{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T21:51:56Z","timestamp":1743112316675,"version":"3.40.3"},"publisher-location":"Cham","reference-count":19,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319394404"},{"type":"electronic","value":"9783319394411"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-39441-1_12","type":"book-chapter","created":{"date-parts":[[2016,6,1]],"date-time":"2016-06-01T07:47:40Z","timestamp":1464767260000},"page":"130-139","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Fast, Simple and Separable Computation of Betti Numbers on Three-Dimensional Cubical Complexes"],"prefix":"10.1007","author":[{"given":"Aldo","family":"Gonzalez-Lorenzo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mateusz","family":"Juda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexandra","family":"Bac","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Luc","family":"Mari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pedro","family":"Real","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,6,2]]},"reference":[{"issue":"3","key":"12_CR1","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1016\/j.cviu.2006.10.004","volume":"105","author":"M Allili","year":"2007","unstructured":"Allili, M., Corriveau, D.: Topological analysis of shapes using Morse theory. Comput. Vis. Image Underst. 105(3), 188\u2013199 (2007)","journal-title":"Comput. Vis. Image Underst."},{"key":"12_CR2","unstructured":"BoostCommunity. Boost Project (2016). \n                      http:\/\/www.boost.org\/"},{"key":"12_CR3","volume-title":"Introduction to Algorithms","author":"TH Cormen","year":"2001","unstructured":"Cormen, T.H., Stein, C., Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms. McGraw-Hill Higher Education, New York (2001)"},{"issue":"4","key":"12_CR4","doi-asserted-by":"publisher","first-page":"1695","DOI":"10.1137\/080735722","volume":"7","author":"S Day","year":"2009","unstructured":"Day, S., Kalies, W.D., Wanner, T.: Verified homology computations for nodal domains. Multiscale Model. Simul. 7(4), 1695\u20131726 (2009)","journal-title":"Multiscale Model. Simul."},{"issue":"7","key":"12_CR5","doi-asserted-by":"publisher","first-page":"771","DOI":"10.1016\/0167-8396(95)00016-Y","volume":"12","author":"JA Cecil","year":"1995","unstructured":"Cecil, J.A., Delfinado, H.E.: An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere. Comput. Aided Geom. Des. 12(7), 771\u2013784 (1995)","journal-title":"Comput. Aided Geom. Des."},{"issue":"1\u20132","key":"12_CR6","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s00200-012-0167-7","volume":"23","author":"P Dlotko","year":"2012","unstructured":"Dlotko, P., Ghrist, R., Juda, M., Mrozek, M.: Distributed computation of coverage in sensor networks by homological methods. Appl. Algebra Eng. Commun. Comput. 23(1\u20132), 29\u201358 (2012)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"issue":"3","key":"12_CR7","first-page":"247","volume":"60","author":"P D\u0142otko","year":"2010","unstructured":"D\u0142otko, P., Specogna, R.: Efficient cohomology computation for electromagnetic modeling. CMES: Comput. Model. Eng. Sci. 60(3), 247\u2013278 (2010)","journal-title":"CMES: Comput. Model. Eng. Sci."},{"key":"12_CR8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511756337","volume-title":"Electromagn. Theory Comput.","author":"PW Gross","year":"2004","unstructured":"Gross, P.W., Robert Kotiuga, P.: Electromagn. Theory Comput. Cambridge University Press, Cambridge (2004). Cambridge Books Online"},{"issue":"1","key":"12_CR9","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s10208-013-9145-0","volume":"14","author":"S Harker","year":"2013","unstructured":"Harker, S., Mischaikow, K., Mrozek, M., Nanda, V.: Discrete morse theoretic algorithms for computing homology of complexes and maps. Found. Comput. Math. 14(1), 151\u2013184 (2013)","journal-title":"Found. Comput. Math."},{"key":"12_CR10","unstructured":"Intel. Threading Building Blocks (2016). \n                      https:\/\/www.threadingbuildingblocks.org\/"},{"key":"12_CR11","unstructured":"Juda, M., Mrozek, M., Brendel, P., Wagner, H., et al.: CAPD: : RedHom (2010\u20132016). \n                      http:\/\/redhom.ii.uj.edu.pl"},{"key":"12_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1007\/978-3-662-44199-2_27","volume-title":"Mathematical Software \u2013 ICMS 2014","author":"M Juda","year":"2014","unstructured":"Juda, M., Mrozek, M.: CAPD:RedHom v2 - homology software based on reduction algorithms. In: Hong, H., Yap, C. (eds.) ICMS 2014. LNCS, vol. 8592, pp. 160\u2013166. Springer, Heidelberg (2014)"},{"key":"12_CR13","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/BFb0095240","volume-title":"Dynamical Systems","author":"K Mischaikow","year":"1995","unstructured":"Mischaikow, K.: Conley index theory. In: Johnson, R. (ed.) Dynamical Systems. Lecture Notes in Mathematics, vol. 1609, pp. 119\u2013207. Springer, Heidelberg (1995)"},{"issue":"1","key":"12_CR14","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/j.patcog.2011.04.020","volume":"45","author":"M Mrozek","year":"2012","unstructured":"Mrozek, M., Zelawski, M., Gryglewski, A., Han, S., Krajniak, A.: Homological methods for extraction and analysis of linear features in multidimensional images. Pattern Recogn. 45(1), 285\u2013298 (2012)","journal-title":"Pattern Recogn."},{"key":"12_CR15","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1007\/s10208-005-0182-1","volume":"6","author":"M Mrozek","year":"2006","unstructured":"Mrozek, M.: Index pairs algorithms. Found. Comput. Math. 6, 457\u2013493 (2006)","journal-title":"Found. Comput. Math."},{"key":"12_CR16","volume-title":"Elements of Algebraic Topology","author":"JR Munkres","year":"1984","unstructured":"Munkres, J.R.: Elements of Algebraic Topology. Addison-Wesley, Reading (1984)"},{"key":"12_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/978-3-540-31965-8_19","volume-title":"Discrete Geometry for Computer Imagery","author":"S Peltier","year":"2005","unstructured":"Peltier, S., Alayrangues, S., Fuchs, L., Lachaud, J.-O.: Computation of homology groups and generators. In: Andr\u00e8s, \u00c9., Damiand, G., Lienhardt, P. (eds.) DGCI 2005. LNCS, vol. 3429, pp. 195\u2013205. Springer, Heidelberg (2005)"},{"issue":"2","key":"12_CR18","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/s13160-010-0014-9","volume":"27","author":"T Teramoto","year":"2010","unstructured":"Teramoto, T., Nishiura, Y.: Morphological characterization of the diblock copolymer problem with topological computation. Jpn. J. Ind. Appl. Math. 27(2), 175\u2013190 (2010)","journal-title":"Jpn. J. Ind. Appl. Math."},{"key":"12_CR19","series-title":"Mathematics and Visualization","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/978-3-642-23175-9_7","volume-title":"Topological Methods in Data Analysis and Visualization II","author":"H Wagner","year":"2012","unstructured":"Wagner, H., Chen, C., Vu\u00e7ini, E.: Efficient computation of persistent homology for cubical data. In: Peikert, R., Hauser, H., Carr, H., Fuchs, R. (eds.) Topological Methods in Data Analysis and Visualization II. Mathematics and Visualization, pp. 91\u2013106. Springer, Berlin Heidelberg (2012)"}],"container-title":["Lecture Notes in Computer Science","Computational Topology in Image Context"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-39441-1_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T00:09:08Z","timestamp":1590970148000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-39441-1_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319394404","9783319394411"],"references-count":19,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-39441-1_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"2 June 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}