A. Attali, D. Glisse, M. Hornus, S. Lazarus, F. Morozov et al., Persistence-sensitive simplification of functions on surfaces in linear time, TopoInVis Workshop, 2009.

T. F. Banchoff, Critical Points and Curvature for Embedded Polyhedral Surfaces, The American Mathematical Monthly, vol.77, issue.5, 1970.
DOI : 10.2307/2317380

P. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci, A multi-resolution data structure for 2-dimensional Morse functions, IEEE Visualization, pp.139-146, 2003.
DOI : 10.1109/visual.2003.1250365

S. Biasotti, D. Giorgio, M. Spagnuolo, and B. Falcidieno, Reeb graphs for shape analysis and applications, Theoretical Computer Science, vol.392, issue.1-3, 2008.
DOI : 10.1016/j.tcs.2007.10.018

URL : http://doi.org/10.1016/j.tcs.2007.10.018

U. Bauer, C. Lange, and M. Wardetzky, Optimal Topological Simplification of Discrete Functions on Surfaces, Discrete & Computational Geometry, vol.33, issue.2, pp.347-377, 2012.
DOI : 10.1007/s00454-004-1146-y

R. L. Boyell and H. Ruston, Hybrid techniques for real-time radar simulation, Proceedings of the November 12-14, 1963, fall joint computer conference on XX, AFIPS '63 (Fall), 1963.
DOI : 10.1145/1463822.1463869

P. Bremer, G. Weber, J. Tierny, V. Pascucci, M. Day et al., Interactive Exploration and Analysis of Large-Scale Simulations Using Topology-Based Data Segmentation, IEEE Transactions on Visualization and Computer Graphics, vol.17, issue.9, 2011.
DOI : 10.1109/TVCG.2010.253

URL : https://hal.archives-ouvertes.fr/hal-01211172

F. Chazal, D. Cohen-steiner, L. J. Guibas, F. Memoli, and S. Y. Oudot, Gromov-Hausdorff Stable Signatures for Shapes using Persistence, Computer Graphics Forum, vol.33, issue.5, 2009.
DOI : 10.1109/TPAMI.2006.208

URL : https://hal.archives-ouvertes.fr/hal-00772413

H. Carr, Z. Geng, J. Tierny, A. Chattopadhyay, and A. Knoll, Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data, Computer Graphics Forum, vol.33, issue.3, 2015.
DOI : 10.1111/cgf.12371

URL : https://hal.archives-ouvertes.fr/hal-01198912

T. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2009.

K. Cole-mclaughlin, H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci, Loops in Reeb graphs of 2- manifolds, Proc. of ACM Symposium on Computational Geometry, pp.344-350, 2003.

F. Chen, H. Obermaier, H. Hagen, B. Hamann, J. Tierny et al., Topology analysis of time-dependent multifluid data using the reeb graph, Computer Aided Geometric Design, 2013.

H. Carr, J. Snoeyink, and U. Axen, Computing contour trees in all dimensions, Proc. of Symposium on Discrete Algorithms, pp.918-926, 2000.
DOI : 10.1016/S0925-7721(02)00093-7

URL : http://doi.org/10.1016/s0925-7721(02)00093-7

D. Cohen-steiner, H. Edelsbrunner, and J. Harer, Stability of persistence diagrams, Proc. of ACM Symposium on Computational Geometry, 2005.
DOI : 10.1145/1064092.1064133

H. Carr, J. Snoeyink, and M. Van-de-panne, Simplifying flexible isosurfaces using local geometric measures, IEEE Visualization 2004, pp.497-504, 2004.
DOI : 10.1109/VISUAL.2004.96

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.106.1632

[. Floriani, L. Fugacci, U. Iuricich, F. Magillo, and P. , Morse complexes for shape segmentation and homological analysis: discrete models and algorithms, Computer Graphics Forum, vol.32, issue.3, 2015.
DOI : 10.1017/CBO9780511546945

S. Dillard, A contour tree library. http://graphics. cs.ucdavis, 2007.

H. Doraiswamy, V. Natarajan, H. Edelsbrunner, and J. Harer, Efficient output sensitive construction of reeb graphs Persistent homology ? a survey, International Symposium on, 2008.

