The robustness of level sets

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6346 LNCS, Issue PART 1, 2010, Pages 1-10

  Bendich, Paul ^a,b,c   Edelsbrunner, Herbert ^a,b,c,e   Morozov, Dmitriy ^d   Patel, Amit ^a,b  

^a INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA   (Austria)

^b Duke University   (United States)

^c DUKE UNIVERSITY   (United States)

^d STANFORD UNIVERSITY   (United States)

^e Geomagic   (United States)

Author keywords

continuous functions; extended persistence; homology; level sets; perturbations; robustness; Topological spaces; well diagrams; well groups

Indexed keywords

CONTINUOUS FUNCTIONS; EXTENDED PERSISTENCE; HOMOLOGY; LEVEL SET; PERTURBATIONS; ROBUSTNESS; TOPOLOGICAL SPACES; WELL GROUPS;

FUNCTIONS; MEDICAL IMAGING; VISUALIZATION;

TOPOLOGY;

EID: 78249236202     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-15775-2_1     Document Type: Conference Paper

References (13)

1. Bajaj, C.L., Pascucci, V., Schikore, D.R.: The contour spectrum. In: Proc. 8th IEEE Conf. Visualization, pp. 167-173 (1997)
2. Carlsson, G., Collins, A., Guibas, L.J., Zomorodian, Z.: Persistence barcodes for shapes. Internat. J. Shape Modeling 11, 149-187 (2005)
3. Carlsson, G., de Silva, V., Morozov, D.: Zigzag persistent homology and real-valued functions. In: Proc. 25th Ann. Sympos. Comput. Geom., pp. 247-256 (2009)
4. Cohen-Steiner, D., Edelsbrunner, H., Harer, J.: Extending persistence using Poincaré and Lefschetz duality. Found. Comput. Math. 9, 79-103 (2009)
5. Edelsbrunner, H., Harer, J.: Persistent homology - a survey. In: Goodman, J.E., Pach, J., Pollack, R. (eds.) Surveys on Discrete and Computational Geometry. Twenty Years Later. Contemporary Mathematics, vol. 453, pp. 257-282. Amer. Math. Soc., Providence (2008)
6. Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discrete Comput. Geom. 28, 511-533 (2002)
7. Edelsbrunner, H., Morozov, D., Patel, A.: The stability of the apparent contour of an orientable 2-manifold. In: Pascucci, V., Tierny, J. (eds.) Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications. Springer, Heidelberg (to appear)
8. Edelsbrunner, H., Morozov, D., Patel, A.: Quantifying transversality by measuring the robustness of intersections. Dept. Comput. Sci., Duke Univ., Durham, North Carolina (2009) (Manuscript)
9. Fang, S., Biddlecome, T., Tuceryan, M.: Image-based transfer function design for data exploration in volume visualization. In: Proc. 9th IEEE Conf. Visualization, pp. 319-326 (1998)
10. van Krefeld, M., van Oostrum, R., Bajaj, C.L., Pascucci, V., Schikore, D.R.: Contour trees and small seed sets for isosurface traversal. In: Proc. 13th Ann. Sympos. Comput. Geom., pp. 212-220 (1997)
11. Munkres, J.R.: Elements of Algebraic Topology. Perseus, Cambridge (1984)
12. Newman, T.S., Yi., H.: A survey of the marching cube algorithm. Computers and Graphics 30, 854-879 (2006)
13. Wittenbrink, C.M., Malzbender, T., Goss, M.E.: Opacity-weighted color interpolation for volume sampling. In: Proc. IEEE Proc. Volume Visualization, pp. 135-142 (1998)