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Volumn 162, Issue 1, 2010, Pages 94-130

Networks of polynomial pieces with application to the analysis of point clouds and images

Author keywords

Beamlets; Detection of filaments; Extracting information from graphs; H lder smoothness classes; Multiscale analysis; Piecewise polynomials

Indexed keywords


EID: 70450265713     PISSN: 00219045     EISSN: 10960430     Source Type: Journal    
DOI: 10.1016/j.jat.2009.03.007     Document Type: Article
Times cited : (7)

References (55)
  • 3
    • 23744478860 scopus 로고    scopus 로고
    • Near-optimal detection of geometric objects by fast multiscale methods
    • Arias-Castro E., Donoho D., and Huo X. Near-optimal detection of geometric objects by fast multiscale methods. IEEE Trans. Inform. Theory 51 7 (2005) 2402-2425
    • (2005) IEEE Trans. Inform. Theory , vol.51 , Issue.7 , pp. 2402-2425
    • Arias-Castro, E.1    Donoho, D.2    Huo, X.3
  • 4
    • 33744797958 scopus 로고    scopus 로고
    • Adaptive multiscale detection of filamentary structures in a background of uniform random points
    • Arias-Castro E., Donoho D., and Huo X. Adaptive multiscale detection of filamentary structures in a background of uniform random points. Ann. Statist. 34 1 (2006) 326-349
    • (2006) Ann. Statist. , vol.34 , Issue.1 , pp. 326-349
    • Arias-Castro, E.1    Donoho, D.2    Huo, X.3
  • 5
    • 27144475603 scopus 로고    scopus 로고
    • Connect the dots: How many random points can a regular curve pass through?
    • Arias-Castro E., Donoho D., Huo X., and Tovey C. Connect the dots: How many random points can a regular curve pass through?. Adv. Appl. Probab. 37 3 (2005) 571-603
    • (2005) Adv. Appl. Probab. , vol.37 , Issue.3 , pp. 571-603
    • Arias-Castro, E.1    Donoho, D.2    Huo, X.3    Tovey, C.4
  • 6
    • 84972496740 scopus 로고
    • Poisson approximation and the Chen-Stein method
    • With comments and a rejoinder by the authors
    • Arratia R., Goldstein L., and Gordon L. Poisson approximation and the Chen-Stein method. Statist. Sci. 5 4 (1990) 403-434 With comments and a rejoinder by the authors
    • (1990) Statist. Sci. , vol.5 , Issue.4 , pp. 403-434
    • Arratia, R.1    Goldstein, L.2    Gordon, L.3
  • 7
    • 1542287742 scopus 로고    scopus 로고
    • Fast slant stack: A notion of radon transform for data in a cartesian grid which is rapidly computible, algebraically exact, geometrically faithful and invertible
    • Tech. Report, Stanford University
    • A. Averbuch, R. Coifman, D. Donoho, M. Israeli, Fast slant stack: A notion of radon transform for data in a cartesian grid which is rapidly computible, algebraically exact, geometrically faithful and invertible, Tech. Report, Stanford University, 2001
    • (2001)
    • Averbuch, A.1    Coifman, R.2    Donoho, D.3    Israeli, M.4
  • 8
    • 0032057918 scopus 로고    scopus 로고
    • New approximation guarantees for minimum-weight k-trees and prize-collecting salesmen
    • (electronic)
    • Awerbuch B., Azar Y., Blum A., and Vempala S. New approximation guarantees for minimum-weight k-trees and prize-collecting salesmen. SIAM J. Comput. 28 1 (1999) 254-262 (electronic)
    • (1999) SIAM J. Comput. , vol.28 , Issue.1 , pp. 254-262
    • Awerbuch, B.1    Azar, Y.2    Blum, A.3    Vempala, S.4
  • 10
    • 0036045780 scopus 로고    scopus 로고
    • Ridgelets and the representation of mutilated Sobolev functions
    • (electronic)
    • Candes E.J. Ridgelets and the representation of mutilated Sobolev functions. SIAM J. Math. Anal. 33 2 (2001) 347-368 (electronic)
