메뉴 건너뛰기




Volumn 23, Issue , 2014, Pages 289-368

Topological pattern recognition for point cloud data

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84900486565     PISSN: 09624929     EISSN: 14740508     Source Type: Journal    
DOI: 10.1017/S0962492914000051     Document Type: Article
Times cited : (240)

References (75)
  • 1
    • 80055014497 scopus 로고    scopus 로고
    • Planck early results XXIV: Dust in the diffuse interstellar medium and the galactic halo
    • A. Abergel et al. (2011). Planck early results XXIV: Dust in the diffuse interstellar medium and the galactic halo. Astron. Astrophys. 536, A24.
    • (2011) Astron. Astrophys. , vol.536
    • Abergel, A.1
  • 2
    • 0003529366 scopus 로고
    • Wiley Series in Probability and Mathematical Statistics
    • R. Adler (1981), The Geometry of Random Fields, Wiley Series in Probability and Mathematical Statistics.
    • (1981) The Geometry of Random Fields
    • Adler, R.1
  • 6
    • 0001839785 scopus 로고
    • The statistics of peaks of Gaussian random fields
    • J. Bardeen, J. Bond, N. Kaiser and A. Szalay (1986). The statistics of peaks of Gaussian random fields. Astrophys. J. 304, 15-61.
    • (1986) Astrophys. J. , vol.304 , pp. 15-61
    • Bardeen, J.1    Bond, J.2    Kaiser, N.3    Szalay, A.4
  • 9
    • 0040211387 scopus 로고
    • Mémoire sur la théorie generale des surfaces
    • O. Bonnet (1848). Mémoire sur la théorie generale des surfaces. Journal de l' Ecole Polytechnique 19, 1-146.
    • (1848) Journal de L' Ecole Polytechnique , vol.19 , pp. 1-146
    • Bonnet, O.1
  • 10
    • 0001925593 scopus 로고
    • A note on the metric properties of trees
    • P. Buneman (1974). A note on the metric properties of trees. J. Combin. Theory B 17, 48-50.
    • (1974) J. Combin. Theory B , vol.17 , pp. 48-50
    • Buneman, P.1
  • 14
    • 67349232288 scopus 로고    scopus 로고
    • The theory of multidimensional persistence
    • G. Carlsson and A. Zomorodian (2009). The theory of multidimensional persistence. Discrete Comput. Geom. 42, 71-93.
    • (2009) Discrete Comput. Geom. , vol.42 , pp. 71-93
    • Carlsson, G.1    Zomorodian, A.2
  • 19
    • 70049101972 scopus 로고    scopus 로고
    • Gromov-Hausdorff stable signatures for shapes using persistence. Eurographics symposium on geometry processing 2009
    • F. Chazal, D. Cohen-Steiner, L. Guibas, F. Memoli and S. Oudot (2009), Gromov-Hausdorff stable signatures for shapes using persistence. In Eurographics Symposium on Geometry Processing 2009. Computer Graphics Forum 28, 1393-1403.
    • (2009) Computer Graphics Forum , vol.28 , pp. 1393-1403
    • Chazal, F.1    Cohen-Steiner, D.2    Guibas, L.3    Memoli, F.4    Oudot, S.5
  • 23
    • 8744243952 scopus 로고    scopus 로고
    • Multisymmetric functions
    • J. Dalbec (1999). Multisymmetric functions. Beiträge Algebra Geom. 40, 27-51
    • (1999) Beiträge Algebra Geom. , vol.40 , pp. 27-51
    • Dalbec, J.1
  • 25
    • 0033248623 scopus 로고    scopus 로고
    • Wedgelets: Nearly minimax estimation of edges
    • D. Donoho (1999). Wedgelets: Nearly minimax estimation of edges. Ann. Statist. 27, 859-897.
    • (1999) Ann. Statist. , vol.27 , pp. 859-897
    • Donoho, D.1
  • 26
    • 0033603539 scopus 로고    scopus 로고
    • Phylogenetic classification and the universal tree
    • W. Doolittle (1999). Phylogenetic classification and the universal tree. Science 284 (5423), 2124-2128.
