{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T08:27:08Z","timestamp":1770539228135,"version":"3.49.0"},"publisher-location":"Cham","reference-count":23,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319040981","type":"print"},{"value":"9783319040998","type":"electronic"}],"license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-319-04099-8_9","type":"book-chapter","created":{"date-parts":[[2014,4,22]],"date-time":"2014-04-22T15:30:30Z","timestamp":1398180630000},"page":"135-150","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Notes on the Simplification of the Morse-Smale Complex"],"prefix":"10.1007","author":[{"given":"David","family":"G\u00fcnther","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Reininghaus","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hans-Peter","family":"Seidel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tino","family":"Weinkauf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,3,19]]},"reference":[{"key":"9_CR1","unstructured":"U. Bauer, Persistence in discrete Morse theory. PhD thesis, University of G\u00f6ttingen, 2011"},{"issue":"5","key":"9_CR2","first-page":"1545","volume":"29","author":"T. Dey","year":"2010","unstructured":"T. Dey, K. Li, C. Luo, P. Ranjan, I. Safa, Y. Wang, Persistent heat signature for pose-oblivious matching of incomplete models. CGF 29(5), 1545\u20131554 (2010)","journal-title":"CGF"},{"key":"9_CR3","first-page":"361","volume-title":"Morse-Smale complexes for piecewise linear 3-manifolds, in 19th Annual Proceedings of SoCG, San Diego","author":"H. Edelsbrunner","year":"2003","unstructured":"H. Edelsbrunner, J. Harer, V. Natarajan, V. Pascucci, Morse-Smale complexes for piecewise linear 3-manifolds, in 19th Annual Proceedings of SoCG, San Diego (ACM, New York, 2003), pp. 361\u2013370"},{"key":"9_CR4","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/s00454-003-2926-5","volume":"30","author":"H. Edelsbrunner","year":"2003","unstructured":"H. Edelsbrunner, J. Harer, A. Zomorodian, Hierarchical Morse complexes for piecewise linear 2-manifolds. Discret. Comput. Geom. 30, 87\u2013107 (2003)","journal-title":"Discret. Comput. Geom."},{"key":"9_CR5","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1007\/s00454-002-2885-2","volume":"28","author":"H. Edelsbrunner","year":"2002","unstructured":"H. Edelsbrunner, D. Letscher, A. Zomorodian, Topological persistence and simplification. Discret. Comput. Geom. 28, 511\u2013533 (2002)","journal-title":"Discret. Comput. Geom."},{"key":"9_CR6","unstructured":"R. Forman, A user\u2019s guide to discrete Morse theory, in Proceedings of the 2001 International Conference on Formal Power Series and Algebraic Combinatorics, USA. Advances in Applied Mathematics (2001)"},{"key":"9_CR7","unstructured":"D. G\u00fcnther, Topological analysis of discrete scalar data. PhD thesis, Saarland University, Saarbr\u00fccken, Germany, 2012"},{"key":"9_CR8","doi-asserted-by":"publisher","first-page":"959","DOI":"10.1007\/s00371-012-0726-8","volume":"28","author":"D. G\u00fcnther","year":"2012","unstructured":"D. G\u00fcnther, J. Reininghaus, H. Wagner, I. Hotz, Efficient computation of 3D Morse-Smale complexes and persistent homology using discrete Morse theory. Vis. Comput. 28, 959\u2013969 (2012)","journal-title":"Vis. Comput."},{"key":"9_CR9","unstructured":"A. Gyulassy, Combinatorial construction of Morse-Smale complexes for data analysis and visualization. PhD thesis, University of California, Davis, 2008"},{"key":"9_CR10","doi-asserted-by":"crossref","unstructured":"A. Gyulassy, P.-T. Bremer, V. Pascucci, B. Hamann, Practical considerations in Morse-Smale complex computation, in Proceedings of the TopoInVis, Zurich (Springer, 2011), pp. 67\u201378","DOI":"10.1007\/978-3-642-15014-2_6"},{"key":"9_CR11","first-page":"1440","volume":"13","author":"A. Gyulassy","year":"2007","unstructured":"A. Gyulassy, V. Natarajan, V. Pascucci, B. Hamann, Efficient computation of Morse-Smale complexes for three-dimensional scalar functions. TVCG 13, 1440\u20131447 (2007)","journal-title":"TVCG"},{"issue":"1","key":"9_CR12","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1137\/S0895480104445885","volume":"20","author":"M. Joswig","year":"2006","unstructured":"M. Joswig, M.E. Pfetsch, Computing optimal Morse matchings. SIAM J. Discret. Math. 20(1), 11\u201325 (2006)","journal-title":"SIAM J. Discret. Math."