Abstract

Several thresholding algorithms are applied to the analysis of drop images, and their performance is compared. Images were obtained by use of a digital camera setup in which drops were illuminated from behind, resulting in an image of the drop silhouette. Each algorithm was evaluated based on the accuracy of the drop diameter obtained from the thresholded image and on the size of the depth of field. Because of the difficulty associated with creating drops that have a known diameter, solid spheres composed of a glass with an index of refraction close to that of water were used in computing the depth of field and in determining the accuracy of measured diameter. The application of this study is to the automatic measurement of raindrops and images were obtained during several storms. With each thresholding algorithm this raindrop imagery was used to compute the probability density function of drop diameter, and the rain rate. The performance of each thresholding algorithm was quantified by comparison of these measurements with simultaneous measurements obtained by use of a Joss–Waldvogel disdrometer.

© 2006 Optical Society of America

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    [CrossRef]
  3. A. Tokay, A. Kruger, and W. F. Krajewski, " Comparison of drop size distribution measurements by impact and optical disdrometers," J. Appl. Meteorol. 40, 2083- 2097 ( 2001).
    [CrossRef]
  4. K. V. Beard and C. Chuang, " A new model for the equilibrium shape of raindrops," J. Atmos. Sci. 44, 1509- 1524 ( 1987).
    [CrossRef]
  5. C. Chuang and K. V. Beard, " A numerical model for the equilibrium shape of electrified raindrops," J. Atmos. Sci. 47, 1374- 1389 ( 1990).
    [CrossRef]
  6. M. Schönhuber, H. E. Urban, J. P. V. Poiares-Baptista, W. L. Randeu, and W. Riedler, " Measurements of precipitation characteristics by a new distrometer," in Proceedings of Atmospheric Physics and Dynamics in the Analysis and Prognosis of Precipitation Fields (SIMA, 1994).
    [PubMed]
  7. J. R. Saylor, B. K. Jones, and L. F. Bliven, " A method for increasing depth of field during droplet imaging," Rev. Sci. Instrum. 73, 2422- 2427 ( 2002).
    [CrossRef]
  8. M. Schönhuber, H. E. Urban, J. P. V. Poiares-Baptista, W. L. Randeu, and W. Riedler, " Weather radar versus 2D-video-distrometer data," in Proceedings of the Third International Symposium on Hydrological Applications of Weather Radars (Wiley, 1995).
  9. L. F. Bliven, (NASA, Wallops Island, Va. 23337 (personal communication, 2001).
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    [CrossRef] [PubMed]
  11. R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw-Hill, 1995).
  12. C. K. Leung and F. K. Lam, " Performance analysis for a class of iterative image thresholding algorithms," Pattern Recogn. 29, 1523- 1530 ( 1996).
    [CrossRef]
  13. N. J. Kapur, P. K. Sahoo, and A. K. Wong, " A new method for gray-level picture thresholding using the entropy of the histogram," Computer Vis. Graph. Image Process. 29, 273- 285 ( 1985).
    [CrossRef]
  14. P. Yin, " Maximum entropy-based optimal threshold selection using deterministic reinforcement learning with controlled randomization," Signal Process. 993- 1006 ( 2002).
    [CrossRef]
  15. N. Ostu, " A threshold selection method from gray-level histograms," IEEE Trans. Syst. Man. Cybern. 9, 62- 66 ( 1979).
    [CrossRef]
  16. W. Tsai, " Moment-preserving thresholding: a new approach," Computer Vis. Graph. Image Process. 29, 377- 393 ( 1985).
    [CrossRef]
  17. P. Liao, T. Chen, and P. Chung, " A fast algorithm for multilevel thresholding," J. Information Sci. and Eng. 17, 713- 727 ( 2001).
  18. L. K. Huang and M. J. J. Wang, " Image thresholding by minimizing the measure of fuzziness," Pattern Recognition 28, 41- 51 ( 1995).
    [CrossRef]
  19. O. J. Tobias and R. Seara, " Image segmentation by histogram thresholding using fuzzy sets," IEEE Trans. Image Process. 11, 1457- 1465 ( 2002).
    [CrossRef]
  20. C. Ho and L. Chen, " A fast ellipse/circle detector using geometric symmetry," Pattern Recogn. 28, 117- 124 ( 1995).
    [CrossRef]
  21. Y. Lei and K. C. Wong, " Ellipse detection based on symmetry," Pattern Recogn. Lett. 20, 41- 47 ( 1999).
    [CrossRef]
  22. E. R. Davies, Machine Vision: Theory, Algorithms, Practicalities (Academic, 1990).
  23. H. K. Yuen, J. Illingworth, and J. Kittler, " Detecting partially occluded ellipses using the Hough transform," Image Vision Comput. 7, 31- 37 ( 1989).
    [CrossRef]
  24. K. V. Beard, H. T. Ochs, and R. J. Kubesh, " Natural oscillations of small raindrops," Nature 342, 408- 410 ( 1989).
    [CrossRef]
  25. K. V. Beard and R. J. Kubesh, " Laboratory measurements of small raindrop distortion. 2. Oscillation frequencies and modes," J. Atmos. Sci. 48, 2245- 2264 ( 1991).
    [CrossRef]
  26. K. Andsager, K. V. Beard, and N. F. Laird, " Laboratory measurements of axis ratios for large raindrops," J. Atmos. Sci. 56, 2673- 2683 ( 1999).
    [CrossRef]
  27. J. Serra, Image Analysis and Mathematical Morphology (Academic, 1982).
  28. F. Xia, " Normal vector and winding number in 2D digital images with their application for hole detection," Pattern Recogn. 36, 1383- 1395 ( 2003).
    [CrossRef]
  29. R. C. Weast, ed. Handbook of Chemistry and Physics, 52nd ed. (Chemical Rubber Company, 1971), Sec. B.
  30. L. Samek and J. Wasylak, " Low-dispersion fluorozirconate glass with spectral dispersion of refractive index similar to that of water," Opt. Eng. 36, 1657- 1659 ( 1997).
    [CrossRef]
  31. J. Lucas, F. Smektala, and J. L. Adam, " Fluorine in optics," J. Fluorine Chem. 114, 113- 118 ( 2002).
    [CrossRef]
  32. J. -P. Thiran, V. Warscotte, and B. Macq, " A queue-based region growing algorithm for accurate segmentation of multi-dimensional digital images," Signal Process. 60, pp. 1- 10 ( 1997).
    [CrossRef]
  33. R. M. Haralick, S. R. Sternberg, and X. Zhuang, " Image analysis using mathematical morphology," IEEE Trans. Pattern Anal. Mach. Intell. 9, 532- 550 ( 1987).
    [CrossRef] [PubMed]
  34. D. Yu and H. Yan, " An efficient algorithm for smoothing, linearization and detection of structural feature points of binary image contours," Pattern Recogn. 30, 57- 69 ( 1997).
    [CrossRef]
  35. D. Atlas, R. C. Srivastava, and R. S. Sekhon, " Doppler radar characteristics of precipitation at vertical incidence," Rev. Geophys. Space Phys. 2, 1- 35 ( 1973).
    [CrossRef]
  36. C. W. Ulbrich, " Natural variations in the analytical form of the raindrop size distribution," J. Climate Appl. Meteorol. 22, 1764- 1775 ( 1983).
    [CrossRef]

