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Volumn 41, Issue 1, 1993, Pages 108-

Measuring the Fractal Dimension of Signals: Morphological Covers and Iterative Optimization

Author keywords

[No Author keywords available]

Indexed keywords

1-D SIGNALS; FRACTAL DIMENSIONS OF SIGNALS; FRACTAL SIGNALS; ITERATIVE OPTIMIZATION; WEIERSTRASS FUNCTIONS;

EID: 0027307340     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/TSP.1993.193131     Document Type: Article
Times cited : (222)

References (43)
  • 1
    • 0001213151 scopus 로고
    • Fractal interpolation
    • M. F. Barnsley, “Fractal interpolation,” Constr. Approx., vol. 2, pp. 303–329, 1986.
    • (1986) Constr. Approx. , vol.2 , pp. 303-329
    • Barnsley, M.F.1
  • 3
    • 84941445456 scopus 로고
    • The Elements of Real Analysis
    • R. G. Bartle, The Elements of Real Analysis. New York: Wiley, 1976.
    • (1976) New York: Wiley
    • Bartle, R.G.1
  • 4
    • 0000955099 scopus 로고
    • On the Weierstrass-Mandelbrot fractal function
    • M. V. Berry and Z. V. Lewis, “On the Weierstrass-Mandelbrot fractal function,” Proc. Roy. Soc., Ser. A, vol. 370, pp. 459–484, 1980.
    • (1980) Proc. Roy. Soc., Ser. A , vol.370 , pp. 459-484
    • Berry, M.V.1    Lewis, Z.V.2
  • 5
    • 0000728518 scopus 로고
    • On the sum of digits of real numbers represented in the dyadic system (On sets of fractional dimension-II)
    • also “Sets of fractional dimension—IV: On rational approximation to real numbers,”
    • A. S. Besicovitch, “On the sum of digits of real numbers represented in the dyadic system (On sets of fractional dimension-II),” Math. Annalen, vol. 110, pp. 321–329, 1934; also “Sets of fractional dimension—IV: On rational approximation to real numbers,” J. London Math. Soc., vol. 9, pp. 126–131, 1934.
    • (1934) J. London Math. Soc. , vol.110 , pp. 321-329
    • Besicovitch, A.S.1
  • 6
    • 84962992649 scopus 로고
    • Sets of fractional dimension-V: On dimensional numbers of some continuous curves
    • A. S. Besicovitch and H. D. Ursell, “Sets of fractional dimension—V: On dimensional numbers of some continuous curves,” J. London Math. Soc., vol. 12, pp. 18–25, 1937.
    • (1937) J. London Math. Soc. , vol.12 , pp. 18-25
    • Besicovitch, A.S.1    Ursell, H.D.2
  • 7
    • 0000636568 scopus 로고
    • Ensembles impropres et nombre dimensionnel
    • 361–376, 1928; also in Bull. Sci. Math, vol. 11–53, pp. 185–192
    • G. Bouligand, “Ensembles impropres et nombre dimensionnel,” Bull. Sci. Math., vol. 11–52, pp. 320–344, 361–376, 1928; also in Bull. Sci. Math, vol. 11–53, pp. 185–192, 1929.
    • (1928) Bull. Sci. Math. , vol.11-52 , pp. 320-344
    • Bouligand, G.1
  • 9
    • 0005625354 scopus 로고
    • Fractal Geometry: Mathematical Foundations and Applications
    • K. Falconer, Fractal Geometry: Mathematical Foundations and Applications. New York: Wiley, 1990.
    • (1990) New York: Wiley
    • Falconer, K.1
  • 10
    • 48749145669 scopus 로고
    • The dimension of chaotic attractors
    • J. D. Farmer, E. Ott, and J. A. Yorke, “The dimension of chaotic attractors,” Physica 7D, pp. 153–180, 1983.
    • (1983) Physica 7D , pp. 153-180
    • Farmer, J.D.1    Ott, E.2    Yorke, J.A.3
  • 12
    • 0040457179 scopus 로고
    • The capacity for a class of fractal functions
    • D. P. Hardin and P. R. Massopust, “The capacity for a class of fractal functions,” Commun. Math. Phys., vol. 105, pp. 455–460, 1986.
    • (1986) Commun. Math. Phys. , vol.105 , pp. 455-460
    • Hardin, D.P.1    Massopust, P.R.2
  • 13
    • 84966204183 scopus 로고
    • Weierstrass's nondifferentiable function
    • G. H. Hardy, “Weierstrass’s nondifferentiable function,” Trans. Amer. Math. Soc., vol. 17, pp. 322–323, 1916.
    • (1916) Trans. Amer. Math. Soc. , vol.17 , pp. 322-323
    • Hardy, G.H.1
  • 14
    • 34250950477 scopus 로고
    • Dimension and ausseres Mass
    • F. Hausdorff, “Dimension and ausseres Mass,” Math. Annalen. vol. 79, pp. 157–179, 1918.
    • (1918) Math. Annalen , vol.79 , pp. 157-179
    • Hausdorff, F.1
  • 15
    • 0025573319 scopus 로고
