Abstract

Optical imaging of raindrops provides important information on the statistical distribution of raindrop size and raindrop shape. These distributions are critical for extracting rainfall rates from both dual- and single-polarization radar signals. A large number of raindrop images are required to obtain these statistics, necessitating automatic processing of the imagery. The accuracy of the measured drop size depends critically on the characteristics of the digital image processing algorithm used to identify and size the drop. Additionally, the algorithm partially determines the effective depth of field of the camera∕image processing system. Because a large number of drop images are required to obtain accurate statistics, a large depth of field is needed, which tends to increase errors in drop size measurement. This trade-off between accuracy and depth of field (dof) is also affected by the algorithm used to identify the drop outline. In this paper, eight edge detection algorithms are investigated and compared to determine which is best suited for accurately extracting the drop outline and measuring the diameter of an imaged raindrop while maintaining a relatively large depth of field. The algorithm which overall gave the largest dof along with the most accurate estimate of the size of the drop was the Hueckel algorithm [J. Assoc. Comput. Mach. 20, 634 (1973)].

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. J. Doviak and D. S. Zrnić, Doppler Radar and Weather Observations (Academic, 1984).
  2. V. N. Bringi and V. Chandrasekar, Polarimetric Doppler Weather Radar (Cambridge U. Press, 2001).
  3. P. Meischner, Weather Radar (Springer, 2004).
  4. K. V. Beard, "Oscillation models for predicting raindrop axis and backscatter ratios," Radio Sci. 19, 67-74 (1984).
    [CrossRef]
  5. K. V. Beard and C. Chuang, "A new model for the equilibrium shape of raindrops," J. Atmos. Sci. 44, 1509-1524 (1987).
    [CrossRef]
  6. K. V. Beard, R. J. Kubesh, and H. T. Ochs, "Laboratory measurements of small raindrop distortion, Pt. 1: axis ratios and fall behavior," J. Atmos. Sci. 48, 698-710 (1991).
    [CrossRef]
  7. K. V. Beard and R. J. Kubesh, "Laboratory measurements of small raindrop distortion. Pt. 2: oscillation frequencies and modes," J. Atmos. Sci. 48, 2245-2264 (1991).
    [CrossRef]
  8. 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]
  9. K. V. Beard and A. Tokay, "A field study of raindrop oscillations: observations of size spectra and evaluation of oscillation causes," Geophys. Res. Lett. 18, 2257-2260 (1991).
    [CrossRef]
  10. J. Joss and A. Waldvogel, "A raindrop spectrograph with automatic analysis," Pure Appl. Geophys. 68, 240-246 (1967).
    [CrossRef]
  11. J. Joss and A. Waldvogel, "Comments on 'Some observations on the Joss-Waldvogel rainfall disdrometer'," J. Appl. Meteorol. 16, 112-113 (1977).
    [CrossRef]
  12. 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]
  13. D. Hauser, P. Amayenc, and B. Nutten, "A new optical instrument for simultaneous measurement of raindrop diameter and fall speed distributions," J. Atmos. Ocean. Technol. 1, 256-269 (1984).
    [CrossRef]
  14. M. Löffler-Mang and J. Joss, "An optical disdrometer for measuring size and velocity of hydrometeors," J. Atmos. Ocean. Technol. 17, 130-139 (2000).
    [CrossRef]
  15. G. Donnadieu, "Mesure de la vitesse terminale des gouttes du pluie au sol à l'aide du spectropluviomètre VIDIAZ," J. Rech. Atmos. 12, 245-259 (1978).
  16. G. Donnadieu, "Comparison of results obtained with the VIDIAZ spectropluviometer and the Joss-Waldvogel rainfall disdrometer in a 'rain of a thundery type'," J. Appl. Meteorol. 19, 593-597 (1980).
    [CrossRef]
  17. M. Grossklaus, K. Uhlig, and L. Hasse, "An optical disdrometer for use in high wind speeds," J. Atmos. Ocean. Technol. 15, 1051-1059 (1998).
    [CrossRef]
  18. J.-Y. Delahaye, L. Barthès, P. Golé, J. Lavergnat, and J. P. Vinson, "A dual-beam spectropluviometer concept," J. Hydrol. 328, 110-120 (2006).
    [CrossRef]
  19. S. Borrmann and R. Jaenicke, "Application of microholography for ground-based in situ measurements in stratus cloud layers: a case study," J. Atmos. Ocean. Technol. 10, 277-293 (1993).
    [CrossRef]
  20. 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).
  21. T. J. Schuur and A. V. Rhyzhkov, "Drop size distributions measured by a 2D video disdrometer: comparison with dual-polarization radar data," J. App. Meteorol. 40, 1019-1034 (2001).
    [CrossRef]
  22. A. Kruger and W. F. Krajewski, "Two-dimensional video disdrometer: a description," J. Atmos. Ocean. Technol. 19, 602-617 (2002).
    [CrossRef]
  23. V. Nĕspor, W. F. Krajewski, and A. Kruger, "Wind-induced error of raindrop size distribution measurement using a two-dimensional video disdrometer," J. Atmos. Ocean. Technol. 17, 1483-1492 (2000).
    [CrossRef]
  24. R. G. Knollenberg, "The optical array: an alternative to scattering or extinction for airborne particle size determination," J. Appl. Meteorol. 9, 86-103 (1970).
    [CrossRef]
  25. R. G. Knollenberg, Clouds: Their Formation, Optical Properties, and Effects (Academic, 1981), pp. 15-89.
  26. T. W. Cannon, "Imaging devices," Atmos. Technol. 8, 32-37 (1976).
  27. R. A. Black and J. Hallett, "Observations of the distribution of ice in hurricanes," J. Atmos. Sci. 43, 802-822 (1986).
    [CrossRef]
  28. G. Frank, T. Härtl, and J. Tschiersch, "The pluviospectrometer: classification of falling hydrometeors via digital image processing," Atmos. Res. 34, 367-378 (1994).
    [CrossRef]
  29. L. Bliven (personal communication, 2001).
  30. 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]
