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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 7, Iss. 6 — Jun. 1, 1990
  • pp: 1101–1112

Multiscale fractal theory and object characterization

T. Peli  »View Author Affiliations

JOSA A, Vol. 7, Issue 6, pp. 1101-1112 (1990)

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A new approach for characterizing man-made and natural objects from two-dimensional data has been developed. The approach is based on the use of a fractal signature, which is a measure of local fractal dimension as a function of scale and space. Estimates of the fractal signature are obtained by using computationally efficient morphological filters. Consistency of the fractal signature and the effects of edges and anomalies are examined by using real and synthetic data. Preliminary results using optical and infrared data demonstrate the potential of using fractal signatures for object characterization and discrimination.

© 1990 Optical Society of America

Original Manuscript: October 17, 1989
Manuscript Accepted: February 9, 1990
Published: June 1, 1990

T. Peli, "Multiscale fractal theory and object characterization," J. Opt. Soc. Am. A 7, 1101-1112 (1990)

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  1. B. L. Bullock, “Finding structure in outdoors scenes,” in Pattern Recognition and Artificial Intelligence, C. H. Chen, ed. (North-Holland, Amsterdam, 1976), pp. 61–85.
  2. R. Nevatia, K. E. Price, “Locating structure in aerial images,” in Digital Image Analysis, Vol. 2 of Digital Image Processing and Analysis, R. Chllapa, A. A. Sawchuck, eds. (Institute of Electrical and Electronics Engineers, New York, 1985), pp. 247–255.
  3. A. D. Gross, A. Rosenfeld, “Multiresolution object detection and delineation,” Comput. Vision Graphics Image Process. 39, 102–115 (1987). [CrossRef]
  4. T. F. Quatieri, “Object detection by two dimensional linear prediction,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 108–111.
  5. A. P. Pentland, “Fractal based description of natural scenes,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 661–674 (1984). [CrossRef]
  6. T. Lundahl, W. Ohley, S. K. Kay, R. Siffert, “Fractional Brownian motion: a maximum likelihood estimator and its application to image texture,” IEEE Trans. Med. Imaging MI-5, 152–161 (1986). [CrossRef]
  7. M. J. Carlotto, M. C. Stein, “Detecting man-made change in imagery,” in Intelligent Robots and Computer Vision: Seventh in a Series, D. P. Casasent, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1002, 6–11 (1985).
  8. S. Peleg, J. Naor, R. Hartely, D. Avnir, “Multiple resolution texture analysis and classification,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 518–523 (1984). [CrossRef]
  9. B. B. Mandelbort, The Fractal Geometry of Nature (Freeman, New York, 1983).
  10. F. Hausdorff, “Dimension and Ausseres Mass,” Math. Annalen 79, 157 (1919). [CrossRef]
  11. P. Kube, A. P. Pentland, “On imaging of fractal surfaces,” IEEE Trans. Pattern Anal. Mach. Intell. 10, 704–707 (1988). [CrossRef]
  12. A. N. Kolmogorov, “A new invariant for transitive dynamical systems,” Dokl. Akad. Nauk SSSR 119, 861–864 (1958).
  13. B. B. Mandelbrot, B. J. Van Ness, “Fractional Brownian motion, fractional noises and applications,” SIAM Rev. 10, 442–438 (1968). [CrossRef]
  14. J. Serra, Image Analysis and Mathematical Morphology (Academic, London, 1982).
  15. F. Arduini, C. Dambra, S. Dellepiane, S. B. Serpico, G. Vernazza, R. Viviani, ”Fractal dimension by adaptive mask selection,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 1116–1119 (1988).
  16. M. Nagao, T. Matsuyama, A Structural Analysis of Complex Aerial Photographs (Plenum, New York, 1980). [CrossRef]

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