    • The algebraic basis of mathematical morphology—Part I: Dilations and erosions
    • H. J. A. M. Heijmans and C. Ronse, “The algebraic basis of mathematical morphology—Part I: Dilations and erosions,” Comput. Vision, Graphics, Image Processing, vol. 50, pp. 245–295. 1990.
    • (1990) Comput. Vision, Graphics, Image Processing , vol.50 , pp. 245-295
    • Heijmans, H.J.A.M.1    Ronse, C.2
  • 17
    • 0001904852 scopus 로고
    • Epsilon-entropy and epsilon-capacity of sets in functional spaces
    • (translated in Trans. Amer. Math. Soc., (ser. 2) vol. 17, pp. 277–364, 1961)
    • A. N. Kolmogorov and V. M. Tihomirov, “Epsilon-entropy and epsilon-capacity of sets in functional spaces,” Usp. Matematicheskikh Nauk. (N.S.), vol. 14, pp. 3–86, 1959 (translated in Trans. Amer. Math. Soc., (ser. 2) vol. 17, pp. 277–364, 1961).
    • (1959) Usp. Matematicheskikh Nauk. (N.S.) , vol.14 , pp. 3-86
    • Kolmogorov, A.N.1    Tihomirov, V.M.2
  • 18
    • 77949515579 scopus 로고
    • Fractional Brownian motion: A maximum likelihood estimator and its application to image texture
    • Sep.
    • T. Lundahl, W. J. Ohley, S. M. Kay, and R. Siffert, “Fractional Brownian motion: A maximum likelihood estimator and its application to image texture,” IEEE Trans. Med. Imaging, vol. MI-5, pp. 152–160, Sep. 1986.
    • (1986) IEEE Trans. Med. Imaging , vol.MI-5 , pp. 152-160
    • Lundahl, T.1    Ohley, W.J.2    Kay, S.M.3    Siffert, R.4
  • 19
  • 20
    • 84931536302 scopus 로고
    • Self-affine fractals and fractal dimension
    • B. B. Mandelbrot, “Self-affine fractals and fractal dimension,” Phys. Scripta, vol. 32, pp. 257–260, 1985.
    • (1985) Phys. Scripta , vol.32 , pp. 257-260
    • Mandelbrot, B.B.1
  • 21
    • 0000501589 scopus 로고
    • Fractional Brownian motion, fractional noise, and applications
    • B. B. Mandelbrot and J. van Ness, “Fractional Brownian motion, fractional noise, and applications,” SUM Rev., vol. 10, no. 4, pp. 422–437, 1968.
    • (1968) SUM Rev. , vol.10 , Issue.4 , pp. 422-437
    • Mandelbrot, B.B.1    van Ness, J.2
  • 22
    • 84944495957 scopus 로고
    • Computer experiments with fractional Brownian motion-Parts 1-3
    • Feb.
    • B. B. Mandelbrot and J. R. Wallis, “Computer experiments with fractional Brownian motion—Parts 1-3,” Water Resources Res., vol. 5, pp. 228–267, Feb. 1969.
    • (1969) Water Resources Res. , vol.5 , pp. 228-267
    • Mandelbrot, B.B.1    Wallis, J.R.2
  • 23
    • 0026392349 scopus 로고
    • Fractals aspects of speech signals: Dimension and interpolation
    • Toronto, Canada, May
    • P. Maragos, “Fractals aspects of speech signals: Dimension and interpolation,” in Proc. IEEE ICASSP-91, Toronto, Canada, May 1991.
    • (1991) Proc. IEEE ICASSP-91
    • Maragos, P.1
  • 24
    • 0023400884 scopus 로고
    • Morphological filters-Part I: Their set-theoretic analysis and relations to linear shift-invariant filters
    • Aug.
    • P. Maragos and R. W. Schafer, “Morphological filters—Part I: Their set-theoretic analysis and relations to linear shift-invariant filters,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 1153–1169, Aug. 1987.
    • (1987) IEEE Trans. Acoust., Speech, Signal Processing , vol.ASSP-35 , pp. 1153-1169
    • Maragos, P.1    Schafer, R.W.2
  • 25
    • 0025415163 scopus 로고
    • Morphological systems for multidimensional signal processing
    • Apr.
    • P. Maragos and R. W. Schafer, “Morphological systems for multidimensional signal processing,” Proc. IEEE, vol. 78, pp. 690–710, Apr. 1990.
    • (1990) Proc. IEEE , vol.78 , pp. 690-710
    • Maragos, P.1    Schafer, R.W.2
  • 26
    • 0024919232 scopus 로고
    • Measuring fractal dimension: Morphological estimates and iterative optimization
    • P. Maragos and F. K. Sun, “Measuring fractal dimension: Morphological estimates and iterative optimization,” in Proc. SPIE Int. Soc. Opt. Eng., vol. 1199, pp. 416–430, 1989.
    • (1989) Proc. SPIE Int. Soc. Opt. Eng. , vol.1199 , pp. 416-430
    • Maragos, P.1    Sun, F.K.2
  • 27
    • 0026402527 scopus 로고
    • Hidden-variable fractal interpolation of discrete sequences