  31. 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]
  32. K. S. Fu and J. K. Mui, "A survey on image segmentation," Pattern Recogn. 13, 3-16 (1981).
    [CrossRef]
  33. K. R. Castleman, Digital Image Processing (Prentice Hall, 1996).
  34. D. D. Saxena and J. R. Saylor, "Use of thresholding algorithms in the processing of raindrop imagery," Appl. Opt. 45, 2672-2688 (2006).
    [CrossRef] [PubMed]
  35. N. A. Sivasubramanian and J. R. Saylor, "Application of a histogram modification algorithm to thresholding of raindrop images," submitted to Opt. Eng.
  36. T. Peli and D. Malah, "A study of edge detection algorithms," Computer Graph. Image Process. 20, 1-21 (1982).
    [CrossRef]
  37. L. G. Roberts, "Machine perception of three-dimensional solids," in Optical and Electro-optical Information Processing, J. T. Tippet, D. A. Berkowitz, L. C. Clapp, C. J. Koester and A. Vanderburgh, eds. (MIT Press, 1965), pp. 159-197.
  38. J. H. G. Hale, "Dectection of elementary features in a picture by non-linear local numerical processing," in Proceedings of the 3rd International Joint Conference on Pattern Recognition (1976), pp. 764-768.
  39. A. Rosenfeld, "A nonlinear edge detection technique," Proc. IEEE 58, 814-816 (1970).
    [CrossRef]
  40. A. Rosenfeld and M. Thurston, "Edge and curve detection for visual scene analysis," IEEE Trans. Comput. C-20, 562-569 (1971).
    [CrossRef]
  41. A. Rosenfeld, M. Thurston, and Y.-H. Lee, "Edge and curve detection: further experiments," IEEE Trans. Comput. C-21, 677-715 (1972).
    [CrossRef]
  42. G. B. Shaw, "Local and regional edge detectors: some comparisons," Computer Graph. Image Process. 9, 135-149 (1979).
    [CrossRef]
  43. I. E. Sobel, Camera Models and Machine Perception (Stanford U. Press, 1970).
  44. L. Mero and Z. Vassy, "A simplified and fast version of the Hueckel operator for finding optimal edges in pictures," in Proceedings of the 4th International Joint Conference on Artificial Intelligence (ASCE, 1975), pp. 650-655.
  45. R. A. Hummel, "Edge detection using basis functions," Technical Report TR-569 (University of Maryland, 1977).
  46. M. H. Hueckel, "An operator which locates edges in digitized pictures," J. Assoc. Comput. Mach. 18, 113-125 (1971).
    [CrossRef]
  47. M. H. Hueckel, "A local visual operator which recognizes edges and lines," J. Assoc. Comput. Mach. 20, 634-647 (1973).
    [CrossRef]
  48. M. C. Shin, D. B. Goldgof, K. W. Bowyer, and S. Nikiforou, "Comparison of edge detection algorithms using a structure from motion task," IEEE Trans. Syst. Man Cybern. 31, 589-601 (2001).
    [CrossRef]
  49. M. J. Black, G. Sapiro, D. H. Marimont, and D. Heeger, "Robust anisotropic diffusion," IEEE Trans. Image Process. 7, 421-432 (1998).
    [CrossRef]
  50. F. Bergholm, "Edge focussing," IEEE Trans. Pattern Anal. Mach. Intell. 9, 726-741 (1987).
    [CrossRef] [PubMed]
  51. J. Canny, "A. computational approach to edge detection," IEEE Trans. Pattern Anal. Mach. Intell. 8, 679-698 (1986).
    [CrossRef] [PubMed]
  52. L. Rosenthaler, F. Heitger, O. Kübler, and R. von der Heydt, "Detection of general edges and keypoints," in Proceedings of the European Conference on Computer Vision, (1992), pp. 78-86.
  53. C. A. Rothwell, J. L. Mundy, W. Hoffman, and V.-D. Nguyen, "Driving vision by topology," in IEEE International Symposium on Computer Vision (IEEE, 1995), pp. 395-400.
  54. S. Y. Sarkar and K. L. Boyer, "Optimal infinite impulse response zero crossing based edge detectors," Comput. Vision Graph. Image Process. 54, 224-243 (1991).
  55. S. M. Smith and J. M. Brady, "SUSAN--A new approach to low level image processing," Int. J. Comput. Vision 23, 45-78 (1997).
    [CrossRef]
  56. M. D. Heath, S. Sarkar, T. Sanocki, and K. W. Bowyer, "Comparison of edge detectors, a methodology and initial study," Comput. Vison Image Understand. 69, 38-54 (1998).
    [CrossRef]
  57. V. S. Nalwa and T. O. Binford, "On detecting edges," IEEE Trans. Pattern Anal. Mach. Intell. 8, 699-714 (1986).
    [CrossRef] [PubMed]
  58. J. R. Fram and E. S. Deutsch, "On the quantitative evaluation of edge detection schemes and their comparison with human performance," IEEE Trans. Comput. 24, 616-628 (1975).
    [CrossRef]
  59. I. D. G. Macleod, "On finding structure in pictures," in Picture Language Machines, S. Kaneff, ed. (Academic, 1970), pp. 231-256.
  60. I. D. G. Macleod, "Comments on techniques of edge detection," Proc. IEEE 60, 344 (1972).
    [CrossRef]
  61. K. C. Hayes and A. Rosenfeld, "Efficient edge detectors and applications," Technical Report TR-207 (University of Maryland, 1972).
  62. I. E. Abdou and W. Pratt, "Quantitative design and evaluation of enhancement/thresholding edge detectors," Proc. IEEE 67, 753-763 (1979).
    [CrossRef]
  63. J. M. S. Prewitt, "Object enhancement and extraction," in Picture Processing and Psychopictorics, B. S. Lipkin and A. Rosenfeld, eds. (Academic, 1970).
  64. R. Kirsch, "Computer determination of the consitituent structure of biological images," Comput. Biomed. Res. 4, 315-328 (1971).
    [CrossRef] [PubMed]
  65. R. Nevatia, "Evaluation of a simplified Hueckel edge-line detector," Comput. Graph. Image Process. 6, 582-588 (1977).
    [CrossRef]
  66. M. Sonka, V. Hlavac, and R. Boyle, Image Processing Analysis and Machine Vision (Thomson-Engineering, 1999).
  67. D. Vernon, Machine Vision (Prentice Hall, 1991).
  68. E. Trucco and A. Verri, Introductory Techniques for 3-D Computer Vision (Prentice Hall, 1998).
  69. J. Lucas, F. Smektala, and J. L. Adam, "Fluorine in optics," J. Fluorine Chem. 114, 113-118 (2002).
    [CrossRef]
  70. S. Peleg, "Iterative histogram modification, 2," IEEE Trans. Syst. Man Cybern. 8, 555-556 (1978).