    • (1999) Science , vol.284 , Issue.5423 , pp. 2124-2128
    • Doolittle, W.1
  • 27
    • 0036021407 scopus 로고    scopus 로고
    • Estimating mutation parameters, population history, and genealogy simultaneously from temporally spaced sequence data
    • A. Drummond, F. Nicholls, A. Rodrigo and W. Solomon (2002). Estimating mutation parameters, population history, and genealogy simultaneously from temporally spaced sequence data. Genetics 161, 1307-1320.
    • (2002) Genetics , vol.161 , pp. 1307-1320
    • Drummond, A.1    Nicholls, F.2    Rodrigo, A.3    Solomon, W.4
  • 29
    • 0037770508 scopus 로고
    • Singular homology theory
    • S. Eilenberg (1944). Singular homology theory. Ann. of Math. 45, 407-447.
    • (1944) Ann. of Math. , vol.45 , pp. 407-447
    • Eilenberg, S.1
  • 32
    • 0040500290 scopus 로고
    • Demonstratio nonnullarum insignium proprietatum quibus solida hedris planis inclusa sunt praedita
    • Opera Omnia (1) 26 94-108
    • L. Euler (1758). Demonstratio nonnullarum insignium proprietatum quibus solida hedris planis inclusa sunt praedita. Novi Commentarii Academiae Scientiarum Petropolitanae 4, 140-160. Opera Omnia (1) 26, 94-108.
    • (1758) Novi Commentarii Academiae Scientiarum Petropolitanae , vol.4 , pp. 140-160
    • Euler, L.1
  • 34
    • 24944522550 scopus 로고
    • L'intégrale abstraite d'une fonction abstraite d'une variable abstraite et son application à la moyenne d'un élément aléatoire de nature quelconque
    • M. Fréchet (1944). L'intégrale abstraite d'une fonction abstraite d'une variable abstraite et son application à la moyenne d'un élément aléatoire de nature quelconque' Rev. Sci. 82, 483-512.
    • (1944) Rev. Sci. , vol.82 , pp. 483-512
    • Fréchet, M.1
  • 35
    • 0000315591 scopus 로고
    • Les éléments aléatoires de nature quelconque dans un espace distancié
    • M. Fréchet (1948). Les éléments aléatoires de nature quelconque dans un espace distancié' Ann. Inst. Henri Poincaré 10, 215-310.
    • (1948) Ann. Inst Henri Poincaré , vol.10 , pp. 215-310
    • Fréchet, M.1
  • 36
    • 0003025155 scopus 로고
    • Unzerlegbare darstellungen i
    • P. Gabriel (1972). Unzerlegbare Darstellungen I. Manuscr. Math. 6, 71-103.
    • (1972) Manuscr. Math. , vol.6 , pp. 71-103
    • Gabriel, P.1
  • 37
    • 67649092284 scopus 로고    scopus 로고
    • Convergence in distribution of random metric measure spaces
    • A. Greven, P. Pfaffelhuber and A. Winter (2009). Convergence in distribution of random metric measure spaces. Probab. Theory Rel. Fields 145, 285-322.
    • (2009) Probab. Theory Rel. Fields , vol.145 , pp. 285-322
    • Greven, A.1    Pfaffelhuber, P.2    Winter, A.3
  • 38
    • 0002357581 scopus 로고
    • The sponge-like topology of largescale structure in the universe
    • J. Gott, M. Dickinson and A. Melott (1986). The sponge-like topology of largescale structure in the universe. Astrophys. J. 306, 341-357.
    • (1986) Astrophys. J. , vol.306 , pp. 341-357
    • Gott, J.1    Dickinson, M.2    Melott, A.3
  • 39
    • 0001876301 scopus 로고
    • The topology of the large-scale structure of the universe
    • A. Hamilton, J. Gott and D. Weinberg (1986). The topology of the large-scale structure of the universe. Astrophys. J. 309, 1-12.
    • (1986) Astrophys. J. , vol.309 , pp. 1-12
    • Hamilton, A.1    Gott, J.2    Weinberg, D.3
  • 40
    • 0004185151 scopus 로고
    • Wiley Series in Probability and Mathematical Statistics
    • J. Hartigan (1975), Clustering Algorithms, Wiley Series in Probability and Mathematical Statistics.