    • (2001) SIAM J. Math. Anal. , vol.33 , Issue.2 , pp. 347-368
    • Candes, E.J.1
  • 11
    • 33646737844 scopus 로고    scopus 로고
    • Multiscale chirplets and near-optimal recovery of chirps
    • Technical Report, Stanford University
    • E.J. Candès, Multiscale chirplets and near-optimal recovery of chirps, Technical Report, Stanford University, 2002
    • (2002)
    • Candès, E.J.1
  • 12
    • 36248976109 scopus 로고    scopus 로고
    • Detecting highly oscillatory signals by chirplet path pursuit
    • Candès E.J., Charlton P.R., and Helgason H. Detecting highly oscillatory signals by chirplet path pursuit. Appl. Comput. Harmon. Anal. 24 1 (2008) 14-40
    • (2008) Appl. Comput. Harmon. Anal. , vol.24 , Issue.1 , pp. 14-40
    • Candès, E.J.1    Charlton, P.R.2    Helgason, H.3
  • 14
    • 70450272558 scopus 로고    scopus 로고
    • Software used in this paper
    • Software used in this paper. http://www.cbl.uh.edu/~efros/research.html
  • 15
    • 8744251037 scopus 로고    scopus 로고
    • B. DasGupta, J. Hespanha, E. Sontag, Computational complexities of honey-pot searching with local sensory information, in: 2004 American Control Conference, ACC 2004, 2004, pp. 2134-2138
    • B. DasGupta, J. Hespanha, E. Sontag, Computational complexities of honey-pot searching with local sensory information, in: 2004 American Control Conference, ACC 2004, 2004, pp. 2134-2138
  • 17
    • 1442332687 scopus 로고    scopus 로고
    • Maximal meaningful events and applications to image analysis
    • Desolneux A., Moisan L., and Morel J.-M. Maximal meaningful events and applications to image analysis. Ann. Statist. 31 6 (2003) 1822-1851
    • (2003) Ann. Statist. , vol.31 , Issue.6 , pp. 1822-1851
    • Desolneux, A.1    Moisan, L.2    Morel, J.-M.3
  • 18
    • 0033248623 scopus 로고    scopus 로고
    • Wedgelets: Nearly minimax estimation of edges
    • Donoho D.L. Wedgelets: Nearly minimax estimation of edges. Ann. Statist. 27 3 (1999) 859-897
    • (1999) Ann. Statist. , vol.27 , Issue.3 , pp. 859-897
    • Donoho, D.L.1
  • 19
    • 0027873602 scopus 로고
    • Unconditional bases are optimal bases for data compression and for statistical estimation
    • Donoho D.L. Unconditional bases are optimal bases for data compression and for statistical estimation. Appl. Comput. Harmon. Anal. 1 1 (1993) 100-115
    • (1993) Appl. Comput. Harmon. Anal. , vol.1 , Issue.1 , pp. 100-115
    • Donoho, D.L.1
  • 20
    • 2642578256 scopus 로고    scopus 로고
    • Beamlets and multiscale image analysis
    • Multiscale and Multiresolution Methods, Springer, Berlin
    • Donoho D.L., and Huo X. Beamlets and multiscale image analysis. Multiscale and Multiresolution Methods. Lect. Notes Comput. Sci. Eng. vol. 20 (2002), Springer, Berlin 149-196
    • (2002) Lect. Notes Comput. Sci. Eng. , vol.20 , pp. 149-196
    • Donoho, D.L.1    Huo, X.2
  • 21
    • 0032334093 scopus 로고    scopus 로고
    • Minimax estimation via wavelet shrinkage
    • Donoho D.L., and Johnstone I.M. Minimax estimation via wavelet shrinkage. Ann. Statist. 26 3 (1998) 879-921
    • (1998) Ann. Statist. , vol.26 , Issue.3 , pp. 879-921
    • Donoho, D.L.1    Johnstone, I.M.2
  • 22
    • 33744801044 scopus 로고    scopus 로고
    • Fast X-ray and beamlet transforms for three-dimensional data
    • Modern Signal Processing, Cambridge Univ. Press, Cambridge
    • Donoho D.L., and Levi O. Fast X-ray and beamlet transforms for three-dimensional data. Modern Signal Processing. Math. Sci. Res. Inst. Publ. vol. 46 (2004), Cambridge Univ. Press, Cambridge 79-116
    • (2004) Math. Sci. Res. Inst. Publ. , vol.46 , pp. 79-116
