004.
[pdf]

Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces.
Dominique Attali and Jean-Daniel Boissonnat.
Discrete and Computational Geometry. Vol. 30, pages 437–452, 2003.
[pdf]

r-regular Shape Reconstruction from Unorganized Points.
Dominique Attali.
Computational Geometry: Theory and Applications, Vol. 10, pages 239–247, 1998.

Computing and Simplifying 2D and 3D Semicontinuous Skeletons of 2D and 3D shapes.
Dominique Attali and Annick Montanvert.
Computer Vision and Image Understanding (CVIU), Vol. 67, No. 3, September, pages 261–273, 1997.
[scanned pdf]

Conferences

Delaunay-like triangulation of smooth orientable submanifolds by L1-norm minimization.
Dominique Attali and André Lieutier.
38th Ann. Sympos. Comput. Geom. (SoCG'22), Berlin, Germany, June 7-10, 2022.
[pdf] [proceedings]

When Convexity Helps Collapsing Complexes.
Dominique Attali, André Lieutier and David Salinas.
In 35th Ann. Sympos. Comput. Geom. (SoCG'19), Portland, USA, June 18-21, 2019.
[pdf] [proceedings]

Restricting Voronoi diagrams to meshes using corner validation.
Maxime Sainlot, Vincent Nivoliers, and Dominique Attali.
In Computer Graphics Forum , volume 36, pages 81–91. Wiley Online Library, 2017.
[pdf]

ε-covering is NP-complete.
In Proc. Dominique Attali, Tuong-Bach Nguyen, and Isabelle Sivignon.
European Workshop on Computational Geometry (EuroCG 2016), Lugano, Switzerland, March 30-April 1, 2016.
[pdf]

Recognizing shrinkable complexes is NP-complete.
Dominique Attali, Olivier Devillers, Marc Glisse, and Sylvain Lazard.
In A. Schulz and D. Wagner, editors, In Proc. 22nd European Symposium on Algorithms (ESA'14), pages 74–86, Wroclaw, Poland, 2014. Springer. []

Homological reconstruction and simplification in R3.
Dominique Attali, Ulich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier.
In Proc. 29th Ann. Sympos. Comput. Geom. (SoCG'13), Rio de Janeiro, Brazil, June 17-20, 2013.
[pdf]

Efficient data structure for representing and simplifying simplicial complexes in high dimension.
Dominique Attali, André Lieutier, and David Salinas.
In Proc. 27th Ann. Sympos. Comput. Geom. (SoCG'11), pages 501–509, Paris, France, June 13-15 2011.
[pdf] [slides]

Vietoris-Rips complexes also provide topologically correct reconstructions of sampled shapes.
Dominique Attali, André Lieutier, and David Salinas.
In Proc. 27th Ann. Sympos. Comput. Geom. (SoCG'11), pages 491–500, Paris, France, June 13-15, 2011.
[pdf]

Optimal reconstruction might be hard.
Dominique Attali and André Lieutier.
In Proc. 26th Ann. Sympos. Comput. Geom. (SoCG'10), pages 334–342, Snowbird, Utah, June 13-16, 2010.
[pdf]

Reconstructing shapes with guarantees by unions of convex sets.
Dominique Attali and André Lieutier.
In Proc. 26th Ann. Sympos. Comput. Geom. (SoCG'10), pages 344–353, Snowbird, Utah, June 13-16, 2010.
[pdf] --- Full version: [Research Report HAL]

A Tight Bound for the Delaunay Triangulation of Points on a Polyhedron.
Dominique Attali, Nina Amenta and Olivier Devillers.
In Proc. 24th European Workshop on Computational Geometry (EuroCG'08), Nancy, France. March 18--20, 2008.
[pdf]

Alpha-Beta Witness Complexes.
Dominique Attali, Herbert Edelsbrunner, John Harer, and Yuriy Mileyko.
In Proc. 10th Workshop on Algorithms and Data Structures (WADS), Halifax, Nova Scotia, Canada, August 15-17, 2007.
[pdf]

Weak Witnesses for Delaunay triangulations of Submanifold.
Dominique Attali, Herbert Edelsbrunner, and Yuriy Mileyko.
In Proc. ACM Sympos. Solid and Physical Modeling (SPM), Beijing, China, June 4-6, pages 143–150, 2007.
[pdf]