2003

J. R. Saylor, B. K. Jones, and L. F. Bliven, " Single-camera method to determine the optical axis position of ellipsoidal drops," Appl. Opt. 42, 972- 978 ( 2003).
[CrossRef] [PubMed]

F. Xia, " Normal vector and winding number in 2D digital images with their application for hole detection," Pattern Recogn. 36, 1383- 1395 ( 2003).
[CrossRef]

2002

J. Lucas, F. Smektala, and J. L. Adam, " Fluorine in optics," J. Fluorine Chem. 114, 113- 118 ( 2002).
[CrossRef]

P. Yin, " Maximum entropy-based optimal threshold selection using deterministic reinforcement learning with controlled randomization," Signal Process. 993- 1006 ( 2002).
[CrossRef]

J. R. Saylor, B. K. Jones, and L. F. Bliven, " A method for increasing depth of field during droplet imaging," Rev. Sci. Instrum. 73, 2422- 2427 ( 2002).
[CrossRef]

O. J. Tobias and R. Seara, " Image segmentation by histogram thresholding using fuzzy sets," IEEE Trans. Image Process. 11, 1457- 1465 ( 2002).
[CrossRef]

2001

P. Liao, T. Chen, and P. Chung, " A fast algorithm for multilevel thresholding," J. Information Sci. and Eng. 17, 713- 727 ( 2001).