2006

J.-Y. Delahaye, L. Barthès, P. Golé, J. Lavergnat, and J. P. Vinson, "A dual-beam spectropluviometer concept," J. Hydrol. 328, 110-120 (2006).
[CrossRef]

D. D. Saxena and J. R. Saylor, "Use of thresholding algorithms in the processing of raindrop imagery," Appl. Opt. 45, 2672-2688 (2006).
[CrossRef] [PubMed]

2004

P. Meischner, Weather Radar (Springer, 2004).

2003

2002

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]

A. Kruger and W. F. Krajewski, "Two-dimensional video disdrometer: a description," J. Atmos. Ocean. Technol. 19, 602-617 (2002).
[CrossRef]

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

2001

M. C. Shin, D. B. Goldgof, K. W. Bowyer, and S. Nikiforou, "Comparison of edge detection algorithms using a structure from motion task," IEEE Trans. Syst. Man Cybern. 31, 589-601 (2001).
[CrossRef]

T. J. Schuur and A. V. Rhyzhkov, "Drop size distributions measured by a 2D video disdrometer: comparison with dual-polarization radar data," J. App. Meteorol. 40, 1019-1034 (2001).
[CrossRef]

V. N. Bringi and V. Chandrasekar, Polarimetric Doppler Weather Radar (Cambridge U. Press, 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]

2000

M. Löffler-Mang and J. Joss, "An optical disdrometer for measuring size and velocity of hydrometeors," J. Atmos. Ocean. Technol. 17, 130-139 (2000).
[CrossRef]

V. Nĕspor, W. F. Krajewski, and A. Kruger, "Wind-induced error of raindrop size distribution measurement using a two-dimensional video disdrometer," J. Atmos. Ocean. Technol. 17, 1483-1492 (2000).
[CrossRef]

1999

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]

M. Sonka, V. Hlavac, and R. Boyle, Image Processing Analysis and Machine Vision (Thomson-Engineering, 1999).

1998

E. Trucco and A. Verri, Introductory Techniques for 3-D Computer Vision (Prentice Hall, 1998).

M. D. Heath, S. Sarkar, T. Sanocki, and K. W. Bowyer, "Comparison of edge detectors, a methodology and initial study," Comput. Vison Image Understand. 69, 38-54 (1998).
[CrossRef]

M. J. Black, G. Sapiro, D. H. Marimont, and D. Heeger, "Robust anisotropic diffusion," IEEE Trans. Image Process. 7, 421-432 (1998).
[CrossRef]

M. Grossklaus, K. Uhlig, and L. Hasse, "An optical disdrometer for use in high wind speeds," J. Atmos. Ocean. Technol. 15, 1051-1059 (1998).
[CrossRef]

1997

S. M. Smith and J. M. Brady, "SUSAN--A new approach to low level image processing," Int. J. Comput. Vision 23, 45-78 (1997).
[CrossRef]

1996

K. R. Castleman, Digital Image Processing (Prentice Hall, 1996).

1995

C. A. Rothwell, J. L. Mundy, W. Hoffman, and V.-D. Nguyen, "Driving vision by topology," in IEEE International Symposium on Computer Vision (IEEE, 1995), pp. 395-400.

1994

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).

G. Frank, T. Härtl, and J. Tschiersch, "The pluviospectrometer: classification of falling hydrometeors via digital image processing," Atmos. Res. 34, 367-378 (1994).
[CrossRef]

1993

S. Borrmann and R. Jaenicke, "Application of microholography for ground-based in situ measurements in stratus cloud layers: a case study," J. Atmos. Ocean. Technol. 10, 277-293 (1993).
[CrossRef]

1992

L. Rosenthaler, F. Heitger, O. Kübler, and R. von der Heydt, "Detection of general edges and keypoints," in Proceedings of the European Conference on Computer Vision, (1992), pp. 78-86.

1991

S. Y. Sarkar and K. L. Boyer, "Optimal infinite impulse response zero crossing based edge detectors," Comput. Vision Graph. Image Process. 54, 224-243 (1991).

D. Vernon, Machine Vision (Prentice Hall, 1991).

K. V. Beard and A. Tokay, "A field study of raindrop oscillations: observations of size spectra and evaluation of oscillation causes," Geophys. Res. Lett. 18, 2257-2260 (1991).
[CrossRef]

K. V. Beard, R. J. Kubesh, and H. T. Ochs, "Laboratory measurements of small raindrop distortion, Pt. 1: axis ratios and fall behavior," J. Atmos. Sci. 48, 698-710 (1991).
[CrossRef]

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

F. Bergholm, "Edge focussing," IEEE Trans. Pattern Anal. Mach. Intell. 9, 726-741 (1987).
[CrossRef] [PubMed]

1986

J. Canny, "A. computational approach to edge detection," IEEE Trans. Pattern Anal. Mach. Intell. 8, 679-698 (1986).
[CrossRef] [PubMed]

V. S. Nalwa and T. O. Binford, "On detecting edges," IEEE Trans. Pattern Anal. Mach. Intell. 8, 699-714 (1986).
[CrossRef] [PubMed]

R. A. Black and J. Hallett, "Observations of the distribution of ice in hurricanes," J. Atmos. Sci. 43, 802-822 (1986).
[CrossRef]

1984

D. Hauser, P. Amayenc, and B. Nutten, "A new optical instrument for simultaneous measurement of raindrop diameter and fall speed distributions," J. Atmos. Ocean. Technol. 1, 256-269 (1984).
[CrossRef]

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

K. V. Beard, "Oscillation models for predicting raindrop axis and backscatter ratios," Radio Sci. 19, 67-74 (1984).
[CrossRef]