    • Donoho, D.L.1    Levi, O.2
  • 25
    • 70450263260 scopus 로고    scopus 로고
    • Scan statistics and applications
    • Glaz J., and Balakrishnan N. (Eds), Birkhäuser Boston Inc., Boston, MA
    • Scan statistics and applications. In: Glaz J., and Balakrishnan N. (Eds). Statistics for Industry and Technology (1999), Birkhäuser Boston Inc., Boston, MA
    • (1999) Statistics for Industry and Technology
  • 27
    • 27844537874 scopus 로고    scopus 로고
    • Jbeam: Multiscale curve coding via beamlets
    • Huo X., and Chen J. Jbeam: Multiscale curve coding via beamlets. IEEE Trans. Image Process. 14 11 (2005) 1665-1677
    • (2005) IEEE Trans. Image Process. , vol.14 , Issue.11 , pp. 1665-1677
    • Huo, X.1    Chen, J.2
  • 28
    • 70450255000 scopus 로고    scopus 로고
    • Dynamic programming methods for 'connecting-the-dots' in scattered point sets
    • in preparation
    • X. Huo, D. Donoho, C. Tovey, E. Arias-Castro, Dynamic programming methods for 'connecting-the-dots' in scattered point sets, (in preparation)
    • Huo, X.1    Donoho, D.2    Tovey, C.3    Arias-Castro, E.4
  • 29
  • 31
    • 0001867234 scopus 로고    scopus 로고
    • On approximating the longest path in a graph
    • Karger D., Motwani R., and Ramkumar G.D.S. On approximating the longest path in a graph. Algorithmica 18 1 (1997) 82-98
    • (1997) Algorithmica , vol.18 , Issue.1 , pp. 82-98
    • Karger, D.1    Motwani, R.2    Ramkumar, G.D.S.3
  • 32
    • 33745811987 scopus 로고    scopus 로고
    • A discrete global minimization algorithm for continuous variational problems
    • Technical Report, Harvard University, Computer Science
    • D. Kirsanov, S. Gortler, A discrete global minimization algorithm for continuous variational problems, Technical Report, Harvard University, Computer Science, 2004
    • (2004)
    • Kirsanov, D.1    Gortler, S.2
  • 33
    • 0003461589 scopus 로고
    • Information theory and the theory of algorithms
    • Selected Works of A. N. Kolmogorov. Vol. III. (A.B. Sossinsky transl.). Shiryayev A.N. (Ed), Kluwer Academic Publishers Group, Dordrecht (Original work published 1987, in Russian)
    • Kolmogorov A.N. Information theory and the theory of algorithms. (A.B. Sossinsky transl.). In: Shiryayev A.N. (Ed). Selected Works of A. N. Kolmogorov. Vol. III. Mathematics and its Applications (Soviet Series) vol. 27 (1993), Kluwer Academic Publishers Group, Dordrecht (Original work published 1987, in Russian)
    • (1993) Mathematics and its Applications (Soviet Series) , vol.27
    • Kolmogorov, A.N.1
  • 34
    • 33745969182 scopus 로고    scopus 로고
    • What metrics can be approximated by geo-cuts, or global optimization of length/area and flux
    • Kolmogorov V., and Boykov Y. What metrics can be approximated by geo-cuts, or global optimization of length/area and flux. iccv 1 (2005) 564-571
    • (2005) iccv , vol.1 , pp. 564-571
    • Kolmogorov, V.1    Boykov, Y.2
  • 38
    • 17544369568 scopus 로고    scopus 로고
    • Sparse geometric image representations with bandelets
    • Le Pennec E., and Mallat S. Sparse geometric image representations with bandelets. IEEE Trans. Image Process. 14 4 (2005) 423-438
    • (2005) IEEE Trans. Image Process. , vol.14 , Issue.4 , pp. 423-438
    • Le Pennec, E.1    Mallat, S.2
  • 39
    • 70450270561 scopus 로고    scopus 로고
    • A new fast algorithm for exact calculation of the discrete 2-d and 3-d x-ray transform
    • ICCMSE
    • Levi O., and Efros B.A. A new fast algorithm for exact calculation of the discrete 2-d and 3-d x-ray transform. ICCMSE. Lecture Series on Computer and Computational Sciences vol. 4 (2005) 319-322