H. Edelsbrunner and J. Harer, Computational Topology: An Introduction, 2009.
DOI : 10.1090/mbk/069

H. Edelsbrunner, J. Harer, and A. K. Patel, Reeb spaces of piecewise linear mappings, Proceedings of the twenty-fourth annual symposium on Computational geometry , SCG '08, 2008.
DOI : 10.1145/1377676.1377720

H. Edelsbrunner, D. Letscher, and A. Zomorodian, Topological Persistence and Simplification, Discrete & Computational Geometry, vol.28, issue.4, pp.511-533, 2002.
DOI : 10.1007/s00454-002-2885-2

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.12.8802

H. Edelsbrunner and E. P. Mucke, Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms, ACM Transactions on Graphics, vol.9, issue.1, pp.66-104, 1990.
DOI : 10.1145/77635.77639

H. Edelsbrunner, D. Morozov, and V. Pascucci, Persistencesensitive simplification of functions on 2-manifolds, Proc. of ACM Symposium on Computational Geometry, pp.127-134, 2006.

G. Favelier, C. Gueunet, and J. Tierny, Visualizing ensembles of viscous fingers, IEEE SciVis Contest, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01359694

R. Forman, A user's guide to discrete morse theory, Proc. of the International Conference on Formal Power Series and Algebraic Combinatorics, 2001.

D. Guenther, R. Alvarez-boto, J. Contreras-garcia, J. Piquemal, and J. Tierny, Characterizing molecular inter- Bibliography actions in chemical systems, Proc. of IEEE VIS, p.34, 2014.

A. Gyulassy, P. Bremer, R. Grout, H. Kolla, J. Chen et al., Stability of Dissipation Elements: A Case Study in Combustion, Computer Graphics Forum, vol.608, issue.10, 2014.
DOI : 10.1017/S0022112008002139

A. Gyulassy, P. T. Bremer, B. Hamann, and V. Pascucci, A Practical Approach to Morse-Smale Complex Computation: Scalability and Generality, Proc. of IEEE VIS, 2008.
DOI : 10.1109/TVCG.2008.110

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.8602

A. Gyulassy, P. T. Bremer, and V. Pascucci, Computing morsesmale complexes with accurate geometry, Proc. of IEEE VIS, 2012.
DOI : 10.1109/tvcg.2012.209

C. Gueunet, P. Fortin, J. Jomier, and J. Tierny, Contour forests: Fast multi-threaded augmented contour trees, 2016 IEEE 6th Symposium on Large Data Analysis and Visualization (LDAV), 2016.
DOI : 10.1109/LDAV.2016.7874333

URL : https://hal.archives-ouvertes.fr/hal-01355328

C. Gueunet, P. Fortin, J. Jomier, and J. Tierny, Task-based augmented merge trees with Fibonacci heaps, Proc. of IEEE Symposium on Large Data Analysis and Visualization, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01575019

A. Gyulassy, D. Guenther, J. A. Levine, J. Tierny, and V. Pascucci, Conforming Morse-Smale Complexes, Proc. of IEEE VIS, 2014.
DOI : 10.1109/TVCG.2014.2346434

URL : https://hal.archives-ouvertes.fr/hal-01146478

R. Ghrist, Barcodes: The persistent topology of data, Bulletin of the American Mathematical Society, vol.45, issue.01, 2007.
DOI : 10.1090/S0273-0979-07-01191-3

A. Gyulassy, V. Natarajan, M. Duchaineau, V. Pascucci, E. Bringa et al., Topologically Clean Distance Fields, Proc. of IEEE VIS), pp.13-1432, 2007.
DOI : 10.1109/TVCG.2007.70603

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.8894

A. Gyulassy, Combinatorial Construction of Morse-Smale Complexes for Data Analysis and Visualization, p.28, 2008.

J. Kasten, J. Reininghaus, I. Hotz, and H. Hege, Twodimensional time-dependent vortex regions based on the acceleration magnitude, IEEE Transactions on Visualization and Computer Graphics, 2011.
DOI : 10.1109/tvcg.2011.249

P. Klacansky, J. Tierny, H. Carr, and Z. Geng, Fast and Exact Fiber Surfaces for Tetrahedral Meshes, IEEE Transactions on Visualization and Computer Graphics, vol.23, issue.7, 2016.
DOI : 10.1109/TVCG.2016.2570215

URL : https://hal.archives-ouvertes.fr/hal-01206120

J. Lukasczyk, G. Aldrich, M. Steptoe, G. Favelier, C. Gueunet et al., Viscous Fingering: A Topological Visual Analytic Approach, Physical Modeling for Virtual Manufacturing Systems and Processes, 2017.
DOI : 10.4028/www.scientific.net/AMM.869.9

URL : https://hal.archives-ouvertes.fr/hal-01547523

D. E. Laney, P. Bremer, A. Mascarenhas, P. Miller, and V. Pascucci, Understanding the Structure of the Turbulent Mixing Layer in Hydrodynamic Instabilities, Proc. of IEEE VIS, 2006.
DOI : 10.1109/TVCG.2006.186

S. Parsa, A deterministic o(m log m) time algorithm for the reeb graph, Proc. of ACM Symposium on Computational Geometry, 2012.