1982

T. Peli and D. Malah, "A study of edge detection algorithms," Computer Graph. Image Process. 20, 1-21 (1982).
[CrossRef]

1981

K. S. Fu and J. K. Mui, "A survey on image segmentation," Pattern Recogn. 13, 3-16 (1981).
[CrossRef]

R. G. Knollenberg, Clouds: Their Formation, Optical Properties, and Effects (Academic, 1981), pp. 15-89.

1980

G. Donnadieu, "Comparison of results obtained with the VIDIAZ spectropluviometer and the Joss-Waldvogel rainfall disdrometer in a 'rain of a thundery type'," J. Appl. Meteorol. 19, 593-597 (1980).
[CrossRef]

1979

I. E. Abdou and W. Pratt, "Quantitative design and evaluation of enhancement/thresholding edge detectors," Proc. IEEE 67, 753-763 (1979).
[CrossRef]

G. B. Shaw, "Local and regional edge detectors: some comparisons," Computer Graph. Image Process. 9, 135-149 (1979).
[CrossRef]

1978

S. Peleg, "Iterative histogram modification, 2," IEEE Trans. Syst. Man Cybern. 8, 555-556 (1978).

G. Donnadieu, "Mesure de la vitesse terminale des gouttes du pluie au sol à l'aide du spectropluviomètre VIDIAZ," J. Rech. Atmos. 12, 245-259 (1978).

1977

J. Joss and A. Waldvogel, "Comments on 'Some observations on the Joss-Waldvogel rainfall disdrometer'," J. Appl. Meteorol. 16, 112-113 (1977).
[CrossRef]

R. Nevatia, "Evaluation of a simplified Hueckel edge-line detector," Comput. Graph. Image Process. 6, 582-588 (1977).
[CrossRef]

R. A. Hummel, "Edge detection using basis functions," Technical Report TR-569 (University of Maryland, 1977).

1976

T. W. Cannon, "Imaging devices," Atmos. Technol. 8, 32-37 (1976).

J. H. G. Hale, "Dectection of elementary features in a picture by non-linear local numerical processing," in Proceedings of the 3rd International Joint Conference on Pattern Recognition (1976), pp. 764-768.

1975

L. Mero and Z. Vassy, "A simplified and fast version of the Hueckel operator for finding optimal edges in pictures," in Proceedings of the 4th International Joint Conference on Artificial Intelligence (ASCE, 1975), pp. 650-655.

J. R. Fram and E. S. Deutsch, "On the quantitative evaluation of edge detection schemes and their comparison with human performance," IEEE Trans. Comput. 24, 616-628 (1975).
[CrossRef]

1973

M. H. Hueckel, "A local visual operator which recognizes edges and lines," J. Assoc. Comput. Mach. 20, 634-647 (1973).
[CrossRef]

1972

A. Rosenfeld, M. Thurston, and Y.-H. Lee, "Edge and curve detection: further experiments," IEEE Trans. Comput. C-21, 677-715 (1972).
[CrossRef]

I. D. G. Macleod, "Comments on techniques of edge detection," Proc. IEEE 60, 344 (1972).
[CrossRef]

K. C. Hayes and A. Rosenfeld, "Efficient edge detectors and applications," Technical Report TR-207 (University of Maryland, 1972).

1971

R. Kirsch, "Computer determination of the consitituent structure of biological images," Comput. Biomed. Res. 4, 315-328 (1971).
[CrossRef] [PubMed]

M. H. Hueckel, "An operator which locates edges in digitized pictures," J. Assoc. Comput. Mach. 18, 113-125 (1971).
[CrossRef]

A. Rosenfeld and M. Thurston, "Edge and curve detection for visual scene analysis," IEEE Trans. Comput. C-20, 562-569 (1971).
[CrossRef]

1970

I. E. Sobel, Camera Models and Machine Perception (Stanford U. Press, 1970).

J. M. S. Prewitt, "Object enhancement and extraction," in Picture Processing and Psychopictorics, B. S. Lipkin and A. Rosenfeld, eds. (Academic, 1970).

I. D. G. Macleod, "On finding structure in pictures," in Picture Language Machines, S. Kaneff, ed. (Academic, 1970), pp. 231-256.

A. Rosenfeld, "A nonlinear edge detection technique," Proc. IEEE 58, 814-816 (1970).
[CrossRef]

R. G. Knollenberg, "The optical array: an alternative to scattering or extinction for airborne particle size determination," J. Appl. Meteorol. 9, 86-103 (1970).
[CrossRef]

1967

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

1965

L. G. Roberts, "Machine perception of three-dimensional solids," in Optical and Electro-optical Information Processing, J. T. Tippet, D. A. Berkowitz, L. C. Clapp, C. J. Koester and A. Vanderburgh, eds. (MIT Press, 1965), pp. 159-197.

Abdou, I. E.

I. E. Abdou and W. Pratt, "Quantitative design and evaluation of enhancement/thresholding edge detectors," Proc. IEEE 67, 753-763 (1979).
[CrossRef]

Adam, J. L.

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

Amayenc, P.

D. Hauser, P. Amayenc, and B. Nutten, "A new optical instrument for simultaneous measurement of raindrop diameter and fall speed distributions," J. Atmos. Ocean. Technol. 1, 256-269 (1984).
[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]

Barthès, L.

J.-Y. Delahaye, L. Barthès, P. Golé, J. Lavergnat, and J. P. Vinson, "A dual-beam spectropluviometer concept," J. Hydrol. 328, 110-120 (2006).
[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. Pt. 2: oscillation frequencies and modes," J. Atmos. Sci. 48, 2245-2264 (1991).
[CrossRef]

K. V. Beard and A. Tokay, "A field study of raindrop oscillations: observations of size spectra and evaluation of oscillation causes," Geophys. Res. Lett. 18, 2257-2260 (1991).
[CrossRef]

K. V. Beard, R. J. Kubesh, and H. T. Ochs, "Laboratory measurements of small raindrop distortion, Pt. 1: axis ratios and fall behavior," J. Atmos. Sci. 48, 698-710 (1991).
[CrossRef]

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

K. V. Beard, "Oscillation models for predicting raindrop axis and backscatter ratios," Radio Sci. 19, 67-74 (1984).
[CrossRef]

Bergholm, F.

F. Bergholm, "Edge focussing," IEEE Trans. Pattern Anal. Mach. Intell. 9, 726-741 (1987).
[CrossRef] [PubMed]

Binford, T. O.