A. Tokay, A. Kruger, and W. F. Krajewski, " Comparison of drop size distribution measurements by impact and optical disdrometers," J. Appl. Meteorol. 40, 2083- 2097 ( 2001).
[CrossRef]

1999

Y. Lei and K. C. Wong, " Ellipse detection based on symmetry," Pattern Recogn. Lett. 20, 41- 47 ( 1999).
[CrossRef]

K. Andsager, K. V. Beard, and N. F. Laird, " Laboratory measurements of axis ratios for large raindrops," J. Atmos. Sci. 56, 2673- 2683 ( 1999).
[CrossRef]

1997

L. Samek and J. Wasylak, " Low-dispersion fluorozirconate glass with spectral dispersion of refractive index similar to that of water," Opt. Eng. 36, 1657- 1659 ( 1997).
[CrossRef]

J. -P. Thiran, V. Warscotte, and B. Macq, " A queue-based region growing algorithm for accurate segmentation of multi-dimensional digital images," Signal Process. 60, pp. 1- 10 ( 1997).
[CrossRef]

D. Yu and H. Yan, " An efficient algorithm for smoothing, linearization and detection of structural feature points of binary image contours," Pattern Recogn. 30, 57- 69 ( 1997).
[CrossRef]

1996

C. K. Leung and F. K. Lam, " Performance analysis for a class of iterative image thresholding algorithms," Pattern Recogn. 29, 1523- 1530 ( 1996).
[CrossRef]

1995

C. Ho and L. Chen, " A fast ellipse/circle detector using geometric symmetry," Pattern Recogn. 28, 117- 124 ( 1995).
[CrossRef]

L. K. Huang and M. J. J. Wang, " Image thresholding by minimizing the measure of fuzziness," Pattern Recognition 28, 41- 51 ( 1995).
[CrossRef]

1991

K. V. Beard and R. J. Kubesh, " Laboratory measurements of small raindrop distortion. 2. Oscillation frequencies and modes," J. Atmos. Sci. 48, 2245- 2264 ( 1991).
[CrossRef]

1990

C. Chuang and K. V. Beard, " A numerical model for the equilibrium shape of electrified raindrops," J. Atmos. Sci. 47, 1374- 1389 ( 1990).
[CrossRef]

1989

H. K. Yuen, J. Illingworth, and J. Kittler, " Detecting partially occluded ellipses using the Hough transform," Image Vision Comput. 7, 31- 37 ( 1989).
[CrossRef]

K. V. Beard, H. T. Ochs, and R. J. Kubesh, " Natural oscillations of small raindrops," Nature 342, 408- 410 ( 1989).
[CrossRef]

1987

K. V. Beard and C. Chuang, " A new model for the equilibrium shape of raindrops," J. Atmos. Sci. 44, 1509- 1524 ( 1987).
[CrossRef]

R. M. Haralick, S. R. Sternberg, and X. Zhuang, " Image analysis using mathematical morphology," IEEE Trans. Pattern Anal. Mach. Intell. 9, 532- 550 ( 1987).
[CrossRef] [PubMed]

1985

N. J. Kapur, P. K. Sahoo, and A. K. Wong, " A new method for gray-level picture thresholding using the entropy of the histogram," Computer Vis. Graph. Image Process. 29, 273- 285 ( 1985).
[CrossRef]

W. Tsai, " Moment-preserving thresholding: a new approach," Computer Vis. Graph. Image Process. 29, 377- 393 ( 1985).
[CrossRef]

1983

C. W. Ulbrich, " Natural variations in the analytical form of the raindrop size distribution," J. Climate Appl. Meteorol. 22, 1764- 1775 ( 1983).
[CrossRef]

1979

N. Ostu, " A threshold selection method from gray-level histograms," IEEE Trans. Syst. Man. Cybern. 9, 62- 66 ( 1979).
[CrossRef]

1973

D. Atlas, R. C. Srivastava, and R. S. Sekhon, " Doppler radar characteristics of precipitation at vertical incidence," Rev. Geophys. Space Phys. 2, 1- 35 ( 1973).
[CrossRef]

1967

J. Joss and A. Waldvogel, " A raindrop spectrograph with automatic analysis," Pure Appl. Geophys. 68, 240- 246 ( 1967).
[CrossRef]

Adam, J. L.

J. Lucas, F. Smektala, and J. L. Adam, " Fluorine in optics," J. Fluorine Chem. 114, 113- 118 ( 2002).
[CrossRef]

Andsager, K.

K. Andsager, K. V. Beard, and N. F. Laird, " Laboratory measurements of axis ratios for large raindrops," J. Atmos. Sci. 56, 2673- 2683 ( 1999).
[CrossRef]

Atlas, D.

