My research projects

For a full list of my publications, click here.

Persistence Theory

Mathieu Carrière and Steve Y. Oudot. Local Equivalence and Intrinsic Metrics between Reeb Graphs. Proc. 33rd International Symposium on Computational Geometry (SoCG), 2017. Full version.
Clément Maria and Steve Y. Oudot. Computing Zigzag Persistent Cohomology. Arxiv preprint arXiv:1608.06039 [cs.CG].
Jérémy Cochoy and Steve Y. Oudot. Decomposition of exact pfd persistence bimodules. arXiv:1605.09726 [math.RT].
Mathieu Carrière and Steve Y. Oudot. Structure and Stability of the 1-Dimensional Mapper. Proc. 32nd International Symposium on Computational Geometry (SoCG), 2016. Full version.
Clément Maria and Steve Y. Oudot. Zigzag Persistence via Reflections and Transpositions. Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA), January 2015.   
S. Y. Oudot and D. R. Sheehy. Zigzag Zoology: Rips Zigzags for Homology Inference. Proc. 29th Annual Symposium on Computational Geometry, June 2013. Full version in J. Foundations of Computational Mathematics.   
F. Chazal, V. de Silva. S. Oudot. Persistence Stability for Geometric Complexes. Geometriae Dedicata, 173(1):193-214, 2014.
F. Chazal, D. Cohen-Steiner, M. Glisse, L. J. Guibas, S. Y. Oudot. Proximity of Persistence Modules and their Diagrams. Proc. 25th ACM Sympos. on Comput. Geom., pages 237-246, 2009 (full version).   

Applications in Topological Data Analysis

Mathieu Carrière, Marco Cuturi and Steve Oudot. Sliced Wasserstein Kernel for Persistence Diagrams. Proc. 34th International Conference on Machine Learning (ICML), 2017.
Mathieu Carrière, Bertrand Michel and Steve Y. Oudot. Statistical Analysis and Parameter Selection for Mapper. arXiv:1706.00204 [cs.CG].
Thomas Bonis, Frédéric Chazal, Steve Oudot and Maksim Ovsjanikov. Persistence-based Pooling for Shape Pose Recognition. Proc. 6th International Workshop on Computational Topology in Image Context (CTIC), June 2016, Marseille.
Mathieu Carrière, Steve Y. Oudot, and Maksim Ovsjanikov. Stable Topological Signatures for Points on 3D Shapes. Proc. Sympos. on Geometry Processing, July 2015.
Mickaël Buchet, Frédéric Chazal, Tamal K. Dey, Fengtao Fan, Steve Y. Oudot, and Yusu Wang. Topological analysis of scalar fields with outliers. Proc. Sympos. on Computational Geometry, June 2015.   
M. Buchet and F. Chazal and S. Y. Oudot and D. R. Sheehy. Efficient and Robust Topological Data Analysis on Metric Spaces. Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA), January 2015.
F. Chazal, L. J. Guibas, S. Y. Oudot, P. Skraba. Persistence-Based Clustering in Riemannian Manifolds. Proc. 27th Annual ACM Symposium on Computational Geometry, pages 97-106, 2011. Full version in Journal of the ACM, volume 60, issue 6, article 41.   
B. Hudson, G. L. Miller, S. Y. Oudot, D. R. Sheehy. Topological Inference via Meshing. Proc. 26th Annual ACM Symposium on Computational Geometry, pages 277-286, 2010.   
F. Chazal, D. Cohen-Steiner, L. J. Guibas, F. Mémoli, S. Y. Oudot. Gromov-Hausdorff Stable Signatures for Shapes using Persistence. Computer Graphics Forum (proc. SGP 2009), pages 1393-1403.   
F. Chazal, L. J. Guibas, S. Y. Oudot, P. Skraba. Analysis of Scalar Fields over Point Cloud Data. Proc. 19th ACM-SIAM Symposium on Discrete Algorithms, pp. 1021-1030, 2009. Full version in Discrete and Computational Geometry (DCG), 46(4):743--775, December 2011 (full version).   
F. Chazal, S. Y. Oudot. Towards Persistence-Based Reconstruction in Euclidean Spaces. Proc. 24th ACM Sympos. on Comput. Geom., pages 232-241, 2008 (full version).   

Reconstruction and Probing

J. Gao, L. Guibas, S. Oudot, and Y. Wang. Geodesic Delaunay Triangulation and Witness Complex in the Plane. Proc. 19th ACM-SIAM Symposium on Discrete Algorithms, pages 571-580, 2008. Full version in Transactions on Algorithms (TALG), 6(4):67:1--67:47, August 2010 (full version).   
J.-D. Boissonnat, L. J. Guibas, and S. Y. Oudot. Manifold Reconstruction in Arbitrary Dimensions using Witness Complexes. Proc. 23rd ACM Sympos. on Comput. Geom., pages 194-203, 2007. Full version in Discrete and Computational Geometry, 42(1):37-70, 2009 (pdf).   
Steve Y. Oudot. On the Topology of the Restricted Delaunay Triangulation and Witness Complex in Higher Dimensions. Technical Report, Stanford University, November 2006. LANL arXiv:0803.1296v1 [cs.CG], http://arxiv.org/abs/0803.1296. Published in the full version of this paper.   
L. J. Guibas, S. Y. Oudot. Reconstruction using Witness Complexes. Proc. 18th ACM-SIAM Sympos. on Discrete Algorithms, pages 1076-1085, 2007. Full version in Discrete and Computational Geometry, 40(3):325-356, 2008 (pdf).   
J.-D. Boissonnat, L. J. Guibas, S. Y. Oudot. Learning Smooth Objects by Probing. Proc. 21st Annual Sympos. on Comput. Geom., pp. 198-207, 2005. Full version in Computational Geometry: Theory and Applications, 37:38-58, 2007 (pdf). Video available here.   

Mesh Generation

J.-D. Boissonnat, S. Y. Oudot. Provably Good Sampling and Meshing of Lipschitz Surfaces. Proc. 22nd Annual ACM Sympos. Comput. Geom., pages 337-346, 2006.   
S. Y. Oudot, L. Rineau, M. Yvinec. Meshing Volumes Bounded by Smooth Surfaces. Proc. 14th Internat. Meshing Roundtable, pp. 203-220, 2005. Full version in Engineering with Computers, 26(3):265-279, 2010 (pdf).   
J.-D. Boissonnat, S. Y. Oudot. Provably Good Sampling and Meshing of Surfaces. Graphical Models, volume 67, issue 5, pages 405-451, September 2005.   
J.-D. Boissonnat, S. Y. Oudot. An effective condition for sampling surfaces with guarantees. Proc. 9th ACM Sympos. on Solid Modeling and Applications, pp. 101-112, 2004.   
J.-D. Boissonnat, S. Y. Oudot. Provably Good Surface Sampling and Approximation. Proc. 1st Symposium on Geometry Processing (SGP), pp. 9-18, 2003.   

Proximity Queries

D. Arthur, S. Y. Oudot. Reverse Nearest Neighbors Search in High Dimensions using Locality-Sensitive Hashing. INRIA research report RR-7084, November 2010. arXiv:1011.4955v1 [cs.CG, cs.DS].