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Volumn 138, Issue 8, 2010, Pages 3003-3017

One-dimensional reduction of multidimensional persistent homology

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EID: 77952057398     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-10-10312-8     Document Type: Article
Times cited : (41)

References (24)
  • 3
    • 0035385214 scopus 로고    scopus 로고
    • Size functions from a categorical viewpoint
    • MR1861130 (2002h:68184)
    • F. Cagliari, M. Ferri and P. Pozzi, Size functions from a categorical viewpoint, Acta Appl. Math. 67 (2001), 225-235. MR1861130 (2002h:68184)
    • (2001) Acta Appl. Math. , vol.67 , pp. 225-235
    • Cagliari, F.1    Ferri, M.2    Pozzi, P.3
  • 4
    • 35348903806 scopus 로고    scopus 로고
    • The theory of multidimensional persistence
    • June 6-8, 2007, Gyeongiu, South Koream, MR2469164
    • G. Carlsson and A. Zomorodian, The theory of multidimensional persistence, Symposium on Computational Geometry, June 6-8, 2007, Gyeongiu, South Korea (2007), 184-193. MR2469164
    • (2007) Symposium on Computational Geometry , pp. 184-193
    • Carlsson, G.1    Zomorodian, A.2
  • 6
    • 45749139651 scopus 로고    scopus 로고
    • Quantifying homology classes
    • Bordeaux, France, Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany
    • C. Chen and D. Freedman, Quantifying homology classes, 25th Symp. on Theoretical Aspects of Computer Science, Bordeaux, France (2008), 169-180, Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany, http://drops.dagstuhl. de/opus/volltexte/2008/1347.
    • (2008) 25th Symp. on Theoretical Aspects of Computer Science , pp. 169-180
    • Chen, C.1    Freedman, D.2
  • 7
    • 33846839317 scopus 로고    scopus 로고
    • Stability of persistence diagrams
    • MR2279866 (2008i:68130)
    • D. Cohen-Steiner, H. Edelsbrunner and J. Harer, Stability of persistence diagrams, Discrete Comput. Geom. 37, no.1 (2007), 103-120. MR2279866 (2008i:68130)
    • (2007) Discrete Comput. Geom. , vol.37 , Issue.1 , pp. 103-120
    • Cohen-Steiner, D.1    Edelsbrunner, H.2    Harer, J.3
  • 8
    • 0002374087 scopus 로고    scopus 로고
    • Δ* reduction of size graphs as a new algorithm for computing size functions of shapes
    • Feb. 27-Mar. 3 2000, Atlantic City
    • M. d'Amico, Δ* reduction of size graphs as a new algorithm for computing size functions of shapes, Proc. Internat. Conf. on Computer Vision, Pattern Recognition and Image Processing, Feb. 27-Mar. 3, 2000, Atlantic City 2 (2000), 107-110.
    • (2000) Proc. Internat. Conf. on Computer Vision, Pattern Recognition and Image Processing , vol.2 , pp. 107-110
    • D'Amico, M.1
  • 9
    • 77949266078 scopus 로고    scopus 로고
    • Natural pseudo-distance and optimal matching between reduced size functions
    • available at
    • M. d'Amico, P. Frosini and C. Landi, Natural pseudo-distance and optimal matching between reduced size functions, Acta Applicandae Mathematicae 109, no.2 (2010), 527-554, available at http://www.springerlink.com/content/ cj84327h4n280144/fulltext.pdf.
    • (2010) Acta Applicandae Mathematicae , vol.109 , Issue.2 , pp. 527-554
    • D'Amico, M.1    Frosini, P.2    Landi, C.3
  • 10
    • 75649148179 scopus 로고    scopus 로고
    • Natural pseudodistances between closed curves
    • P. Donatini and P. Frosini, Natural pseudodistances between closed curves, Forum Math. 21, no.6 (2009), 981-999.
    • (2009) Forum Math. , vol.21 , Issue.6 , pp. 981-999
    • Donatini, P.1    Frosini, P.2
  • 11
    • 17044398347 scopus 로고    scopus 로고
    • Jacobi sets of multiple Morse functions
    • Minneapolis 2002, Cambridge Univ. Press, Cambridge, MR2189626 (2006j:58014)
    • H. Edelsbrunner and J. Harer. Jacobi sets of multiple Morse functions, Foundations of Computational Mathematics, Minneapolis, 2002, Cambridge Univ. Press, Cambridge (2004), 37-57. MR2189626 (2006j:58014)
    • (2004) Foundations of Computational Mathematics , pp. 37-57
    • Edelsbrunner, H.1    Harer, J.2
  • 12
    • 70349220130 scopus 로고    scopus 로고
    • Persistent homology - A survey
    • Contemporary Mathematics, Providence, RI, MR2405684 (2009h:55003)