D. Atlas, R. C. Srivastava, and R. S. Sekhon, " Doppler radar characteristics of precipitation at vertical incidence," Rev. Geophys. Space Phys. 2, 1- 35 ( 1973).
[CrossRef]

Beard, K. V.

K. Andsager, K. V. Beard, and N. F. Laird, " Laboratory measurements of axis ratios for large raindrops," J. Atmos. Sci. 56, 2673- 2683 ( 1999).
[CrossRef]

K. V. Beard and R. J. Kubesh, " Laboratory measurements of small raindrop distortion. 2. Oscillation frequencies and modes," J. Atmos. Sci. 48, 2245- 2264 ( 1991).
[CrossRef]

C. Chuang and K. V. Beard, " A numerical model for the equilibrium shape of electrified raindrops," J. Atmos. Sci. 47, 1374- 1389 ( 1990).
[CrossRef]

K. V. Beard, H. T. Ochs, and R. J. Kubesh, " Natural oscillations of small raindrops," Nature 342, 408- 410 ( 1989).
[CrossRef]

K. V. Beard and C. Chuang, " A new model for the equilibrium shape of raindrops," J. Atmos. Sci. 44, 1509- 1524 ( 1987).
[CrossRef]

Bliven, L. F.

J. R. Saylor, B. K. Jones, and L. F. Bliven, " Single-camera method to determine the optical axis position of ellipsoidal drops," Appl. Opt. 42, 972- 978 ( 2003).
[CrossRef] [PubMed]

J. R. Saylor, B. K. Jones, and L. F. Bliven, " A method for increasing depth of field during droplet imaging," Rev. Sci. Instrum. 73, 2422- 2427 ( 2002).
[CrossRef]

L. F. Bliven, (NASA, Wallops Island, Va. 23337 (personal communication, 2001).

Chen, L.

C. Ho and L. Chen, " A fast ellipse/circle detector using geometric symmetry," Pattern Recogn. 28, 117- 124 ( 1995).
[CrossRef]

Chen, T.

P. Liao, T. Chen, and P. Chung, " A fast algorithm for multilevel thresholding," J. Information Sci. and Eng. 17, 713- 727 ( 2001).

Chuang, C.

C. Chuang and K. V. Beard, " A numerical model for the equilibrium shape of electrified raindrops," J. Atmos. Sci. 47, 1374- 1389 ( 1990).
[CrossRef]

K. V. Beard and C. Chuang, " A new model for the equilibrium shape of raindrops," J. Atmos. Sci. 44, 1509- 1524 ( 1987).
[CrossRef]

Chung, P.

P. Liao, T. Chen, and P. Chung, " A fast algorithm for multilevel thresholding," J. Information Sci. and Eng. 17, 713- 727 ( 2001).

Davies, E. R.

E. R. Davies, Machine Vision: Theory, Algorithms, Practicalities (Academic, 1990).

Doviak, R. J.

R. J. Doviak and D. S. Zrnic, Doppler Radar and Weather Observations (Academic, 1984).

Haralick, R. M.

R. M. Haralick, S. R. Sternberg, and X. Zhuang, " Image analysis using mathematical morphology," IEEE Trans. Pattern Anal. Mach. Intell. 9, 532- 550 ( 1987).
[CrossRef] [PubMed]

Ho, C.

C. Ho and L. Chen, " A fast ellipse/circle detector using geometric symmetry," Pattern Recogn. 28, 117- 124 ( 1995).
[CrossRef]

Huang, L. K.

L. K. Huang and M. J. J. Wang, " Image thresholding by minimizing the measure of fuzziness," Pattern Recognition 28, 41- 51 ( 1995).
[CrossRef]

Illingworth, J.

H. K. Yuen, J. Illingworth, and J. Kittler, " Detecting partially occluded ellipses using the Hough transform," Image Vision Comput. 7, 31- 37 ( 1989).
[CrossRef]

Jain, R.

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw-Hill, 1995).

Jones, B. K.

J. R. Saylor, B. K. Jones, and L. F. Bliven, " Single-camera method to determine the optical axis position of ellipsoidal drops," Appl. Opt. 42, 972- 978 ( 2003).
[CrossRef] [PubMed]

J. R. Saylor, B. K. Jones, and L. F. Bliven, " A method for increasing depth of field during droplet imaging," Rev. Sci. Instrum. 73, 2422- 2427 ( 2002).
[CrossRef]

Joss, J.