},{"issue":"4","key":"9_CR13","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1080\/10586458.2005.10128941","volume":"14","author":"H. King","year":"2005","unstructured":"H. King, K. Knudson, N. Mramor, Generating discrete Morse functions from point data. Exp. Math. 14(4), 435\u2013444 (2005)","journal-title":"Exp. Math."},{"key":"9_CR14","unstructured":"T. Lewiner, Geometric discrete Morse complexes. PhD thesis, PUC-Rio, 2005"},{"issue":"3","key":"9_CR15","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/S0925-7721(03)00014-2","volume":"26","author":"T. Lewiner","year":"2003","unstructured":"T. Lewiner, H. Lopes, G. Tavares, Optimal discrete Morse functions for 2-manifolds. Comput. Geom. 26(3), 221\u2013233 (2003)","journal-title":"Comput. Geom."},{"key":"9_CR16","doi-asserted-by":"crossref","DOI":"10.1515\/9781400881802","volume-title":"Morse Theory","author":"J. Milnor","year":"1963","unstructured":"J. Milnor, Morse Theory (Princeton University Press, Princeton, 1963)"},{"key":"9_CR17","doi-asserted-by":"crossref","unstructured":"M. Morse, The Calculus of Variations in the Large. Colloquium Publications, vol. 18 (AMS, New York, 1934)","DOI":"10.1090\/coll\/018"},{"key":"9_CR18","unstructured":"J. Reininghaus, Computational discrete Morse theory. PhD thesis, Freie Universit\u00e4t, 2012"},{"issue":"8","key":"9_CR19","doi-asserted-by":"publisher","first-page":"1646","DOI":"10.1109\/TPAMI.2011.95","volume":"33","author":"V. Robins","year":"2011","unstructured":"V. Robins, P.J. Wood, A.P. Sheppard, Theory and algorithms for constructing discrete Morse complexes from grayscale digital images. IEEE PAMI 33(8), 1646\u20131658 (2011)","journal-title":"IEEE PAMI"},{"issue":"3pt1","key":"9_CR20","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1111\/j.1467-8659.2012.03089.x","volume":"31","author":"N. Shivashankar","year":"2012","unstructured":"N. Shivashankar, V. Natarajan, Parallel computation of 3D Morse-Smale complexes. Comput. Graph. Forum 31(3pt1), 965\u2013974 (2012)","journal-title":"Comput. Graph. Forum"},{"key":"9_CR21","doi-asserted-by":"publisher","first-page":"199","DOI":"10.2307\/1970311","volume":"74","author":"S. Smale","year":"1961","unstructured":"S. Smale, On gradient dynamical systems. Ann. Math. 74, 199\u2013206 (1961)","journal-title":"Ann. Math."},{"key":"9_CR22","doi-asserted-by":"crossref","unstructured":"H. Theisel, T. Weinkauf, H.-C. Hege, H.-P. Seidel, On the applicability of topological methods for complex flow data, in Proceedings of the TopoInVis, Grimma (Springer, 2007), pp. 105\u2013120","DOI":"10.1007\/978-3-540-70823-0_8"},{"issue":"2","key":"9_CR23","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1109\/TVCG.2007.47","volume":"13","author":"G. Weber","year":"2007","unstructured":"G. Weber, S. Dillard, H. Carr, V. Pascucci, B. Hamann, Topology-controlled volume rendering. IEEE Trans. Vis. Comput. Graph. 13(2), 330\u2013341 (2007)","journal-title":"IEEE Trans. Vis. Comput. Graph."}],"container-title":["Mathematics and Visualization","Topological Methods in Data Analysis and Visualization III"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-04099-8_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,14]],"date-time":"2023-02-14T16:04:51Z","timestamp":1676390691000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-04099-8_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783319040981","9783319040998"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-04099-8_9","relation":{},"ISSN":["1612-3786","2197-666X"],"issn-type":[{"value":"1612-3786","type":"print"},{"value":"2197-666X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]},"assertion":[{"value":"19 March 2014","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}