    • H. Edelsbrunner and J. Harer. Persistent homology - a survey, Contemporary Mathematics, 453, Amer. Math. Soc., Providence, RI (2008), 257-282. MR2405684 (2009h:55003)
    • (2008) Amer. Math. Soc. , vol.453 , pp. 257-282
    • Edelsbrunner, H.1    Harer, J.2
  • 13
    • 0036883297 scopus 로고    scopus 로고
    • Topological persistence and simplification
    • MR1949898 (2003m:52019)
    • H. Edelsbrunner, D. Letscher and A. Zomorodian, Topological persistence and simplification, Discrete Comput. Geom. 28 (2002), 511-533. MR1949898 (2003m:52019)
    • (2002) Discrete Comput. Geom. , vol.28 , pp. 511-533
    • Edelsbrunner, H.1    Letscher, D.2    Zomorodian, A.3
  • 14
    • 84971812714 scopus 로고
    • A distance for similarity classes of submanifolds of a Euclidean space
    • MR1083277 (91j:53005)
    • P. Frosini, A distance for similarity classes of submanifolds of a Euclidean space, Bulletin of the Australian Mathematical Society 42 (3) (1990), 407-416. MR1083277 (91j:53005)
    • (1990) Bulletin of the Australian Mathematical Society , vol.42 , Issue.3 , pp. 407-416
    • Frosini, P.1
  • 16
    • 0034816035 scopus 로고    scopus 로고
    • Size functions and formal series
    • MR1855041 (2002g:68126)
    • P. Frosini and C. Landi, Size functions and formal series, Appl. Algebra Eng. Commun. Computing 12 (2001), 327-349. MR1855041 (2002g:68126)
    • (2001) Appl. Algebra Eng. Commun. Computing , vol.12 , pp. 327-349
    • Frosini, P.1    Landi, C.2
  • 17
    • 0001365833 scopus 로고    scopus 로고
    • Size homotopy groups for computation of natural size distances
    • MR1721761 (2000g:55017)
    • P. Frosini and M. Mulazzani, Size homotopy groups for computation of natural size distances, Bull. Belg. Math. Soc. 6 (1999), 455-464. MR1721761 (2000g:55017)
    • (1999) Bull. Belg. Math. Soc. , vol.6 , pp. 455-464
    • Frosini, P.1    Mulazzani, M.2
  • 18
    • 41849100389 scopus 로고    scopus 로고
    • Barcodes: The persistent topology of data
    • MR2358377 (2008i:55007)
    • R. Ghrist, Barcodes: The persistent topology of data, Bull. Amer. Math. Soc. 45 (2008), 61-75. MR2358377 (2008i:55007)
    • (2008) Bull. Amer. Math. Soc. , vol.45 , pp. 61-75
    • Ghrist, R.1
  • 19
  • 20
    • 45749148753 scopus 로고    scopus 로고
    • A refinement of multi-dimensional persistence
    • MR2399474 (2009d:55008)
    • K. P. Knudson, A refinement of multi-dimensional persistence, Homology, Homotopy and Applications 10, no.1 (2008), 259-281. MR2399474 (2009d:55008)
    • (2008) Homology, Homotopy and Applications , vol.10 , Issue.1 , pp. 259-281
    • Knudson, K.P.1
  • 21
    • 0002582525 scopus 로고    scopus 로고
    • New pseudodistances for the size function space
    • Vision Geometry, VI, Robert A. Melter, Angela Y. Wu, Longin J. Latecki (eds.), SPIE
    • C. Landi and P. Frosini, New pseudodistances for the size function space, Proc. SPIE, Vol.3168, Vision Geometry. VI, Robert A. Melter, Angela Y. Wu, Longin J. Latecki (eds.), SPIE (1997), 52-60.
    • (1997) Proc. SPIE , vol.3168 , pp. 52-60
    • Landi, C.1    Frosini, P.2
  • 22
    • 0031165463 scopus 로고    scopus 로고
    • Computing size functions from edge maps
    • C. Uras and A. Verri, Computing size functions from edge maps, Internat. J. Comput. Vision 23, no.2 (1997), 169-183.
    • (1997) Internat. J. Comput. Vision , vol.23 , Issue.2 , pp. 169-183
    • Uras, C.1    Verri, A.2
  • 23
    • 0030123418 scopus 로고    scopus 로고
    • Metric-topological approach to shape representation and recognition
    • A. Verri and C. Uras, Metric-topological approach to shape representation and recognition, Image Vision Comput. 14 (1996), 189-207.
    • (1996) Image Vision Comput. , vol.14 , pp. 189-207
    • Verri, A.1    Uras, C.2
  • 24
    • 0027711145 scopus 로고
    • On the use of size functions for shape analysis
    • A. Verri, C. Uras, P. Frosini and M. Ferri, On the use of size functions for shape analysis, Biol. Cybern. 70 (1993), 99-107.
    • (1993) Biol. Cybern. , vol.70 , pp. 99-107
    • Verri, A.1    Uras, C.2    Frosini, P.3    Ferri, M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.