J. Joss and A. Waldvogel, " A raindrop spectrograph with automatic analysis," Pure Appl. Geophys. 68, 240- 246 ( 1967).
[CrossRef]

Kapur, N. J.

N. J. Kapur, P. K. Sahoo, and A. K. Wong, " A new method for gray-level picture thresholding using the entropy of the histogram," Computer Vis. Graph. Image Process. 29, 273- 285 ( 1985).
[CrossRef]

Kasturi, R.

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw-Hill, 1995).

Kittler, J.

H. K. Yuen, J. Illingworth, and J. Kittler, " Detecting partially occluded ellipses using the Hough transform," Image Vision Comput. 7, 31- 37 ( 1989).
[CrossRef]

Krajewski, W. F.

A. Tokay, A. Kruger, and W. F. Krajewski, " Comparison of drop size distribution measurements by impact and optical disdrometers," J. Appl. Meteorol. 40, 2083- 2097 ( 2001).
[CrossRef]

Kruger, A.

A. Tokay, A. Kruger, and W. F. Krajewski, " Comparison of drop size distribution measurements by impact and optical disdrometers," J. Appl. Meteorol. 40, 2083- 2097 ( 2001).
[CrossRef]

Kubesh, R. J.

K. V. Beard and R. J. Kubesh, " Laboratory measurements of small raindrop distortion. 2. Oscillation frequencies and modes," J. Atmos. Sci. 48, 2245- 2264 ( 1991).
[CrossRef]

K. V. Beard, H. T. Ochs, and R. J. Kubesh, " Natural oscillations of small raindrops," Nature 342, 408- 410 ( 1989).
[CrossRef]

Laird, N. F.

K. Andsager, K. V. Beard, and N. F. Laird, " Laboratory measurements of axis ratios for large raindrops," J. Atmos. Sci. 56, 2673- 2683 ( 1999).
[CrossRef]

Lam, F. K.

C. K. Leung and F. K. Lam, " Performance analysis for a class of iterative image thresholding algorithms," Pattern Recogn. 29, 1523- 1530 ( 1996).
[CrossRef]

Lei, Y.

Y. Lei and K. C. Wong, " Ellipse detection based on symmetry," Pattern Recogn. Lett. 20, 41- 47 ( 1999).
[CrossRef]

Leung, C. K.

C. K. Leung and F. K. Lam, " Performance analysis for a class of iterative image thresholding algorithms," Pattern Recogn. 29, 1523- 1530 ( 1996).
[CrossRef]

Liao, P.

P. Liao, T. Chen, and P. Chung, " A fast algorithm for multilevel thresholding," J. Information Sci. and Eng. 17, 713- 727 ( 2001).

Lucas, J.

J. Lucas, F. Smektala, and J. L. Adam, " Fluorine in optics," J. Fluorine Chem. 114, 113- 118 ( 2002).
[CrossRef]

Macq, B.

J. -P. Thiran, V. Warscotte, and B. Macq, " A queue-based region growing algorithm for accurate segmentation of multi-dimensional digital images," Signal Process. 60, pp. 1- 10 ( 1997).
[CrossRef]

Ochs, H. T.

K. V. Beard, H. T. Ochs, and R. J. Kubesh, " Natural oscillations of small raindrops," Nature 342, 408- 410 ( 1989).
[CrossRef]

Ostu, N.

N. Ostu, " A threshold selection method from gray-level histograms," IEEE Trans. Syst. Man. Cybern. 9, 62- 66 ( 1979).
[CrossRef]

Poiares-Baptista, J. P. V.

M. Schönhuber, H. E. Urban, J. P. V. Poiares-Baptista, W. L. Randeu, and W. Riedler, " Measurements of precipitation characteristics by a new distrometer," in Proceedings of Atmospheric Physics and Dynamics in the Analysis and Prognosis of Precipitation Fields (SIMA, 1994).
[PubMed]

M. Schönhuber, H. E. Urban, J. P. V. Poiares-Baptista, W. L. Randeu, and W. Riedler, " Weather radar versus 2D-video-distrometer data," in Proceedings of the Third International Symposium on Hydrological Applications of Weather Radars (Wiley, 1995).

Randeu, W. L.

M. Schönhuber, H. E. Urban, J. P. V. Poiares-Baptista, W. L. Randeu, and W. Riedler, " Weather radar versus 2D-video-distrometer data," in Proceedings of the Third International Symposium on Hydrological Applications of Weather Radars (Wiley, 1995).