    • (1975) Clustering Algorithms
    • Hartigan, J.1
  • 42
    • 0032492432 scopus 로고    scopus 로고
    • Independent component filters of natural images compared with simple cells in primary visual cortex
    • J. Van Hateren and A. Van Der Schaaf (1998). Independent component filters of natural images compared with simple cells in primary visual cortex. Proc. R. Soc. Lond. B 265, 359-366.
    • (1998) Proc. R. Soc. Lond. , vol.B265 , pp. 359-366
    • Van Hateren, J.1    Schaaf Der A.Van2
  • 44
    • 13844312649 scopus 로고    scopus 로고
    • ZINC: A free database of commercially available compounds for virtual screening
    • J. Irwin and B. Schoichet (2005). ZINC: A free database of commercially available compounds for virtual screening. J. Chem. Inf. Model. 45, 177-182.
    • (2005) J. Chem. Inf. Model. , vol.45 , pp. 177-182
    • Irwin, J.1    Schoichet, B.2
  • 45
    • 84980162923 scopus 로고
    • Riemannian center of mass and mollifier smoothing
    • H. Karcher (1977). Riemannian center of mass and mollifier smoothing. Comm. Pure Appl. Math. 30, 509-541.
    • (1977) Comm. Pure Appl. Math. , vol.30 , pp. 509-541
    • Karcher, H.1
  • 46
    • 84960586494 scopus 로고
    • Probability, convexity, and harmonic maps with small image I: Uniqueness and fine existence
    • W. Kendall (1990). Probability, convexity, and harmonic maps with small image I: Uniqueness and fine existence. Proc. London Math. Soc. 61, 371-406.
    • (1990) Proc. London Math. Soc. , vol.61 , pp. 371-406
    • Kendall, W.1
  • 48
    • 0141853951 scopus 로고    scopus 로고
    • The non-linear statistics of high contrast patches in natural images. Internat
    • A. Lee, K. Pedersen and D. Mumford (2003). The non-linear statistics of high contrast patches in natural images. Internat. J. Computer Vision 54, 83-103.
    • (2003) J. Computer Vision , vol.54 , pp. 83-103
    • Lee, A.1    Pedersen, K.2    Mumford, D.3
  • 50
    • 0346075262 scopus 로고
    • Vandenhoeck und Ruprecht. P. Lum, G. Singh, J. Carlsson, A. Lehman, T. Ishkhanov M. Vejdemo-Johansson
    • J. Listing (1848), Vorstudien zur Topologie, Vandenhoeck und Ruprecht. P. Lum, G. Singh, J. Carlsson, A. Lehman, T. Ishkhanov, M. Vejdemo-Johansson
    • (1848) Vorstudien Zur Topologie
    • Listing, J.1
  • 51
    • 84873637974 scopus 로고    scopus 로고
    • Extracting insights from the shape of complex data using topology
    • M. Alagappan and G. Carlsson (2013), Extracting insights from the shape of complex data using topology. Nature Scientific Reports 3, #1236.
    • (2013) Nature Scientific Reports , vol.3 , pp. 1236
    • Alagappan, M.1    Carlsson, G.2
  • 54
    • 82255172087 scopus 로고    scopus 로고
    • Probability measures on the space of persistence diagrams
    • Y. Mileyko, S. Mukherjee and J. Harer (2011). Probability measures on the space of persistence diagrams. Inverse Problems 27, 1-22.
    • (2011) Inverse Problems , vol.27 , pp. 1-22
    • Mileyko, Y.1    Mukherjee, S.2    Harer, J.3
  • 55
    • 0004190360 scopus 로고
    • Princeton University Press
    • J. Milnor (1963), Morse Theory, Princeton University Press.
    • (1963) Morse Theory
    • Milnor, J.1
  • 57
    • 79955561607 scopus 로고    scopus 로고
    • Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival
    • M. Nicolau, A. Levine and G. Carlsson (2011), Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival. Proc. Nat. Acad. Sci. 108, 7265-7270.
    • (2011) Proc. Nat. Acad. Sci. , vol.108 , pp. 7265-7270
    • Nicolau, M.1    Levine, A.2    Carlsson, G.3
  • 58
    • 40349102105 scopus 로고    scopus 로고
    • Finding the homology of submanifolds with high confidence from random samples
    • P. Niyogi, S. Smale and S. Weinberger (2008). Finding the homology of submanifolds with high confidence from random samples. Discrete Comput. Geom. 39, 419-441.