V. S. Nalwa and T. O. Binford, "On detecting edges," IEEE Trans. Pattern Anal. Mach. Intell. 8, 699-714 (1986).
[CrossRef] [PubMed]

Black, M. J.

M. J. Black, G. Sapiro, D. H. Marimont, and D. Heeger, "Robust anisotropic diffusion," IEEE Trans. Image Process. 7, 421-432 (1998).
[CrossRef]

Black, R. A.

R. A. Black and J. Hallett, "Observations of the distribution of ice in hurricanes," J. Atmos. Sci. 43, 802-822 (1986).
[CrossRef]

Bliven, L.

L. Bliven (personal communication, 2001).

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]

Borrmann, S.

S. Borrmann and R. Jaenicke, "Application of microholography for ground-based in situ measurements in stratus cloud layers: a case study," J. Atmos. Ocean. Technol. 10, 277-293 (1993).
[CrossRef]

Bowyer, K. W.

M. C. Shin, D. B. Goldgof, K. W. Bowyer, and S. Nikiforou, "Comparison of edge detection algorithms using a structure from motion task," IEEE Trans. Syst. Man Cybern. 31, 589-601 (2001).
[CrossRef]

M. D. Heath, S. Sarkar, T. Sanocki, and K. W. Bowyer, "Comparison of edge detectors, a methodology and initial study," Comput. Vison Image Understand. 69, 38-54 (1998).
[CrossRef]

Boyer, K. L.

S. Y. Sarkar and K. L. Boyer, "Optimal infinite impulse response zero crossing based edge detectors," Comput. Vision Graph. Image Process. 54, 224-243 (1991).

Boyle, R.

M. Sonka, V. Hlavac, and R. Boyle, Image Processing Analysis and Machine Vision (Thomson-Engineering, 1999).

Brady, J. M.

S. M. Smith and J. M. Brady, "SUSAN--A new approach to low level image processing," Int. J. Comput. Vision 23, 45-78 (1997).
[CrossRef]

Bringi, V. N.

V. N. Bringi and V. Chandrasekar, Polarimetric Doppler Weather Radar (Cambridge U. Press, 2001).

Cannon, T. W.

T. W. Cannon, "Imaging devices," Atmos. Technol. 8, 32-37 (1976).

Canny, J.

J. Canny, "A. computational approach to edge detection," IEEE Trans. Pattern Anal. Mach. Intell. 8, 679-698 (1986).
[CrossRef] [PubMed]

Castleman, K. R.

K. R. Castleman, Digital Image Processing (Prentice Hall, 1996).

Chandrasekar, V.

V. N. Bringi and V. Chandrasekar, Polarimetric Doppler Weather Radar (Cambridge U. Press, 2001).

Chuang, C.

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

Delahaye, J.-Y.

J.-Y. Delahaye, L. Barthès, P. Golé, J. Lavergnat, and J. P. Vinson, "A dual-beam spectropluviometer concept," J. Hydrol. 328, 110-120 (2006).
[CrossRef]

Deutsch, E. S.

J. R. Fram and E. S. Deutsch, "On the quantitative evaluation of edge detection schemes and their comparison with human performance," IEEE Trans. Comput. 24, 616-628 (1975).
[CrossRef]

Donnadieu, G.

G. Donnadieu, "Comparison of results obtained with the VIDIAZ spectropluviometer and the Joss-Waldvogel rainfall disdrometer in a 'rain of a thundery type'," J. Appl. Meteorol. 19, 593-597 (1980).
[CrossRef]

G. Donnadieu, "Mesure de la vitesse terminale des gouttes du pluie au sol à l'aide du spectropluviomètre VIDIAZ," J. Rech. Atmos. 12, 245-259 (1978).

Doviak, R. J.

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

Fram, J. R.

J. R. Fram and E. S. Deutsch, "On the quantitative evaluation of edge detection schemes and their comparison with human performance," IEEE Trans. Comput. 24, 616-628 (1975).
[CrossRef]

Frank, G.

G. Frank, T. Härtl, and J. Tschiersch, "The pluviospectrometer: classification of falling hydrometeors via digital image processing," Atmos. Res. 34, 367-378 (1994).
[CrossRef]

Fu, K. S.

K. S. Fu and J. K. Mui, "A survey on image segmentation," Pattern Recogn. 13, 3-16 (1981).
[CrossRef]

Goldgof, D. B.

M. C. Shin, D. B. Goldgof, K. W. Bowyer, and S. Nikiforou, "Comparison of edge detection algorithms using a structure from motion task," IEEE Trans. Syst. Man Cybern. 31, 589-601 (2001).
[CrossRef]

Golé, P.

J.-Y. Delahaye, L. Barthès, P. Golé, J. Lavergnat, and J. P. Vinson, "A dual-beam spectropluviometer concept," J. Hydrol. 328, 110-120 (2006).
[CrossRef]

Grossklaus, M.

M. Grossklaus, K. Uhlig, and L. Hasse, "An optical disdrometer for use in high wind speeds," J. Atmos. Ocean. Technol. 15, 1051-1059 (1998).
[CrossRef]

Hale, J. H. G.

J. H. G. Hale, "Dectection of elementary features in a picture by non-linear local numerical processing," in Proceedings of the 3rd International Joint Conference on Pattern Recognition (1976), pp. 764-768.

Hallett, J.

R. A. Black and J. Hallett, "Observations of the distribution of ice in hurricanes," J. Atmos. Sci. 43, 802-822 (1986).
[CrossRef]

Härtl, T.

G. Frank, T. Härtl, and J. Tschiersch, "The pluviospectrometer: classification of falling hydrometeors via digital image processing," Atmos. Res. 34, 367-378 (1994).
[CrossRef]

Hasse, L.

M. Grossklaus, K. Uhlig, and L. Hasse, "An optical disdrometer for use in high wind speeds," J. Atmos. Ocean. Technol. 15, 1051-1059 (1998).
[CrossRef]

Hauser, D.

D. Hauser, P. Amayenc, and B. Nutten, "A new optical instrument for simultaneous measurement of raindrop diameter and fall speed distributions," J. Atmos. Ocean. Technol. 1, 256-269 (1984).
[CrossRef]

Hayes, K. C.

