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Volumn 14, Issue 2, 2008, Pages 145-179

FFTs on the rotation group

Author keywords

Discrete polynomial transform; Fast Fourier transform; Pattern matching; Rotation group; Spherical harmonics; Wigner D function

Indexed keywords


EID: 40449094055     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-008-9013-5     Document Type: Article
Times cited : (175)

References (39)
  • 5
    • 0001181359 scopus 로고
    • Computation of spherical harmonic expansion coefficients via FFTs
    • 3
    • Dilts, G.A.: Computation of spherical harmonic expansion coefficients via FFTs. J. Comput. Phys. 57(3), 439-453 (1985)
    • (1985) J. Comput. Phys. , vol.57 , pp. 439-453
    • Dilts, G.A.1
  • 6
    • 0024772342 scopus 로고
    • Computing Fourier transforms and convolutions on the 2-sphere
    • (extended abstract)
    • Driscoll, J.R., Healy, D.: Computing Fourier transforms and convolutions on the 2-sphere (extended abstract). In: Proc. 34th IEEE FOCS (1989), pp. 344-349.
    • (1989) Proc. 34th IEEE FOCS , pp. 344-349
    • Driscoll, J.R.1    Healy, D.2
  • 7
    • 0000273884 scopus 로고
    • Adv. in Appl. Math., vol. 15, pp. 202-250 (1994)
    • (1994) Adv. in Appl. Math. , vol.15 , pp. 202-250
  • 8
    • 0031209710 scopus 로고    scopus 로고
    • Fast discrete polynomial transforms with applications to data analysis for distance transitive graphs
    • 4
    • Driscoll, J.R., Healy, D., Rockmore, D.: Fast discrete polynomial transforms with applications to data analysis for distance transitive graphs. SIAM J. Comput. 26(4), 1066-1099 (1997)
    • (1997) SIAM J. Comput. , vol.26 , pp. 1066-1099
    • Driscoll, J.R.1    Healy, D.2    Rockmore, D.3
  • 11
    • 40449116504 scopus 로고    scopus 로고
    • FFTW is a free collection of fast C routines for computing the Discrete Fourier Transform in one or more dimensions. It includes complex, real, symmetric, and parallel transforms, and can handle arbitrary array sizes efficiently; FFTW is available at
    • FFTW is a free collection of fast C routines for computing the Discrete Fourier Transform in one or more dimensions. It includes complex, real, symmetric, and parallel transforms, and can handle arbitrary array sizes efficiently; FFTW is available at www.fftw.org
  • 13
    • 2942750101 scopus 로고    scopus 로고
    • Detection of three-dimensional objects under arbitrary rotations based on range images
    • 25
    • Garcia, J., Valles, J.J., Ferreira, C.: Detection of three-dimensional objects under arbitrary rotations based on range images. Optic Express 11(25), 3352 (2003)
    • (2003) Optic Express , vol.11 , pp. 3352
    • Garcia, J.1    Valles, J.J.2    Ferreira, C.3
  • 16
    • 0030543857 scopus 로고    scopus 로고
    • An empirical Bayes approach to directional data and efficient computation on the sphere
    • 1
    • Healy, D., Kim, P.: An empirical Bayes approach to directional data and efficient computation on the sphere. Ann. Stat. 24(1), 232-254 (1996)
    • (1996) Ann. Stat. , vol.24 , pp. 232-254
    • Healy, D.1    Kim, P.2
  • 18
    • 4043150726 scopus 로고    scopus 로고
    • Towards safe and effective high-order Legendre transforms with applications to FFTs for the 2-sphere
    • 1-2
    • Healy, D.M., Kostelec, P., Rockmore, D.: Towards safe and effective high-order Legendre transforms with applications to FFTs for the 2-sphere. Adv. Comput. Math. 21(1-2), 59-105 (2004)
    • (2004) Adv. Comput. Math. , vol.21 , pp. 59-105
    • Healy, D.M.1    Kostelec, P.2    Rockmore, D.3
  • 20
    • 85089921422 scopus 로고    scopus 로고
    • Rotation invariant spherical harmonic representation of 3D shape descriptors
    • Kobbelt, L., Schröder, P., Hoppe, H. (eds.)
    • Kazhdan, M., Funkhouser, T., Rusinkiewicz, S.: Rotation invariant spherical harmonic representation of 3D shape descriptors. In: Kobbelt, L., Schröder, P., Hoppe, H. (eds.) Eurographics Symposium in Geometry Processing, pp. 167-175 (2003)