    • (2008) Discrete Comput. Geom. , vol.39 , pp. 419-441
    • Niyogi, P.1    Smale, S.2    Weinberger, S.3
  • 60
    • 84894467705 scopus 로고    scopus 로고
    • A Klein bottle-based dictionary for texture representation
    • J. Perea and G. Carlsson (2014). A Klein bottle-based dictionary for texture representation. Internat. J. Computer Vision 107, 75-97.
    • (2014) Internat. J. Computer Vision , vol.107 , pp. 75-97
    • Perea, J.1    Carlsson, G.2
  • 64
    • 33244484866 scopus 로고    scopus 로고
    • Towards computing homology from finite approximations
    • V. Robins (1999). Towards computing homology from finite approximations. Topology Proceedings 24 (1), 503-532.
    • (1999) Topology Proceedings , vol.24 , Issue.1 , pp. 503-532
    • Robins, V.1
  • 65
    • 51649180460 scopus 로고
    • Classifying spaces and spectral sequences
    • G. Segal (1968). Classifying spaces and spectral sequences. Inst. Hautes Etudes Sci. Publ. Math. 34, 105-112.
    • (1968) Inst. Hautes Etudes Sci. Publ. Math. , vol.34 , pp. 105-112
    • Segal, G.1
  • 67
    • 85076471198 scopus 로고    scopus 로고
    • Topological methods for the analysis of high dimensional data sets and 3D object recognition
    • M. Botsch and R. Pajarola, eds)
    • G. Singh, F. Mémoli and G. Carlsson (2007), Topological methods for the analysis of high dimensional data sets and 3D object recognition. In Proc. Eurographics Symposium on Point-Based Graphics 2007 (M. Botsch and R. Pajarola, eds).
    • (2007) Proc. Eurographics Symposium on Point-Based Graphics 2007
    • Singh, G.1    Mémoli, F.2    Carlsson, G.3
  • 68
    • 79957900658 scopus 로고    scopus 로고
    • The persistent cosmic web and its filamentary structure I: Theory and implementation
    • T. Sousbie (2011). The persistent cosmic web and its filamentary structure I: Theory and implementation. Mon. Not. R. Astron. Soc. 414, 350-383.
    • (2011) Mon. Not. R. Astron. Soc. , vol.414 , pp. 350-383
    • Sousbie, T.1
  • 69
    • 79957916820 scopus 로고    scopus 로고
    • The persistent cosmic web and its filamentary structure II: Illustrations
    • T. Sousbie, C. Pichon and H. Kawahara (2011). The persistent cosmic web and its filamentary structure II: Illustrations. Mon. Not. R. Astron. Soc. 414, 384-403.
    • (2011) Mon. Not. R. Astron. Soc. , vol.414 , pp. 384-403
    • Sousbie, T.1    Pichon, C.2    Kawahara, H.3
  • 71
    • 84904425827 scopus 로고    scopus 로고
    • arXiv:1206.27902 A. Vandermonde (1774), Remarques sur les problèmes de situation. Mémoires de l'Académie Royale des Sciences pour 1771, Paris
    • K. Turner, Y. Mileyko, S. Mukherjee and J. Harer (2014), Fréchet means for distributions of persistence diagrams. arXiv:1206.27902 A. Vandermonde (1774), Remarques sur les problèmes de situation. In Mémoires de l'Académie Royale des Sciences pour 1771, Paris, pp. 556-574.
    • (2014) Fréchet Means for Distributions of Persistence Diagrams , pp. 556-574
    • Turner, K.1    Mileyko, Y.2    Mukherjee, S.3    Harer, J.4
  • 74
    • 77954929689 scopus 로고    scopus 로고
    • The tidy set: A minimal simplicial set for computing homology of clique complexes
    • ACM
    • A. Zomorodian (2010), The tidy set: A minimal simplicial set for computing homology of clique complexes. In Proc. 2010 Annual Symposium on Computational Geometry, ACM, pp. 257-266.
    • (2010) Proc. 2010 Annual Symposium on Computational Geometry , pp. 257-266
    • Zomorodian, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.