메뉴 건너뛰기




Volumn 50, Issue 2, 2013, Pages 330-353

Morse Theory for Filtrations and Efficient Computation of Persistent Homology

Author keywords

Computational topology; Discrete Morse theory; Persistent homology

Indexed keywords


EID: 84881611962     PISSN: 01795376     EISSN: 14320444     Source Type: Journal    
DOI: 10.1007/s00454-013-9529-6     Document Type: Article
Times cited : (293)

References (35)
  • 2
    • 0001309062 scopus 로고    scopus 로고
    • On discrete Morse functions and combinatorial decompositions
    • Discrete Math, 1997
    • Chari, M. K.: On discrete Morse functions and combinatorial decompositions. In: Proc. Formal Power Series and Algebraic Combinatorics (Vienna) (1997). Discrete Math. 217(1-3), 101-113 (2000).
    • (2000) In: Proc. Formal Power Series and Algebraic Combinatorics (Vienna) , vol.217 , Issue.1-3 , pp. 101-113
    • Chari, M.K.1
  • 4
    • 10044257064 scopus 로고
    • An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere: Grid generation, finite elements, and geometric design
    • Delfinado, C. J. A., Edelsbrunner, H.: An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere: Grid generation, finite elements, and geometric design. Comput. Aided Geom. Des. 12(7), 771-784 (1995).
    • (1995) Comput. Aided Geom. Des. , vol.12 , Issue.7 , pp. 771-784
    • Delfinado, C.J.A.1    Edelsbrunner, H.2
  • 5
    • 12944285986 scopus 로고    scopus 로고
    • Computing simplicial homology based on efficient Smith normal form algorithms
    • In: Joswig, M., Takayama, N. (eds.), Springer, Berlin
    • Dumas, J.-G., Heckenbach, F., Saunders, D., Welker, V.: Computing simplicial homology based on efficient Smith normal form algorithms. In: Joswig, M., Takayama, N. (eds.) Algebra, Geometry, and Software Systems, pp. 177-206. Springer, Berlin (2003).
    • (2003) Algebra, Geometry, and Software Systems , pp. 177-206
    • Dumas, J.-G.1    Heckenbach, F.2    Saunders, D.3    Welker, V.4
  • 9
    • 0002910255 scopus 로고    scopus 로고
    • Morse theory for cell complexes
    • Forman, R.: Morse theory for cell complexes. Adv. Math. 134, 90-145 (1998).
    • (1998) Adv. Math. , vol.134 , pp. 90-145
    • Forman, R.1
  • 10
    • 41849100389 scopus 로고    scopus 로고
    • Barcodes: the persistent topology of data
    • Ghrist, R.: Barcodes: the persistent topology of data. Bull. Am. Math. Soc. (N. S.), 45(1), 61-75 (2008).
    • (2008) Bull. Am. Math. Soc. (N. S.) , vol.45 , Issue.1 , pp. 61-75
    • Ghrist, R.1
  • 12
    • 0026403469 scopus 로고
    • Asymptotically fast triangularization of matrices over rings
    • Hafner, J., McCurley, K.: Asymptotically fast triangularization of matrices over rings. SIAM J. Comput. 20(6), 1068-1083 (1991).
    • (1991) SIAM J. Comput. , vol.20 , Issue.6 , pp. 1068-1083
    • Hafner, J.1    McCurley, K.2
  • 14
    • 84895063231 scopus 로고    scopus 로고
    • Discrete Morse theoretic algorithms for computing homology of complexes and maps
    • doi:10.1007/s10208-013-9145-0
    • Harker, S., Mischaikow, K., Mrozek, M., Nanda, V.: Discrete Morse theoretic algorithms for computing homology of complexes and maps. Found. Comput. Math. (2013). doi: 10. 1007/s10208-013-9145-0.
    • (2013) Found. Comput. Math.
    • Harker, S.1    Mischaikow, K.2    Mrozek, M.3    Nanda, V.4
  • 15
    • 33847612091 scopus 로고    scopus 로고
    • Computing optimal Morse matchings
    • Joswig, M., Pfetsch, M.: Computing optimal Morse matchings. SIAM J. Discrete Math 20(1), 11-25 (2006).
    • (2006) SIAM J. Discrete Math , vol.20 , Issue.1 , pp. 11-25
    • Joswig, M.1    Pfetsch, M.2
  • 16
    • 21344457001 scopus 로고    scopus 로고