    • (2003) Eurographics Symposium in Geometry Processing , pp. 167-175
    • Kazhdan, M.1    Funkhouser, T.2    Rusinkiewicz, S.3
  • 21
    • 0012431491 scopus 로고    scopus 로고
    • Computational harmonic analysis for tensor fields on the two-sphere
    • Kostelec, P.J., Maslen, D.K., Healy, D.M., Rockmore, D.N.: Computational harmonic analysis for tensor fields on the two-sphere. J. Comput. Phys. 162, 514-535 (2000)
    • (2000) J. Comput. Phys. , vol.162 , pp. 514-535
    • Kostelec, P.J.1    Maslen, D.K.2    Healy, D.M.3    Rockmore, D.N.4
  • 23
    • 1842665792 scopus 로고    scopus 로고
    • Efficient computation of Fourier transform on compact groups
    • 1
    • Maslen, D.: Efficient computation of Fourier transform on compact groups. J. Fourier Anal. Appl. 4(1), 19-52 (1998)
    • (1998) J. Fourier Anal. Appl. , vol.4 , pp. 19-52
    • Maslen, D.1
  • 25
    • 85009731502 scopus 로고    scopus 로고
    • Separation of variables and the computation of Fourier transforms on finite groups, i
    • 1
    • Maslen, D., Rockmore, D.: Separation of variables and the computation of Fourier transforms on finite groups, I. J. Am. Math. Soc. 10(1), 169-214 (1997)
    • (1997) J. Am. Math. Soc. , vol.10 , pp. 169-214
    • Maslen, D.1    Rockmore, D.2
  • 26
    • 40449089613 scopus 로고    scopus 로고
    • located in Boulder, Colorado, is a part of the US Department of Commerce (USDOC), National Oceanic & Atmospheric Administration (NOAA), National Environmental Satellite, Data and Information Service (NESDIS). They are one of three NOAA National Data Centers
    • The National Geophysical Data Center (NGDC), located in Boulder, Colorado, is a part of the US Department of Commerce (USDOC), National Oceanic & Atmospheric Administration (NOAA), National Environmental Satellite, Data and Information Service (NESDIS). They are one of three NOAA National Data Centers, www.ngdc.noaa.gov
  • 29
    • 0029730011 scopus 로고    scopus 로고
    • Fourier transform summation of Legendre series and D-functions
    • Risbo, T.: Fourier transform summation of Legendre series and D-functions. J. Geod. 70, 383-396 (1996)
    • (1996) J. Geod. , vol.70 , pp. 383-396
    • Risbo, T.1
  • 30
    • 33751218044 scopus 로고    scopus 로고
    • Fast algorithms for spherical harmonic expansions
    • 6
    • Rokhlin, V., Tygert, M.: Fast algorithms for spherical harmonic expansions. SIAM J. Comput. 27(6), 1903-1928 (2006)
    • (2006) SIAM J. Comput. , vol.27 , pp. 1903-1928
    • Rokhlin, V.1    Tygert, M.2
  • 31
    • 40449120415 scopus 로고    scopus 로고
    • The Princeton Shape Retrieval and Analysis Group
    • The Princeton Shape Retrieval and Analysis Group, www.cs.princeton.edu/ gfx/proj/shape/, whose goal is to "... investigate issues in shape-based retrieval and analysis of 3D models," has developed a 3D search engine as part of their work shape.cs.princeton.edu
  • 32
    • 40449086160 scopus 로고    scopus 로고
    • SpharmonicKit is a freely available collection of C programs for doing Legendre and scalar spherical transforms. Developed at Dartmouth College by S. Moore, D. Healy, D. Rockmore, and P. Kostelec, available at
    • SpharmonicKit is a freely available collection of C programs for doing Legendre and scalar spherical transforms. Developed at Dartmouth College by S. Moore, D. Healy, D. Rockmore, and P. Kostelec, available at www.cs.dartmouth. edu/~geelong/sphere/
  • 33
    • 40449120079 scopus 로고    scopus 로고
    • 2, The package is available at
    • 2, The package is available at www.cs.dartmouth.edu/~geelong/soft/
  • 36
    • 0034897006 scopus 로고    scopus 로고
    • Fast convolution on the sphere
    • Wandelt, B.D., Górski, K.M.: Fast convolution on the sphere. Phys. Rev. D 63, 123002 (2001)
    • (2001) Phys. Rev. D , vol.63 , pp. 123002
    • Wandelt, B.D.1    Górski, K.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.