K. C. Hayes and A. Rosenfeld, "Efficient edge detectors and applications," Technical Report TR-207 (University of Maryland, 1972).

Heath, M. D.

M. D. Heath, S. Sarkar, T. Sanocki, and K. W. Bowyer, "Comparison of edge detectors, a methodology and initial study," Comput. Vison Image Understand. 69, 38-54 (1998).
[CrossRef]

Heeger, D.

M. J. Black, G. Sapiro, D. H. Marimont, and D. Heeger, "Robust anisotropic diffusion," IEEE Trans. Image Process. 7, 421-432 (1998).
[CrossRef]

Heitger, F.

L. Rosenthaler, F. Heitger, O. Kübler, and R. von der Heydt, "Detection of general edges and keypoints," in Proceedings of the European Conference on Computer Vision, (1992), pp. 78-86.

Hlavac, V.

M. Sonka, V. Hlavac, and R. Boyle, Image Processing Analysis and Machine Vision (Thomson-Engineering, 1999).

Hoffman, W.

C. A. Rothwell, J. L. Mundy, W. Hoffman, and V.-D. Nguyen, "Driving vision by topology," in IEEE International Symposium on Computer Vision (IEEE, 1995), pp. 395-400.

Hueckel, M. H.

M. H. Hueckel, "A local visual operator which recognizes edges and lines," J. Assoc. Comput. Mach. 20, 634-647 (1973).
[CrossRef]

M. H. Hueckel, "An operator which locates edges in digitized pictures," J. Assoc. Comput. Mach. 18, 113-125 (1971).
[CrossRef]

Hummel, R. A.

R. A. Hummel, "Edge detection using basis functions," Technical Report TR-569 (University of Maryland, 1977).

Jaenicke, R.

S. Borrmann and R. Jaenicke, "Application of microholography for ground-based in situ measurements in stratus cloud layers: a case study," J. Atmos. Ocean. Technol. 10, 277-293 (1993).
[CrossRef]

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.

M. Löffler-Mang and J. Joss, "An optical disdrometer for measuring size and velocity of hydrometeors," J. Atmos. Ocean. Technol. 17, 130-139 (2000).
[CrossRef]

J. Joss and A. Waldvogel, "Comments on 'Some observations on the Joss-Waldvogel rainfall disdrometer'," J. Appl. Meteorol. 16, 112-113 (1977).
[CrossRef]

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

Kirsch, R.

R. Kirsch, "Computer determination of the consitituent structure of biological images," Comput. Biomed. Res. 4, 315-328 (1971).
[CrossRef] [PubMed]

Knollenberg, R. G.

R. G. Knollenberg, Clouds: Their Formation, Optical Properties, and Effects (Academic, 1981), pp. 15-89.

R. G. Knollenberg, "The optical array: an alternative to scattering or extinction for airborne particle size determination," J. Appl. Meteorol. 9, 86-103 (1970).
[CrossRef]

Krajewski, W. F.

A. Kruger and W. F. Krajewski, "Two-dimensional video disdrometer: a description," J. Atmos. Ocean. Technol. 19, 602-617 (2002).
[CrossRef]

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]

V. Nĕspor, W. F. Krajewski, and A. Kruger, "Wind-induced error of raindrop size distribution measurement using a two-dimensional video disdrometer," J. Atmos. Ocean. Technol. 17, 1483-1492 (2000).
[CrossRef]

Kruger, A.

A. Kruger and W. F. Krajewski, "Two-dimensional video disdrometer: a description," J. Atmos. Ocean. Technol. 19, 602-617 (2002).
[CrossRef]

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]

V. Nĕspor, W. F. Krajewski, and A. Kruger, "Wind-induced error of raindrop size distribution measurement using a two-dimensional video disdrometer," J. Atmos. Ocean. Technol. 17, 1483-1492 (2000).
[CrossRef]

Kubesh, R. J.

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

K. V. Beard, R. J. Kubesh, and H. T. Ochs, "Laboratory measurements of small raindrop distortion, Pt. 1: axis ratios and fall behavior," J. Atmos. Sci. 48, 698-710 (1991).
[CrossRef]

Kübler, O.

L. Rosenthaler, F. Heitger, O. Kübler, and R. von der Heydt, "Detection of general edges and keypoints," in Proceedings of the European Conference on Computer Vision, (1992), pp. 78-86.

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]

Lavergnat, J.

J.-Y. Delahaye, L. Barthès, P. Golé, J. Lavergnat, and J. P. Vinson, "A dual-beam spectropluviometer concept," J. Hydrol. 328, 110-120 (2006).
[CrossRef]

Lee, Y.-H.

A. Rosenfeld, M. Thurston, and Y.-H. Lee, "Edge and curve detection: further experiments," IEEE Trans. Comput. C-21, 677-715 (1972).
[CrossRef]

Löffler-Mang, M.

M. Löffler-Mang and J. Joss, "An optical disdrometer for measuring size and velocity of hydrometeors," J. Atmos. Ocean. Technol. 17, 130-139 (2000).
[CrossRef]

Lucas, J.

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

Macleod, I. D. G.

I. D. G. Macleod, "Comments on techniques of edge detection," Proc. IEEE 60, 344 (1972).
[CrossRef]

I. D. G. Macleod, "On finding structure in pictures," in Picture Language Machines, S. Kaneff, ed. (Academic, 1970), pp. 231-256.

Malah, D.

T. Peli and D. Malah, "A study of edge detection algorithms," Computer Graph. Image Process. 20, 1-21 (1982).
[CrossRef]

Marimont, D. H.

M. J. Black, G. Sapiro, D. H. Marimont, and D. Heeger, "Robust anisotropic diffusion," IEEE Trans. Image Process. 7, 421-432 (1998).
[CrossRef]

Meischner, P.

P. Meischner, Weather Radar (Springer, 2004).

Mero, L.

L. Mero and Z. Vassy, "A simplified and fast version of the Hueckel operator for finding optimal edges in pictures," in Proceedings of the 4th International Joint Conference on Artificial Intelligence (ASCE, 1975), pp. 650-655.

Mui, J. K.

