Required Reading

  • Edelsbrunner and Harer, Computational Topology: An Introduction, IX.1, IX.2

Suggested Papers to Present

  • Hamish Carr, Zhao Geng, Julien Tierny, Amit Chattopadhyay, Aaron Knoll: Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data. Comput. Graph. Forum 34(3): 241-250 (2015)

  • Hamish Carr, Jack Snoeyink, Ulrike Axen: Computing contour trees in all dimensions. Comput. Geom. 24(2): 75-94 (2003)

  • Hamish Carr, Jack Snoeyink, Michiel van de Panne: Simplifying Flexible Isosurfaces Using Local Geometric Measures. IEEE Visualization 2004: 497-504

  • Guoning Chen, Konstantin Mischaikow, Robert S. Laramee, Pawel Pilarczyk, Eugene Zhang: Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition. IEEE Trans. Vis. Comput. Graph. 13(4): 769-785 (2007)

  • David Cohen-Steiner, Herbert Edelsbrunner, John Harer: Stability of Persistence Diagrams. Discrete & Computational Geometry 37(1): 103-120 (2007)

  • Vin de Silva, Dmitriy Morozov, Mikael Vejdemo-Johansson: Persistent Cohomology and Circular Coordinates. Discrete & Computational Geometry 45(4): 737-759 (2011)

  • Harish Doraiswamy, Vijay Natarajan: Output-Sensitive Construction of Reeb Graphs. IEEE Trans. Vis. Comput. Graph. 18(1): 146-159 (2012)

  • Harish Doraiswamy, Vijay Natarajan: Computing Reeb Graphs as a Union of Contour Trees. IEEE Trans. Vis. Comput. Graph. 19(2): 249-262 (2013)

  • Herbert Edelsbrunner, John Harer: Jacobi sets of multiple morse functions. Foundations of Computational Mathematics. Cambridge University Press: 37–57 (2002)

  • Herbert Edelsbrunner, Ernst P. Mücke: Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms. ACM Trans. Graph. 9(1): 66-104 (1990)

  • Robin Forman: A user’s guide to discrete Morse theory. Adv. in Math. (1998)

  • Samuel Gerber, Peer-Timo Bremer, Valerio Pascucci, Ross T. Whitaker: Visual Exploration of High Dimensional Scalar Functions. IEEE Trans. Vis. Comput. Graph. 16(6): 1271-1280 (2010)

  • Attila Gyulassy, Peer-Timo Bremer, Bernd Hamann, Valerio Pascucci: A Practical Approach to Morse-Smale Complex Computation: Scalability and Generality. IEEE Trans. Vis. Comput. Graph. 14(6): 1619-1626 (2008)

  • Attila Gyulassy, Peer-Timo Bremer, Valerio Pascucci: Computing Morse-Smale Complexes with Accurate Geometry. IEEE Trans. Vis. Comput. Graph. 18(12): 2014-2022 (2012)

  • Attila Gyulassy, Mark A. Duchaineau, Vijay Natarajan, Valerio Pascucci, Eduardo Bringa, Andrew Higginbotham, Bernd Hamann: Topologically Clean Distance Fields. IEEE Trans. Vis. Comput. Graph. 13(6): 1432-1439 (2007)

  • Lars Huettenberger, Christian Heine, Hamish Carr, Gerik Scheuermann, Christoph Garth: Towards Multifield Scalar Topology Based on Pareto Optimality. Comput. Graph. Forum 32(3): 341-350 (2013)

  • Federico Iuricich, Ulderico Fugacci, Leila De Floriani: Topologically-consistent simplification of discrete Morse complex. Computers & Graphics 51: 157-166 (2015)

  • Pavol Klacansky, Julien Tierny, Hamish Carr, Zhao Geng: Fast and Exact Fiber Surfaces for Tetrahedral Meshes. IEEE Trans. Vis. Comput. Graph. 23(7): 1782-1795 (2017)

  • Daniel E. Laney, Peer-Timo Bremer, Ajith Mascarenhas, P. Miller, Valerio Pascucci: Understanding the Structure of the Turbulent Mixing Layer in Hydrodynamic Instabilities. IEEE Trans. Vis. Comput. Graph. 12(5): 1053-1060 (2006)

  • Valerio Pascucci, Giorgio Scorzelli, Peer-Timo Bremer, Ajith Mascarenhas: Robust on-line computation of Reeb graphs: simplicity and speed. ACM Trans. Graph. 26(3): 58 (2007)

  • Vanessa Robins, Peter John Wood, Adrian P. Sheppard: Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images. IEEE Trans. Pattern Anal. Mach. Intell. 33(8): 1646-1658 (2011)

  • Nithin Shivashankar, Vijay Natarajan: Parallel Computation of 3D Morse-Smale Complexes. Comput. Graph. Forum 31(3): 965-974 (2012)

  • Nithin Shivashankar, Senthilnathan Maadasamy, Vijay Natarajan: Parallel Computation of 2D Morse-Smale Complexes. IEEE Trans. Vis. Comput. Graph. 18(10): 1757-1770 (2012)

  • Nithin Shivashankar, Pratyush Pranav, Vijay Natarajan, Rien van de Weygaert, E. G. Patrick Bos, Steven Rieder: Felix: A Topology Based Framework for Visual Exploration of Cosmic Filaments. IEEE Trans. Vis. Comput. Graph. 22(6): 1745-1759 (2016)

  • Primoz Skraba, Paul Rosen, Bei Wang, Guoning Chen, Harsh Bhatia, Valerio Pascucci: Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion. IEEE Trans. Vis. Comput. Graph. 22(6): 1683-1693 (2016)

  • Bong-Soo Sohn, Chandrajit L. Bajaj: Time-Varying Contour Topology. IEEE Trans. Vis. Comput. Graph. 12(1): 14-25 (2006)

  • Dilip Mathew Thomas, Vijay Natarajan: Multiscale Symmetry Detection in Scalar Fields by Clustering Contours. IEEE Trans. Vis. Comput. Graph. 20(12): 2427-2436 (2014)

  • Julien Tierny, Hamish Carr: Jacobi Fiber Surfaces for Bivariate Reeb Space Computation. IEEE Trans. Vis. Comput. Graph. 23(1): 960-969 (2017)

  • Julien Tierny, Attila Gyulassy, Eddie Simon, Valerio Pascucci: Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees. IEEE Trans. Vis. Comput. Graph. 15(6): 1177-1184 (2009)

  • Julien Tierny, Valerio Pascucci: Generalized Topological Simplification of Scalar Fields on Surfaces. IEEE Trans. Vis. Comput. Graph. 18(12): 2005-2013 (2012)

  • Marc J. van Kreveld, René van Oostrum, Chandrajit L. Bajaj, Valerio Pascucci, Daniel Schikore: Contour Trees and Small Seed Sets for Isosurface Traversal. Symposium on Computational Geometry 1997: 212-220

  • Gunther H. Weber, Scott E. Dillard, Hamish Carr, Valerio Pascucci, Bernd Hamann: Topology-Controlled Volume Rendering. IEEE Trans. Vis. Comput. Graph. 13(2): 330-341 (2007)

  • Kenneth Weiss, Federico Iuricich, Riccardo Fellegara, Leila De Floriani: A primal/dual representation for discrete Morse complexes on tetrahedral meshes. Comput. Graph. Forum 32(3): 361-370 (2013)