M. Schönhuber, H. E. Urban, J. P. V. Poiares-Baptista, W. L. Randeu, and W. Riedler, " Measurements of precipitation characteristics by a new distrometer," in Proceedings of Atmospheric Physics and Dynamics in the Analysis and Prognosis of Precipitation Fields (SIMA, 1994).
[PubMed]

Riedler, W.

M. Schönhuber, H. E. Urban, J. P. V. Poiares-Baptista, W. L. Randeu, and W. Riedler, " Measurements of precipitation characteristics by a new distrometer," in Proceedings of Atmospheric Physics and Dynamics in the Analysis and Prognosis of Precipitation Fields (SIMA, 1994).
[PubMed]

M. Schönhuber, H. E. Urban, J. P. V. Poiares-Baptista, W. L. Randeu, and W. Riedler, " Weather radar versus 2D-video-distrometer data," in Proceedings of the Third International Symposium on Hydrological Applications of Weather Radars (Wiley, 1995).

Sahoo, P. K.

N. J. Kapur, P. K. Sahoo, and A. K. Wong, " A new method for gray-level picture thresholding using the entropy of the histogram," Computer Vis. Graph. Image Process. 29, 273- 285 ( 1985).
[CrossRef]

Samek, L.

L. Samek and J. Wasylak, " Low-dispersion fluorozirconate glass with spectral dispersion of refractive index similar to that of water," Opt. Eng. 36, 1657- 1659 ( 1997).
[CrossRef]

Saylor, J. R.

J. R. Saylor, B. K. Jones, and L. F. Bliven, " Single-camera method to determine the optical axis position of ellipsoidal drops," Appl. Opt. 42, 972- 978 ( 2003).
[CrossRef] [PubMed]

J. R. Saylor, B. K. Jones, and L. F. Bliven, " A method for increasing depth of field during droplet imaging," Rev. Sci. Instrum. 73, 2422- 2427 ( 2002).
[CrossRef]

Schönhuber, M.

M. Schönhuber, H. E. Urban, J. P. V. Poiares-Baptista, W. L. Randeu, and W. Riedler, " Measurements of precipitation characteristics by a new distrometer," in Proceedings of Atmospheric Physics and Dynamics in the Analysis and Prognosis of Precipitation Fields (SIMA, 1994).
[PubMed]

M. Schönhuber, H. E. Urban, J. P. V. Poiares-Baptista, W. L. Randeu, and W. Riedler, " Weather radar versus 2D-video-distrometer data," in Proceedings of the Third International Symposium on Hydrological Applications of Weather Radars (Wiley, 1995).

Schunck, B. G.

R. Jain, R. Kasturi, and B. G. Schunck, Machine Vision (McGraw-Hill, 1995).

Seara, R.

O. J. Tobias and R. Seara, " Image segmentation by histogram thresholding using fuzzy sets," IEEE Trans. Image Process. 11, 1457- 1465 ( 2002).
[CrossRef]

Sekhon, R. S.

D. Atlas, R. C. Srivastava, and R. S. Sekhon, " Doppler radar characteristics of precipitation at vertical incidence," Rev. Geophys. Space Phys. 2, 1- 35 ( 1973).
[CrossRef]

Serra, J.

J. Serra, Image Analysis and Mathematical Morphology (Academic, 1982).

Smektala, F.

J. Lucas, F. Smektala, and J. L. Adam, " Fluorine in optics," J. Fluorine Chem. 114, 113- 118 ( 2002).
[CrossRef]

Srivastava, R. C.

D. Atlas, R. C. Srivastava, and R. S. Sekhon, " Doppler radar characteristics of precipitation at vertical incidence," Rev. Geophys. Space Phys. 2, 1- 35 ( 1973).
[CrossRef]

Sternberg, S. R.

R. M. Haralick, S. R. Sternberg, and X. Zhuang, " Image analysis using mathematical morphology," IEEE Trans. Pattern Anal. Mach. Intell. 9, 532- 550 ( 1987).
[CrossRef] [PubMed]

Thiran, J. -P.

J. -P. Thiran, V. Warscotte, and B. Macq, " A queue-based region growing algorithm for accurate segmentation of multi-dimensional digital images," Signal Process. 60, pp. 1- 10 ( 1997).
[CrossRef]

Tobias, O. J.

O. J. Tobias and R. Seara, " Image segmentation by histogram thresholding using fuzzy sets," IEEE Trans. Image Process. 11, 1457- 1465 ( 2002).
[CrossRef]

Tokay, A.