    • Discrete Morse theory for free chain complexes
    • Kozlov, D.: Discrete Morse theory for free chain complexes. C. R. Math. 340, 867-872 (2005).
    • (2005) C. R. Math. , vol.340 , pp. 867-872
    • Kozlov, D.1
  • 18
    • 0003205192 scopus 로고
    • Algebraic Topology. American Mathematical Society Colloquium Publications, vol. 27
    • New York
    • Lefschetz, S.: Algebraic Topology. American Mathematical Society Colloquium Publications, vol. 27. American Mathematical Society, New York (1942).
    • (1942) American Mathematical Society
    • Lefschetz, S.1
  • 19
    • 43049107822 scopus 로고    scopus 로고
    • Ph. D. Dissertation. Department of Mathematics, PUC-Rio
    • Lewiner, T.: Geometric discrete Morse complexes. Ph. D. Dissertation. Department of Mathematics, PUC-Rio. http://thomas. lewiner. org/pdfs/tomlew_phd_puc. pdf (2005).
    • (2005) Geometric discrete Morse complexes
    • Lewiner, T.1
  • 20
    • 1642318759 scopus 로고    scopus 로고
    • Toward optimality in discrete Morse theory
    • Lewiner, T., Lopes, H., Tavares, G.: Toward optimality in discrete Morse theory. Exp. Math. 12(3), 271-286 (2003).
    • (2003) Exp. Math. , vol.12 , Issue.3 , pp. 271-286
    • Lewiner, T.1    Lopes, H.2    Tavares, G.3
  • 23
    • 57849165859 scopus 로고    scopus 로고
    • The coreduction homology algorithm
    • Mrozek, M., Batko, B.: The coreduction homology algorithm. Discrete Comput. Geom. 41, 96-118 (2009).
    • (2009) Discrete Comput. Geom. , vol.41 , pp. 96-118
    • Mrozek, M.1    Batko, B.2
  • 24
    • 78049247046 scopus 로고    scopus 로고
    • Coreduction homology algorithm for inclusions and persistent homology
    • Mrozek, M., Wanner, T.: Coreduction homology algorithm for inclusions and persistent homology. Comput. Math. Appl. 60(10), 2812-2833 (2010).
    • (2010) Comput. Math. Appl. , vol.60 , Issue.10 , pp. 2812-2833
    • Mrozek, M.1    Wanner, T.2
  • 25
    • 0003734371 scopus 로고
    • Menlo Park: The Benjamin/Cummings Publishing Company, Inc
    • Munkres, J. R.: Elements of Algebraic Topology. The Benjamin/Cummings Publishing Company, Inc., Menlo Park (1984).
    • (1984) Elements of Algebraic Topology
    • Munkres, J.R.1
  • 26
    • 84881616729 scopus 로고    scopus 로고
    • Perseus, the Persistent Homology Software
    • Perseus, the Persistent Homology Software. http://www. math. rutgers. edu/vidit/perseus.
  • 27
    • 80855137629 scopus 로고    scopus 로고
    • Theory and algorithms for constructing discrete Morse complexes from grayscale digital images
    • Robins, V., Wood, P. J., Sheppard, A. P.: Theory and algorithms for constructing discrete Morse complexes from grayscale digital images. IEEE Trans. Pattern Anal. Mach. Intell., 1-14 (2010).
    • (2010) IEEE Trans. Pattern Anal. Mach. Intell. , pp. 1-14
    • Robins, V.1    Wood, P.J.2    Sheppard, A.P.3
  • 30
    • 0030401841 scopus 로고    scopus 로고
    • Nearly optimal algorithms for computing Smith normal forms of integer matrices, vol. 96
    • Storjohann, A.: Nearly optimal algorithms for computing Smith normal forms of integer matrices, vol. 96. In: Proceedings of ISSAC, pp. 267-274 (1996).
    • (1996) In: Proceedings of ISSAC , pp. 267-274
    • Storjohann, A.1
  • 31
    • 34250487811 scopus 로고
    • Gaussian elimination is not optimal
    • Strassen, V.: Gaussian elimination is not optimal. Numer. Math. 13, 354-356 (1969).
    • (1969) Numer. Math. , vol.13 , pp. 354-356
    • Strassen, V.1
  • 32
    • 84881615759 scopus 로고
    • Cell spaces
    • Tucker, A. W.: Cell spaces. Ann. Math. 37, 92-100 (1936).
    • (1936) Ann. Math. , vol.37 , pp. 92-100
    • Tucker, A.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.