K. S. Fu and J. K. Mui, "A survey on image segmentation," Pattern Recogn. 13, 3-16 (1981).
[CrossRef]

Mundy, J. L.

C. A. Rothwell, J. L. Mundy, W. Hoffman, and V.-D. Nguyen, "Driving vision by topology," in IEEE International Symposium on Computer Vision (IEEE, 1995), pp. 395-400.

Nalwa, V. S.

V. S. Nalwa and T. O. Binford, "On detecting edges," IEEE Trans. Pattern Anal. Mach. Intell. 8, 699-714 (1986).
[CrossRef] [PubMed]

Nespor, V.

V. Nĕspor, W. F. Krajewski, and A. Kruger, "Wind-induced error of raindrop size distribution measurement using a two-dimensional video disdrometer," J. Atmos. Ocean. Technol. 17, 1483-1492 (2000).
[CrossRef]

Nevatia, R.

R. Nevatia, "Evaluation of a simplified Hueckel edge-line detector," Comput. Graph. Image Process. 6, 582-588 (1977).
[CrossRef]

Nguyen, V.-D.

C. A. Rothwell, J. L. Mundy, W. Hoffman, and V.-D. Nguyen, "Driving vision by topology," in IEEE International Symposium on Computer Vision (IEEE, 1995), pp. 395-400.

Nikiforou, S.

M. C. Shin, D. B. Goldgof, K. W. Bowyer, and S. Nikiforou, "Comparison of edge detection algorithms using a structure from motion task," IEEE Trans. Syst. Man Cybern. 31, 589-601 (2001).
[CrossRef]

Nutten, B.

D. Hauser, P. Amayenc, and B. Nutten, "A new optical instrument for simultaneous measurement of raindrop diameter and fall speed distributions," J. Atmos. Ocean. Technol. 1, 256-269 (1984).
[CrossRef]

Ochs, H. T.

K. V. Beard, R. J. Kubesh, and H. T. Ochs, "Laboratory measurements of small raindrop distortion, Pt. 1: axis ratios and fall behavior," J. Atmos. Sci. 48, 698-710 (1991).
[CrossRef]

Peleg, S.

S. Peleg, "Iterative histogram modification, 2," IEEE Trans. Syst. Man Cybern. 8, 555-556 (1978).

Peli, T.

T. Peli and D. Malah, "A study of edge detection algorithms," Computer Graph. Image Process. 20, 1-21 (1982).
[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).

Pratt, W.

I. E. Abdou and W. Pratt, "Quantitative design and evaluation of enhancement/thresholding edge detectors," Proc. IEEE 67, 753-763 (1979).
[CrossRef]

Prewitt, J. M. S.

J. M. S. Prewitt, "Object enhancement and extraction," in Picture Processing and Psychopictorics, B. S. Lipkin and A. Rosenfeld, eds. (Academic, 1970).

Randeu, W. L.

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).

Rhyzhkov, A. V.

T. J. Schuur and A. V. Rhyzhkov, "Drop size distributions measured by a 2D video disdrometer: comparison with dual-polarization radar data," J. App. Meteorol. 40, 1019-1034 (2001).
[CrossRef]

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).

Roberts, L. G.

L. G. Roberts, "Machine perception of three-dimensional solids," in Optical and Electro-optical Information Processing, J. T. Tippet, D. A. Berkowitz, L. C. Clapp, C. J. Koester and A. Vanderburgh, eds. (MIT Press, 1965), pp. 159-197.

Rosenfeld, A.

A. Rosenfeld, M. Thurston, and Y.-H. Lee, "Edge and curve detection: further experiments," IEEE Trans. Comput. C-21, 677-715 (1972).
[CrossRef]

K. C. Hayes and A. Rosenfeld, "Efficient edge detectors and applications," Technical Report TR-207 (University of Maryland, 1972).

A. Rosenfeld and M. Thurston, "Edge and curve detection for visual scene analysis," IEEE Trans. Comput. C-20, 562-569 (1971).
[CrossRef]

A. Rosenfeld, "A nonlinear edge detection technique," Proc. IEEE 58, 814-816 (1970).
[CrossRef]

Rosenthaler, L.

L. Rosenthaler, F. Heitger, O. Kübler, and R. von der Heydt, "Detection of general edges and keypoints," in Proceedings of the European Conference on Computer Vision, (1992), pp. 78-86.

Rothwell, C. A.

C. A. Rothwell, J. L. Mundy, W. Hoffman, and V.-D. Nguyen, "Driving vision by topology," in IEEE International Symposium on Computer Vision (IEEE, 1995), pp. 395-400.

Sanocki, T.

M. D. Heath, S. Sarkar, T. Sanocki, and K. W. Bowyer, "Comparison of edge detectors, a methodology and initial study," Comput. Vison Image Understand. 69, 38-54 (1998).
[CrossRef]

Sapiro, G.

M. J. Black, G. Sapiro, D. H. Marimont, and D. Heeger, "Robust anisotropic diffusion," IEEE Trans. Image Process. 7, 421-432 (1998).
[CrossRef]

Sarkar, S.

M. D. Heath, S. Sarkar, T. Sanocki, and K. W. Bowyer, "Comparison of edge detectors, a methodology and initial study," Comput. Vison Image Understand. 69, 38-54 (1998).
[CrossRef]

Sarkar, S. Y.

S. Y. Sarkar and K. L. Boyer, "Optimal infinite impulse response zero crossing based edge detectors," Comput. Vision Graph. Image Process. 54, 224-243 (1991).

Saxena, D. D.

Saylor, J. R.

D. D. Saxena and J. R. Saylor, "Use of thresholding algorithms in the processing of raindrop imagery," Appl. Opt. 45, 2672-2688 (2006).
[CrossRef] [PubMed]

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]

N. A. Sivasubramanian and J. R. Saylor, "Application of a histogram modification algorithm to thresholding of raindrop images," submitted to Opt. Eng.

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).

Schuur, T. J.

T. J. Schuur and A. V. Rhyzhkov, "Drop size distributions measured by a 2D video disdrometer: comparison with dual-polarization radar data," J. App. Meteorol. 40, 1019-1034 (2001).
[CrossRef]

Shaw, G. B.