A. Tokay, A. Kruger, and W. F. Krajewski, " Comparison of drop size distribution measurements by impact and optical disdrometers," J. Appl. Meteorol. 40, 2083- 2097 ( 2001).
[CrossRef]

Tsai, W.

W. Tsai, " Moment-preserving thresholding: a new approach," Computer Vis. Graph. Image Process. 29, 377- 393 ( 1985).
[CrossRef]

Ulbrich, C. W.

C. W. Ulbrich, " Natural variations in the analytical form of the raindrop size distribution," J. Climate Appl. Meteorol. 22, 1764- 1775 ( 1983).
[CrossRef]

Urban, H. E.

M. Schönhuber, H. E. Urban, J. P. V. Poiares-Baptista, W. L. Randeu, and W. Riedler, " Measurements of precipitation characteristics by a new distrometer," in Proceedings of Atmospheric Physics and Dynamics in the Analysis and Prognosis of Precipitation Fields (SIMA, 1994).
[PubMed]

M. Schönhuber, H. E. Urban, J. P. V. Poiares-Baptista, W. L. Randeu, and W. Riedler, " Weather radar versus 2D-video-distrometer data," in Proceedings of the Third International Symposium on Hydrological Applications of Weather Radars (Wiley, 1995).

Waldvogel, A.

J. Joss and A. Waldvogel, " A raindrop spectrograph with automatic analysis," Pure Appl. Geophys. 68, 240- 246 ( 1967).
[CrossRef]

Wang, M. J. J.

L. K. Huang and M. J. J. Wang, " Image thresholding by minimizing the measure of fuzziness," Pattern Recognition 28, 41- 51 ( 1995).
[CrossRef]

Warscotte, V.

J. -P. Thiran, V. Warscotte, and B. Macq, " A queue-based region growing algorithm for accurate segmentation of multi-dimensional digital images," Signal Process. 60, pp. 1- 10 ( 1997).
[CrossRef]

Wasylak, J.

L. Samek and J. Wasylak, " Low-dispersion fluorozirconate glass with spectral dispersion of refractive index similar to that of water," Opt. Eng. 36, 1657- 1659 ( 1997).
[CrossRef]

Weast, R. C.

R. C. Weast, ed. Handbook of Chemistry and Physics, 52nd ed. (Chemical Rubber Company, 1971), Sec. B.

Wong, A. K.

N. J. Kapur, P. K. Sahoo, and A. K. Wong, " A new method for gray-level picture thresholding using the entropy of the histogram," Computer Vis. Graph. Image Process. 29, 273- 285 ( 1985).
[CrossRef]

Wong, K. C.

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Figures (21)

Fig. 1
Fig. 1

DSD obtained with a JWD from rain during the 0th hour of July 1.

Fig. 2
Fig. 2

Setup for obtaining raindrop images.

Fig. 3
Fig. 3

(a) Sample gray-scale image frame. (b) Binary version of the image frame obtained with fixed thresholding. Drop images indicated by arrows are in focus.

Fig. 4
Fig. 4

Magnified images of the two in-focus drops identified in Fig. 3(b).

Fig. 5
Fig. 5

Sample histogram of a raindrop image obtained with the setup in Fig. 2. Note that the large value at i = 255 corresponds to the background.

Fig. 6
Fig. 6

Setup for obtaining laboratory data: A, CCD camera; B, lamp; C, translation stage along the optical axis (z axis); D, translation stage along the x axis; E, dropping arm.

Fig. 7
Fig. 7

Gray scale (leftmost column) and binary images of a 3 mm sphere.

Fig. 8
Fig. 8

Sample plot of measured diameter Dm versus zd for an 8 mm sphere obtained by double thresholding. Each cross (×) represents a sphere image with diameter Dm and z position zd. The numbers at the top are the total count of sphere images (nt ), and the numbers below are the count of sphere images with holes (nh ).

Fig. 9
Fig. 9

All calculated ze and zs values for each sphere and each thresholding algorithm.

Fig. 10
Fig. 10

Variation of dof with D for all thresholding algorithms.

Fig. 11
Fig. 11

Variation of measured diameter Dm within the depth of field for the 8 mm sphere obtained from double thresholding. The dotted curve is the fourth-order polynomial fitted to all the data points. A value of 〈Dm 〉 = 7.17 mm was obtained from Eq. (22).

Fig. 12
Fig. 12

Variation of 〈Dm 〉 with D for all thresholding algorithms and each sphere diameter.

Fig. 13
Fig. 13

DSDs of the rain that occurred during the 0th hour of 1 July obtained from all the algorithms and the JWD.