Complexity of Delaunay Triangulation for Points on Lower-dimensional Polyhedra.
Nina Amenta, Dominique Attali, and Olivier Devillers.
In Proc. ACM-SIAM Sympos. Discrete Algorithms (SODA07), New-Orleans, Lousiane, USA, January 7-9, 2007.
[pdf]

Extraction and Simplification of Iso-surfaces in Tandem.
Dominique Attali, David Cohen-Steiner, and Herbert Edelsbrunner.
In Proc. 3rd Ann. Sympos. Geom. Process. (SGP), Vienna, Autria, July 4-6, pages 139–148, 2005.
[pdf]

Inclusion-exclusion formulas from independent complexes.
Dominique Attali and Herbert Edelsbrunner.
In Proc. 21st Ann. Sympos. Comput. Geom. (SoCG), pages 247–254, 2005.
[pdf]

Complexity of the Delaunay triangulation of Points on Surfaces: the Smooth Case.
Dominique Attali, Jean-Daniel Boissonnat, and André Lieutier.
In Proc. of the 19th ACM Symposium on Computational Geometry (SoCG), pages 201–210, San-Diego, California, USA, June 2003.
[pdf]

A Linear Bound on the Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces.
Dominique Attali and Jean-Daniel Boissonnat.
In Proc. of the 7th ACM Symposium on Solid Modeling and Applications, pages 139–145, Saarbrücken, Germany, June 17-21, 2002.
[pdf] [slides] [slides 16x16]

r-Regular Shape Reconstruction from Unorganized Points.
Dominique Attali.
In Proc. of the 13th ACM Symposium on Computational Geometry (SoCG), pages 248–253, Nice, France, June 1997.
[pdf]

Modeling noise for a better simplification of skeletons.
Dominique Attali and Annick Montanvert.
In Proc. of the International Conference on Image Processing (ICIP), Volume III, pages 13–16, Lausanne, Switzerland, September 1996.
[pdf]

Using polyballs to approximate shapes and skeletons.
Dominique Attali, Pascal Bertolino, and Annick Montanvert.
In 12th International Conference on Pattern Recognition (ICPR), pages 626–628, Jerusalem, Israël, October 1994.
[scanned pdf]

	(δ,ε)-ball approximation of a shape: definition and complexity. Dominique Attali, Tuong-Bach Nguyen, and Isabelle Sivignon. Discrete and Computationa Geometry, 61:595–625, 2019. [pdf] [hal]
	Recognizing shrinkable complexes is NP-complete. Dominique Attali, Olivier Devillers, Marc Glisse, and Sylvain Lazard. Journal of Computational Geometry (JoCG), 7(1):430–443, 2016. [Doi] [pdf]
	Far-field reflector problem under design constraints. Julien André, Dominique Attali, Quentin Mérigot and Boris Thibert. International Journal of Computational Geometry & Applications (IJCGA), 25(2), June 2015. [Doi] [pdf]
	Geometry driven collapses for converting a Čech complex into a triangulation of a nicely triangulable shape. Dominique Attali and André Lieutier. Discrete and Computational Geometry, 54(4):798–825, 2015. [Doi] [pdf] [arXiv]
	Homological Reconstruction and Simplification in R3. Dominique Attali, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. Computational Geometry: Theory and Applications (CGTA), 48(8):606–621, September 2015. [pdf]
	Optimal Reconstruction Might be Hard. Dominique Attali and André Lieutier. Discrete and Computational Geometry, 49(2):133–156, 2013. [Doi] [pdf]
	Efficient data structure for representing and simplifying simplicial complexes in high dimensions. Dominique Attali, André Lieutier, and David Salinas. International Journal of Computational Geometry and Applications (IJCGA), 22(4):279–303, 2012. [pdf]
	Vietoris-Rips complexes also provide topologically correct reconstructions of sampled shapes. Dominique Attali, André Lieutier, and David Salinas. Computational Geometry: Theory and Applications (CGTA), 46:448–465, 2012. [Doi] [pdf] [Errata]
	A tight bound for the Delaunay triangulation of points on a polyhedron. Nina Amenta, Dominique Attali, and Olivier Devillers. Discrete and Computational Geometry, 48(1):19–38, 2012. [pdf] --- Old version:[Research Report INRIA]
	Stability and Computation of the Medial Axes — A State-of-the-Art Report. Dominique Attali, Jean-Daniel Boissonnat, and Herbert Edelsbrunner. In T. Möller, B. Hamann, and R. Russell, editors, Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration, Mathematics and Vizualization, pages 109–125. Springer-Verlag, Berlin, Germany, 2009. [pdf]
	Représentation par axe médian. Dominique Attali, David Coeurjolly et Eric Remy. Chapitre 9 du livre "Géométrie discrète et images numériques" par David Coeurjolly, Annick Montanvert, and Jean-Marc Chassery. Ouvrage collectif. Traité IC2 série signal et image, Hermès, 2007. [pdf]
	Inclusion-exclusion formulas from independent complexes. Dominique Attali and Herbert Edelsbrunner. Discrete and Computational Geometry. Vol. 37, No. 1, January, pages 59–77, 2007. [pdf]
	A Linear Bound on the Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces. Dominique Attali and Jean-Daniel Boissonnat. Discrete and Computational Geometry. Vol. 31, No. 3, February, pages 369–384, 2004. [pdf]
	Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces. Dominique Attali and Jean-Daniel Boissonnat. Discrete and Computational Geometry. Vol. 30, pages 437–452, 2003. [pdf]
	r-regular Shape Reconstruction from Unorganized Points. Dominique Attali. Computational Geometry: Theory and Applications, Vol. 10, pages 239–247, 1998.
	Computing and Simplifying 2D and 3D Semicontinuous Skeletons of 2D and 3D shapes. Dominique Attali and Annick Montanvert. Computer Vision and Image Understanding (CVIU), Vol. 67, No. 3, September, pages 261–273, 1997. [scanned pdf]