    • (2005) Lecture Series on Computer and Computational Sciences , vol.4 , pp. 319-322
    • Levi, O.1    Efros, B.A.2
  • 45
    • 0004198869 scopus 로고
    • (D.H. Salinger transl.), Cambridge University Press, Cambridge (Original work published 1990, in French)
    • Meyer Y. (D.H. Salinger transl.). Wavelets and Operators. Cambridge Studies in Advanced Mathematics vol. 37 (1992), Cambridge University Press, Cambridge (Original work published 1990, in French)
    • (1992) Cambridge Studies in Advanced Mathematics , vol.37
    • Meyer, Y.1
  • 46
    • 0038718854 scopus 로고    scopus 로고
    • The structure and function of complex networks
    • Newman M.E.J. The structure and function of complex networks. SIAM Rev. 45 (2003) 167-256
    • (2003) SIAM Rev. , vol.45 , pp. 167-256
    • Newman, M.E.J.1
  • 47
    • 3042699485 scopus 로고    scopus 로고
    • Multiscale advanced raster map analysis system: Definition, design and development
    • Patil G.P., Balbus J., Biging G., Jaja J., Myers W.L., and Taillie C. Multiscale advanced raster map analysis system: Definition, design and development. Environ. Ecol. Stat. 11 2 (2004) 113-138
    • (2004) Environ. Ecol. Stat. , vol.11 , Issue.2 , pp. 113-138
    • Patil, G.P.1    Balbus, J.2    Biging, G.3    Jaja, J.4    Myers, W.L.5    Taillie, C.6
  • 48
    • 3042824653 scopus 로고    scopus 로고
    • Upper level set scan statistic for detecting arbitrarily shaped hotspots
    • Patil G.P., and Taillie C. Upper level set scan statistic for detecting arbitrarily shaped hotspots. Environ. Ecol. Stat. 11 2 (2004) 183-197
    • (2004) Environ. Ecol. Stat. , vol.11 , Issue.2 , pp. 183-197
    • Patil, G.P.1    Taillie, C.2
  • 49
    • 0030415741 scopus 로고    scopus 로고
    • V. Prinet, O. Monga, S. Ma, Extraction of vascular network in 3d images, in: Proceedings: The IEEE International Conference on Image Processing, September 1996, pp. 307-310
    • V. Prinet, O. Monga, S. Ma, Extraction of vascular network in 3d images, in: Proceedings: The IEEE International Conference on Image Processing, September 1996, pp. 307-310
  • 50
    • 70450228379 scopus 로고    scopus 로고
    • Sloan Digital Sky Survey. http://www.sdss.org
  • 51
    • 0024168435 scopus 로고    scopus 로고
    • A. Sha'asua, S. Ullman, Structural saliency: The detection of globally salient structures using a locally connected network, in: Computer Vision., Second International Conference on, December 1988, pp. 321-327
    • A. Sha'asua, S. Ullman, Structural saliency: The detection of globally salient structures using a locally connected network, in: Computer Vision., Second International Conference on, December 1988, pp. 321-327
  • 53
    • 70450272557 scopus 로고
    • Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • Wahba G. Spline Models for Observational data. CBMS-NSF Regional Conference Series in Applied Mathematics vol. 59 (1990), Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • (1990) CBMS-NSF Regional Conference Series in Applied Mathematics , vol.59
    • Wahba, G.1
  • 55
    • 0038321621 scopus 로고    scopus 로고
    • Platelets: A multiscale approach for recovering edges and surfaces in photon-limited medical imaging
    • Willett R., and Nowak R. Platelets: A multiscale approach for recovering edges and surfaces in photon-limited medical imaging. IEEE Trans. Medical Imaging 22 3 (2003) 332-350
    • (2003) IEEE Trans. Medical Imaging , vol.22 , Issue.3 , pp. 332-350
    • Willett, R.1    Nowak, R.2


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