Fig. 14
Fig. 14

RA from the double thresholding algorithm versus RJ.

Fig. 15
Fig. 15

RA versus RJ for four of the thresholding algorithms.

Fig. 16
Fig. 16

Mapping of Dm to D for double thresholding. Solid line, mapping corresponding to the average value; i.e., for a given Dm on average, the actual diameter D will be obtained from this line. The dotted and dashed lines are the fitted lines for the maximum and minimum values of Dm , respectively.

Fig. 17
Fig. 17

DSD for the rain that occurred during the 0th hour of 1 July obtained from double thresholding when the Dm -to-D mapping was changed. Dotted curve, the DSD obtained when Dm was mapped to the maximum value that D can take. Dashed curve, DSD obtained when Dm was mapped to the minimum value.

Fig. 18
Fig. 18

Gray-scale and binary images from entropy and MP thresholding algorithms of a 3 mm sphere at zd = 185 cm. Note that the gray-scale image is very blurry and should be rejected. The binary images show the presence of a small hole near the boundary of the image. These images were wrongly accepted as in-focus images.

Fig. 19
Fig. 19

Examples of out-of-focus drops selected as in focus. (a) MP thresholding, D = 0.59 mm; (b) entropy thresholding, D = 1.04 mm; (c) double thresholding, D = 0.50 mm.

Fig. 20
Fig. 20

Percentage error EP in accepting out-of-focus drops as in focus for the bins of D shown.

Fig. 21
Fig. 21

DSDs for the rain that occurred during the 0th hour of 1 July after morphological closing was applied to smooth the images. The original DSDs are presented in Fig. 13.

Tables (7)

Tables Icon

Table 1 Slope and Intercept of the Lines Shown in Fig. 10 and 95% Confidence Level of the Linear Fit Presented in Eq. (21)

Tables Icon

Table 2 Slope and Intercept of the Lines Shown in Fig. 12

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Table 3 Tabulation of 〈Dm〉, Db, σ1, and σ2 for Each D Investigated a

Tables Icon

Table 4 Rain Rates (mm h−1) Obtained for Each of the 15 h of Recorded Rain Data a

Tables Icon

Table 5 Parameters Relevant to the Linear Fits of RA to RJ in Figs. 14 and 15

Tables Icon

Table 6 Total Number of Examined Drops Accepted as In Focus H( D) and Number of Out-of-Focus Drops Incorrectly Accepted Ho(D) for Each Thresholding Algorithm and Each Diameter Range

Tables Icon

Table 7 Rain Rates (mm h−1) Obtained for Rain That Occurred During the 0th Hour of 1 July with the Simple Boundary Counting Algorithm and the Boundary Counting Algorithms with Image Smoothing a

Equations (28)

Equations on this page are rendered with MathJax. Learn more.

R = ( π / 6 ) 0 D 3 N ( D ) w t ( D ) d D ,
M = ( π ρ / 6 ) 0 N ( D ) D 3 d D ,
Z = 0 N ( D ) D 6 d D .
e = { 1 α 2 } 1 / 2 ,
α = v / h .
M = D m / D ,
μ 0 = i = 0 T i p ( i ) ,
μ b = i = T + 1 255 i p ( i ) ,
T = ( μ 0 + μ b ) / 2 .
H o = i = 0 T p ( i ) q o ( T ) × log p ( i ) q o ( T ) ,
H b = i = T + 1 255 p ( i ) q b ( T ) × log p ( i ) q b ( T ) .
q o ( T ) = i = 0 T p ( i ) ,
q b ( T ) = i = T + 1 255 p ( i ) .
m k = i = 0 255 p ( i ) i k .
b k = q o ( T ) μ o ( T ) k + q b ( T ) μ b ( T ) k ,
D m = ( 4 A π ) 1 / 2 ,
A = P × 0.1 × 0.05 ,
dof = z e z s .
N ( D k ) = H ( D k ) R v × l ,
R v = ( h D k ) × ( w D k ) × ( dof D k ) × N f .
dof = s D + i .
D m = 1 dof z s z e F ( D m ) d D m ,
D = D m i s ,
R = π 6 k = 1 640 D k     3 × N ( D k ) × w t ( D k ) × 0.05 ,
w t ( D k ) = 9.65 10.3 × exp ( 600 × D k ) ,
R J = R A c m [ mm   hr 1 ] ,
γ = R A R J R A R J σ A σ J ,
E p ( D ) = H o ( D ) H ( D ) × 100

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