V. Pascucci, G. Scorzelli, P. T. Bremer, and A. Mascarenhas, Robust on-line computation of Reeb graphs, ACM Transactions on Graphics, vol.26, issue.3, pp.58-59, 2007.
DOI : 10.1145/1276377.1276449

G. Patane, M. Spagnuolo, and B. Falcidieno, Reeb graph computation based on a minimal contouring, 2008 IEEE International Conference on Shape Modeling and Applications, 2008.
DOI : 10.1109/SMI.2008.4547953

G. Reeb, Sur les points singuliers d'une forme de Pfaff complètement intégrable ou d'une fonction numérique. Comptesrendus de l, Académie des Sciences, vol.222, issue.26, pp.847-849, 1946.

B. Rieck and H. Leitte, Persistent Homology for the Evaluation of Dimensionality Reduction Schemes, Computer Graphics Forum, vol.28, issue.12, 2015.
DOI : 10.1016/S0008-8846(98)00165-3

V. Robins, P. Wood, and A. Sheppard, Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.33, issue.8, 2011.
DOI : 10.1109/TPAMI.2011.95

B. S. Sohn and C. L. Bajaj, Time-varying contour topology, Proc. of IEEE VIS, 2006.
DOI : 10.1109/TVCG.2006.16

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2703823

N. Shivashankar, Parallel implementation of 3d morsesmale complex computation, p.2012

Y. Shinagawa, T. Kunii, and Y. L. Kergosien, Surface coding based on Morse theory, IEEE Computer Graphics and Applications, vol.11, issue.5, 1991.
DOI : 10.1109/38.90568

N. Shivashankar and V. Natarajan, Parallel Computation of 3D Morse-Smale Complexes, Computer Graphics Forum, vol.99, issue.10, 2012.
DOI : 10.1111/j.1467-8659.2012.03089.x

T. Sousbie, The persistent cosmic web and its filamentary structure - I. Theory and implementation, Monthly Notices of the Royal Astronomical Society, vol.414, issue.1, 2011.
DOI : 10.1111/j.1365-2966.2011.18394.x

URL : https://academic.oup.com/mnras/article-pdf/414/1/384/3811918/mnras0414-0384.pdf

J. Tierny and H. Carr, Jacobi Fiber Surfaces for Bivariate Reeb Space Computation, Proc. of IEEE VIS, 2016.
DOI : 10.1109/TVCG.2016.2599017

URL : https://hal.archives-ouvertes.fr/hal-01349907

J. Tierny, A. Gyulassy, E. Simon, V. Pascucci, and J. Tierny, Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees, IEEE Transactions on Visualization and Computer Graphics, vol.15, issue.6, pp.1177-1184, 2008.
DOI : 10.1109/TVCG.2009.163

URL : https://hal.archives-ouvertes.fr/hal-01211176

D. M. Thomas and V. Natarajan, Multiscale Symmetry Detection in Scalar Fields by Clustering Contours, Proc. of IEEE VIS, 2014.
DOI : 10.1109/TVCG.2014.2346332

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.650.8489

J. Tierny and V. Pascucci, Generalized Topological Simplification of Scalar Fields on Surfaces, Proc. of IEEE VIS, 2012.
DOI : 10.1109/TVCG.2012.228

URL : https://hal.archives-ouvertes.fr/hal-01206877

S. Tarasov and M. Vyali, ) steps, Proceedings of the fourteenth annual symposium on Computational geometry , SCG '98, 1998.
DOI : 10.1145/276884.276892

A. Vintescu, F. Dupont, G. Lavoué, P. Memari, and J. Tierny, Conformal factor persistence for fast hierarchical cone extraction, Eurographics, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01508966

M. Van-kreveld, R. Van-oostrum, C. Bajaj, V. Pasucci, and D. Schikore, Contour trees and small seed sets for isosurface traversal, Proceedings of the thirteenth annual symposium on Computational geometry , SCG '97, p.32, 1997.
DOI : 10.1145/262839.269238

G. Weber, S. E. Dillard, H. Carr, V. Pascucci, and B. Hamann, Topology-Controlled Volume Rendering, IEEE Transactions on Visualization and Computer Graphics, vol.13, issue.2, 2007.
DOI : 10.1109/TVCG.2007.47