    • Toronto, Canada, May
    • D. S. Mazel and M. H. Hayes, III, “Hidden-variable fractal interpolation of discrete sequences,” in Proc. IEEE ICASSP 91, Toronto, Canada, May 1991.
    • (1991) Proc. IEEE ICASSP , pp. 91
    • Mazel, D.S.1    Hayes, M.H.2
  • 28
    • 84972500327 scopus 로고
    • The Hausdorff dimension of general Sierpinski carpets
    • C. McMullen, “The Hausdorff dimension of general Sierpinski carpets,” Nagoya Math. J., vol. 96, pp. 1–9, 1984.
    • (1984) Nagoya Math. J. , vol.96 , pp. 1-9
    • McMullen, C.1
  • 29
    • 29444445446 scopus 로고
    • Diffusion-controlled cluster formation in 2 – 6 dimensional space
    • P. Meakin, “Diffusion-controlled cluster formation in 2–6 dimensional space,” Phys. Rev. A, vol. 23, no. 3, pp. 1495–1507, 1983.
    • (1983) Phys. Rev. A , vol.23 , Issue.3 , pp. 1495-1507
    • Meakin, P.1
  • 30
    • 0007649243 scopus 로고
    • Uber die Begriffe Lange, Oberflache und Volumen
    • H. Minkowski, “Uber die Begriffe Lange, Oberflache und Volumen,” Jahresber. Deutch. Mathematikerverein., vol. 9, pp. 115–121, 1901.
    • (1901) Jahresber. Deutch. Mathematikerverein. , vol.9 , pp. 115-121
    • Minkowski, H.1
  • 31
    • 84945723489 scopus 로고
    • The problem of robust shape description
    • London, U.K.
    • D. Mumford, “The problem of robust shape description,” in Proc. 1st Int. Conf. Comput. Vision, London, U.K., 1987.
    • (1987) Proc. 1st Int. Conf. Comput. Vision
    • Mumford, D.1
  • 33
    • 0024872688 scopus 로고
    • Multiscale fractal and correlation signatures for image screening and natural clutter suppression
    • T. Peli, V. Tom, and B. Lee, “Multiscale fractal and correlation signatures for image screening and natural clutter suppression,” Proc. SPIE Int. Soc. Opt. Eng., vol. 1199, pp. 402–415, 1989.
    • (1989) Proc. SPIE Int. Soc. Opt. Eng. , vol.1199 , pp. 402-415
    • Peli, T.1    Tom, V.2    Lee, B.3
  • 34
    • 0021523150 scopus 로고
    • Fractal-based description of natural scenes
    • Nov.
    • A. P. Pentland, “Fractal-based description of natural scenes,” IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, pp. 661–674, Nov. 1984.
    • (1984) IEEE Trans. Patt. Anal. Machine Intell. , vol.PAMI-6 , pp. 661-674
    • Pentland, A.P.1
  • 35
    • 1542319659 scopus 로고
    • Image Analysis and Mathematical Morphology
    • J. Serra, Image Analysis and Mathematical Morphology. New York: Academic, 1982.
    • (1982) New York: Academic
    • Serra, J.1
  • 36
    • 0026721882 scopus 로고
    • An overview of morphological filtering
    • J. Serra and L. Vincent, “An overview of morphological filtering,” Circuits, Syst., Signal Processing, vol. 11, no. 1, pp. 47–108, 1992.
    • (1992) Circuits, Syst., Signal Processing , vol.11 , Issue.1 , pp. 47-108
    • Serra, J.1    Vincent, L.2
  • 39
    • 0001917246 scopus 로고
    • Localized measurement of image fractal dimension using Gabor filters
    • June
    • B. J. Super and A. C. Bovik, “Localized measurement of image fractal dimension using Gabor filters,” J. Visual Commun. Image Represent., vol. 2, pp. 114–128, June 1991.
    • (1991) J. Visual Commun. Image Represent. , vol.2 , pp. 114-128
    • Super, B.J.1    Bovik, A.C.2
  • 40
    • 0026398588 scopus 로고
    • Maximum likelihood estimation of the fractal dimensions of stochastic fractals and Cramer-Rao bounds
    • Toronto, Canada, May
    • A. H. Tewfik and M. Deriche, “Maximum likelihood estimation of the fractal dimensions of stochastic fractals and Cramer-Rao bounds,” in Proc. IEEE ICASSP-91, Toronto, Canada, May 1991.
    • (1991) Proc. IEEE ICASSP-91
    • Tewfik, A.H.1    Deriche, M.2
  • 42
    • 0002998107 scopus 로고
    • Fractals in nature: From characterization to simulation
    • H.-O. Peitgen and D. Saupe, Eds. New York: Springer-Verlag
    • R. F. Voss, “Fractals in nature: From characterization to simulation,” in The Science of Fractal Images, H.-O. Peitgen and D. Saupe, Eds. New York: Springer-Verlag, 1988.
    • (1988) The Science of Fractal Images
    • Voss, R.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.