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Fast Algorithms for Low-Level Vision

Published: 01 January 1990 Publication History

Abstract

A recursive filtering structure is proposed that drastically reduces the computational effort required for smoothing, performing the first and second directional derivatives, and carrying out the Laplacian of an image. These operations are done with a fixed number of multiplications and additions per output point independently of the size of the neighborhood considered. The key to the approach is, first, the use of an exponentially based filter family and, second, the use of the recursive filtering. Applications to edge detection problems and multiresolution techniques are considered, and an edge detector allowing the extraction of zero-crossings of an image with only 14 operations per output element at any resolution is proposed. Various experimental results are shown.

References

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{1} M. Thurston and A. Rosenfeld. "Edge and curve detection for visual scene analysis," IEEE Trans. Comput., vol. C-20, no. 5, pp. 562- 569, May 1971.
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{2} D. Marr and E. Hildreth, "Theory of edge detection," in Proc. Roy. Soc. London, pp. 187-217, 1980.
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{3} A. Witkin, "Scale-space filtering," in Proc. Int. Joint Conf. Artificial Intelligence, Karlsruhe, West Germany, 1983, pp. 1019-1021.
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{4} J. F. Canny, "Finding edges and lines in images." Artificial Intelligence Lab., M.I.T., Cambridge, MA, Tech. Rep. 720, June 1983.
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{5} P. J. Burt, "Fast algorithms for estimating local image properties," Comput. Vision, Graphics, Image Processing, vol. 21, pp. 368-382. Mar. 1983.
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{6} A. Rosenfeld, Multiresolution Image Processing and Analysis. Berlin: Springer-Verlag, 1984.
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{7} R. M. Haralick, "Digital step edge from zero-crossing of second directional derivatives," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 1, pp. 58-68, Jan. 1984.
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{8} J. L. Crowley and A. C. Parker, "A representation for shape based on peaks and ridges in the difference of low-pass transform." IEEE Trans. Partern Anal. Machine Intell., vol. PAMI-6, no. 2, pp. 156- 170, 1984.
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{9} J. S. Chen, A. Huertas and G. Medioni, "Very fast convolution with Laplacian-of-Gaussian masks," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, no. 4, pp. 584-590, July 1987.
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{10} V. Terre and T. A. Poggio, "On edge detection," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 2, pp. 187-163, Mar. 1986
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{11} R. Deriche, "Optimal edge detection using recursive filtering." in Proc. First Int. Conf. Computer Vision, London, June 8-12, 1987.
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{12} R. Deriche, "Separable recursive filtering for efficient multi-scale edge detection," in Proc. Int. Workshop Machine Vision and Machine Intelligence , Tokyo, Japan, Feb. 2-5, 1987, pp. 18-23.
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{13} R. Deriche, "Using Canny's criteria to derive a recursively implemented optimal edge detector," Int. J. Computer Vision, vol. 1, no. 2, no. pp. 167-187, May 1987.
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{14} J. Shen and S. Castan, "An optimal linear operator for edge detection," in Proc. CVPR, Miami, FL. June 1986, pp. 109-114.

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Information

Published In

cover image IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence  Volume 12, Issue 1
January 1990
112 pages
ISSN:0162-8828
Issue’s Table of Contents

Publisher

IEEE Computer Society

United States

Publication History

Published: 01 January 1990

Author Tags

  1. Laplacian
  2. computational effort
  3. computer vision
  4. edge detection
  5. filtering and prediction theory
  6. low-level vision
  7. multiresolution techniques
  8. recursive filtering structure
  9. smoothing
  10. zero-crossings

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