{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T11:58:20Z","timestamp":1773230300934,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":15,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642106309","type":"print"},{"value":"9783642106316","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-642-10631-6_74","type":"book-chapter","created":{"date-parts":[[2009,12,4]],"date-time":"2009-12-04T02:03:43Z","timestamp":1259892223000},"page":"730-739","source":"Crossref","is-referenced-by-count":32,"title":["Computing Multidimensional Persistence"],"prefix":"10.1007","author":[{"given":"Gunnar","family":"Carlsson","sequence":"first","affiliation":[]},{"given":"Gurjeet","family":"Singh","sequence":"additional","affiliation":[]},{"given":"Afra","family":"Zomorodian","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"issue":"1","key":"74_CR1","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s00454-009-9176-0","volume":"42","author":"G. Carlsson","year":"2009","unstructured":"Carlsson, G., Zomorodian, A.: The theory of multidimensional persistence. Discrete & Computational Geometry\u00a042(1), 71\u201393 (2009)","journal-title":"Discrete & Computational Geometry"},{"key":"74_CR2","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/978-1-4613-9586-7_3","volume-title":"Essays in Group Theory","author":"M. Gromov","year":"1987","unstructured":"Gromov, M.: Hyperbolic groups. In: Gersten, S. (ed.) Essays in Group Theory, pp. 75\u2013263. Springer, New York (1987)"},{"key":"74_CR3","unstructured":"de Silva, V., Carlsson, G.: Topological estimation using witness complexes. In: Proc. Symposium on Point-Based Graphics, pp. 157\u2013166 (2004)"},{"issue":"2","key":"74_CR4","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/s00454-004-1146-y","volume":"33","author":"A. Zomorodian","year":"2005","unstructured":"Zomorodian, A., Carlsson, G.: Computing persistent homology. Discrete & Computational Geometry\u00a033(2), 249\u2013274 (2005)","journal-title":"Discrete & Computational Geometry"},{"key":"74_CR5","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1016\/j.cag.2004.08.015","volume":"28","author":"A. Collins","year":"2004","unstructured":"Collins, A., Zomorodian, A., Carlsson, G., Guibas, L.: A barcode shape descriptor for curve point cloud data. Computers and Graphics\u00a028, 881\u2013894 (2004)","journal-title":"Computers and Graphics"},{"key":"74_CR6","unstructured":"Gyulassy, A., Natarajan, V., Pascucci, V., Bremer, P.T., Hamann, B.: Topology-based simplification for feature extraction from 3D scalar fields. In: Proc. IEEE Visualization, pp. 275\u2013280 (2005)"},{"key":"74_CR7","doi-asserted-by":"crossref","unstructured":"de Silva, V., Ghrist, R., Muhammad, A.: Blind swarms for coverage in 2-D. In: Proceedings of Robotics: Science and Systems (2005), http:\/\/www.roboticsproceedings.org\/rss01\/","DOI":"10.15607\/RSS.2005.I.044"},{"issue":"8","key":"74_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1167\/8.8.11","volume":"8","author":"G. Singh","year":"2008","unstructured":"Singh, G., Memoli, F., Ishkhanov, T., Sapiro, G., Carlsson, G., Ringach, D.L.: Topological analysis of population activity in visual cortex. Journal of Vision\u00a08(8), 1\u201318 (2008)","journal-title":"Journal of Vision"},{"issue":"1","key":"74_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11263-007-0056-x","volume":"76","author":"G. Carlsson","year":"2008","unstructured":"Carlsson, G., Ishkhanov, T., de Silva, V., Zomorodian, A.: On the local behavior of spaces of natural images. International Journal of Computer Vision\u00a076(1), 1\u201312 (2008)","journal-title":"International Journal of Computer Vision"},{"issue":"3","key":"74_CR10","doi-asserted-by":"crossref","first-page":"455","DOI":"10.36045\/bbms\/1103065863","volume":"6","author":"P. Frosini","year":"1999","unstructured":"Frosini, P., Mulazzani, M.: Size homotopy groups for computation of natural size distances. Bull. Belg. Math. Soc. Simon Stevin\u00a06(3), 455\u2013464 (1999)","journal-title":"Bull. Belg. Math. Soc. Simon Stevin"},{"key":"74_CR11","doi-asserted-by":"crossref","unstructured":"Cohen-Steiner, D., Edelsbrunner, H., Morozov, D.: Vines and vineyards by updating persistence in linear time. In: Proc. ACM Symposium on Computational Geometry, pp. 119\u2013126 (2006)","DOI":"10.1145\/1137856.1137877"},{"key":"74_CR12","unstructured":"Carlsson, G., Singh, G., Zomorodian, A.: Computing multidimensional persistence, http:\/\/arxiv.org\/abs\/0907.2423"},{"key":"74_CR13","series-title":"Graduate Texts in Mathematics","volume-title":"Using algebraic geometry","author":"D.A. Cox","year":"2005","unstructured":"Cox, D.A., Little, J., O\u2019Shea, D.: Using algebraic geometry, 2nd edn. Graduate Texts in Mathematics, vol.\u00a0185. Springer, New York (2005)","edition":"2"},{"issue":"3","key":"74_CR14","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1006\/jcom.1997.0447","volume":"13","author":"E.W. Mayr","year":"1997","unstructured":"Mayr, E.W.: Some complexity results for polynomial ideals. Journal of Complexity\u00a013(3), 303\u2013325 (1997)","journal-title":"Journal of Complexity"},{"key":"74_CR15","volume-title":"Modern Computer Algebra","author":"J. von zur Gathen","year":"2003","unstructured":"von zur Gathen, J., Gerhard, J.: Modern Computer Algebra, 2nd edn. Cambridge University Press, Cambridge (2003)","edition":"2"}],"container-title":["Lecture Notes in Computer Science","Algorithms and Computation"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-10631-6_74.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,23]],"date-time":"2020-11-23T21:32:23Z","timestamp":1606167143000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-10631-6_74"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783642106309","9783642106316"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-10631-6_74","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009]]}}}