	Delaunay-like triangulation of smooth orientable submanifolds by L1-norm minimization. Dominique Attali and André Lieutier. 38th Ann. Sympos. Comput. Geom. (SoCG'22), Berlin, Germany, June 7-10, 2022. [pdf] [proceedings]
	When Convexity Helps Collapsing Complexes. Dominique Attali, André Lieutier and David Salinas. In 35th Ann. Sympos. Comput. Geom. (SoCG'19), Portland, USA, June 18-21, 2019. [pdf] [proceedings]
	Restricting Voronoi diagrams to meshes using corner validation. Maxime Sainlot, Vincent Nivoliers, and Dominique Attali. In Computer Graphics Forum , volume 36, pages 81–91. Wiley Online Library, 2017. [pdf]
	ε-covering is NP-complete. In Proc. Dominique Attali, Tuong-Bach Nguyen, and Isabelle Sivignon. European Workshop on Computational Geometry (EuroCG 2016), Lugano, Switzerland, March 30-April 1, 2016. [pdf]
	Recognizing shrinkable complexes is NP-complete. Dominique Attali, Olivier Devillers, Marc Glisse, and Sylvain Lazard. In A. Schulz and D. Wagner, editors, In Proc. 22nd European Symposium on Algorithms (ESA'14), pages 74–86, Wroclaw, Poland, 2014. Springer. []
	Homological reconstruction and simplification in R3. Dominique Attali, Ulich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. In Proc. 29th Ann. Sympos. Comput. Geom. (SoCG'13), Rio de Janeiro, Brazil, June 17-20, 2013. [pdf]
	Efficient data structure for representing and simplifying simplicial complexes in high dimension. Dominique Attali, André Lieutier, and David Salinas. In Proc. 27th Ann. Sympos. Comput. Geom. (SoCG'11), pages 501–509, Paris, France, June 13-15 2011. [pdf] [slides]
	Vietoris-Rips complexes also provide topologically correct reconstructions of sampled shapes. Dominique Attali, André Lieutier, and David Salinas. In Proc. 27th Ann. Sympos. Comput. Geom. (SoCG'11), pages 491–500, Paris, France, June 13-15, 2011. [pdf]
	Optimal reconstruction might be hard. Dominique Attali and André Lieutier. In Proc. 26th Ann. Sympos. Comput. Geom. (SoCG'10), pages 334–342, Snowbird, Utah, June 13-16, 2010. [pdf]
	Reconstructing shapes with guarantees by unions of convex sets. Dominique Attali and André Lieutier. In Proc. 26th Ann. Sympos. Comput. Geom. (SoCG'10), pages 344–353, Snowbird, Utah, June 13-16, 2010. [pdf] --- Full version: [Research Report HAL]
	A Tight Bound for the Delaunay Triangulation of Points on a Polyhedron. Dominique Attali, Nina Amenta and Olivier Devillers. In Proc. 24th European Workshop on Computational Geometry (EuroCG'08), Nancy, France. March 18--20, 2008. [pdf]
	Alpha-Beta Witness Complexes. Dominique Attali, Herbert Edelsbrunner, John Harer, and Yuriy Mileyko. In Proc. 10th Workshop on Algorithms and Data Structures (WADS), Halifax, Nova Scotia, Canada, August 15-17, 2007. [pdf]
	Weak Witnesses for Delaunay triangulations of Submanifold. Dominique Attali, Herbert Edelsbrunner, and Yuriy Mileyko. In Proc. ACM Sympos. Solid and Physical Modeling (SPM), Beijing, China, June 4-6, pages 143–150, 2007. [pdf]
	Complexity of Delaunay Triangulation for Points on Lower-dimensional Polyhedra. Nina Amenta, Dominique Attali, and Olivier Devillers. In Proc. ACM-SIAM Sympos. Discrete Algorithms (SODA07), New-Orleans, Lousiane, USA, January 7-9, 2007. [pdf]
	Extraction and Simplification of Iso-surfaces in Tandem. Dominique Attali, David Cohen-Steiner, and Herbert Edelsbrunner. In Proc. 3rd Ann. Sympos. Geom. Process. (SGP), Vienna, Autria, July 4-6, pages 139–148, 2005. [pdf]
	Inclusion-exclusion formulas from independent complexes. Dominique Attali and Herbert Edelsbrunner. In Proc. 21st Ann. Sympos. Comput. Geom. (SoCG), pages 247–254, 2005. [pdf]
	Complexity of the Delaunay triangulation of Points on Surfaces: the Smooth Case. Dominique Attali, Jean-Daniel Boissonnat, and André Lieutier. In Proc. of the 19th ACM Symposium on Computational Geometry (SoCG), pages 201–210, San-Diego, California, USA, June 2003. [pdf]
	A Linear Bound on the Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces. Dominique Attali and Jean-Daniel Boissonnat. In Proc. of the 7th ACM Symposium on Solid Modeling and Applications, pages 139–145, Saarbrücken, Germany, June 17-21, 2002. [pdf] [slides] [slides 16x16]
	r-Regular Shape Reconstruction from Unorganized Points. Dominique Attali. In Proc. of the 13th ACM Symposium on Computational Geometry (SoCG), pages 248–253, Nice, France, June 1997. [pdf]
	Modeling noise for a better simplification of skeletons. Dominique Attali and Annick Montanvert. In Proc. of the International Conference on Image Processing (ICIP), Volume III, pages 13–16, Lausanne, Switzerland, September 1996. [pdf]
	Using polyballs to approximate shapes and skeletons. Dominique Attali, Pascal Bertolino, and Annick Montanvert. In 12th International Conference on Pattern Recognition (ICPR), pages 626–628, Jerusalem, Israël, October 1994. [scanned pdf]

	Flat Delaunay complexes for homeomorphic manifold reconstruction. Dominique Attali and André Lieutier. Research Report, March 2022, arXiv:2203.05943. [arXiv]
	Delaunay-like triangulation of smooth orientable submanifolds by L1-norm minimization. Dominique Attali and André Lieutier. Research Report, March 2022, arXiv:2203.06008. [arXiv]
	Tight Bounds for the Learning of Homotopy à la Niyogi, Smale, and Weinberger for Subsets of Euclidean Spaces and of Riemannian Manifolds. Dominique Attali, Hana Dal Poz Kouřimská, Christopher Fillmore, Ishika Ghosh, André Lieutier, Elizabeth Stephenson, and Mathijs Wintraecken. Research Report, June 2022, arXiv:2206.10485. [arXiv] [HAL] A short version of the paper has been accepted to SoCG 2024! A video is available on YouTube.