G. B. Shaw, "Local and regional edge detectors: some comparisons," Computer Graph. Image Process. 9, 135-149 (1979).
[CrossRef]

Shin, M. C.

M. C. Shin, D. B. Goldgof, K. W. Bowyer, and S. Nikiforou, "Comparison of edge detection algorithms using a structure from motion task," IEEE Trans. Syst. Man Cybern. 31, 589-601 (2001).
[CrossRef]

Sivasubramanian, N. A.

N. A. Sivasubramanian and J. R. Saylor, "Application of a histogram modification algorithm to thresholding of raindrop images," submitted to Opt. Eng.

Smektala, F.

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

Smith, S. M.

S. M. Smith and J. M. Brady, "SUSAN--A new approach to low level image processing," Int. J. Comput. Vision 23, 45-78 (1997).
[CrossRef]

Sobel, I. E.

I. E. Sobel, Camera Models and Machine Perception (Stanford U. Press, 1970).

Sonka, M.

M. Sonka, V. Hlavac, and R. Boyle, Image Processing Analysis and Machine Vision (Thomson-Engineering, 1999).

Thurston, M.

A. Rosenfeld, M. Thurston, and Y.-H. Lee, "Edge and curve detection: further experiments," IEEE Trans. Comput. C-21, 677-715 (1972).
[CrossRef]

A. Rosenfeld and M. Thurston, "Edge and curve detection for visual scene analysis," IEEE Trans. Comput. C-20, 562-569 (1971).
[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]

K. V. Beard and A. Tokay, "A field study of raindrop oscillations: observations of size spectra and evaluation of oscillation causes," Geophys. Res. Lett. 18, 2257-2260 (1991).
[CrossRef]

Trucco, E.

E. Trucco and A. Verri, Introductory Techniques for 3-D Computer Vision (Prentice Hall, 1998).

Tschiersch, J.

G. Frank, T. Härtl, and J. Tschiersch, "The pluviospectrometer: classification of falling hydrometeors via digital image processing," Atmos. Res. 34, 367-378 (1994).
[CrossRef]

Uhlig, K.

M. Grossklaus, K. Uhlig, and L. Hasse, "An optical disdrometer for use in high wind speeds," J. Atmos. Ocean. Technol. 15, 1051-1059 (1998).
[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).

Vassy, Z.

L. Mero and Z. Vassy, "A simplified and fast version of the Hueckel operator for finding optimal edges in pictures," in Proceedings of the 4th International Joint Conference on Artificial Intelligence (ASCE, 1975), pp. 650-655.

Vernon, D.

D. Vernon, Machine Vision (Prentice Hall, 1991).

Verri, A.

E. Trucco and A. Verri, Introductory Techniques for 3-D Computer Vision (Prentice Hall, 1998).

Vinson, J. P.

J.-Y. Delahaye, L. Barthès, P. Golé, J. Lavergnat, and J. P. Vinson, "A dual-beam spectropluviometer concept," J. Hydrol. 328, 110-120 (2006).
[CrossRef]

von der Heydt, R.

L. Rosenthaler, F. Heitger, O. Kübler, and R. von der Heydt, "Detection of general edges and keypoints," in Proceedings of the European Conference on Computer Vision, (1992), pp. 78-86.

Waldvogel, A.

J. Joss and A. Waldvogel, "Comments on 'Some observations on the Joss-Waldvogel rainfall disdrometer'," J. Appl. Meteorol. 16, 112-113 (1977).
[CrossRef]

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

Zrnic, D. S.

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

Appl. Opt.

Atmos. Res.

G. Frank, T. Härtl, and J. Tschiersch, "The pluviospectrometer: classification of falling hydrometeors via digital image processing," Atmos. Res. 34, 367-378 (1994).
[CrossRef]

Atmos. Technol.

T. W. Cannon, "Imaging devices," Atmos. Technol. 8, 32-37 (1976).

Comput. Biomed. Res.

R. Kirsch, "Computer determination of the consitituent structure of biological images," Comput. Biomed. Res. 4, 315-328 (1971).
[CrossRef] [PubMed]

Comput. Graph. Image Process.

R. Nevatia, "Evaluation of a simplified Hueckel edge-line detector," Comput. Graph. Image Process. 6, 582-588 (1977).
[CrossRef]

Comput. Vision

S. Y. Sarkar and K. L. Boyer, "Optimal infinite impulse response zero crossing based edge detectors," Comput. Vision Graph. Image Process. 54, 224-243 (1991).

Comput. Vison Image Understand.

M. D. Heath, S. Sarkar, T. Sanocki, and K. W. Bowyer, "Comparison of edge detectors, a methodology and initial study," Comput. Vison Image Understand. 69, 38-54 (1998).
[CrossRef]

Computer Graph. Image Process.

G. B. Shaw, "Local and regional edge detectors: some comparisons," Computer Graph. Image Process. 9, 135-149 (1979).
[CrossRef]

T. Peli and D. Malah, "A study of edge detection algorithms," Computer Graph. Image Process. 20, 1-21 (1982).
[CrossRef]

Geophys. Res. Lett.

K. V. Beard and A. Tokay, "A field study of raindrop oscillations: observations of size spectra and evaluation of oscillation causes," Geophys. Res. Lett. 18, 2257-2260 (1991).
[CrossRef]

IEEE Trans. Comput.

A. Rosenfeld and M. Thurston, "Edge and curve detection for visual scene analysis," IEEE Trans. Comput. C-20, 562-569 (1971).
[CrossRef]

A. Rosenfeld, M. Thurston, and Y.-H. Lee, "Edge and curve detection: further experiments," IEEE Trans. Comput. C-21, 677-715 (1972).
[CrossRef]

J. R. Fram and E. S. Deutsch, "On the quantitative evaluation of edge detection schemes and their comparison with human performance," IEEE Trans. Comput. 24, 616-628 (1975).
[CrossRef]

IEEE Trans. Image Process.

M. J. Black, G. Sapiro, D. H. Marimont, and D. Heeger, "Robust anisotropic diffusion," IEEE Trans. Image Process. 7, 421-432 (1998).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

F. Bergholm, "Edge focussing," IEEE Trans. Pattern Anal. Mach. Intell. 9, 726-741 (1987).
[CrossRef] [PubMed]

J. Canny, "A. computational approach to edge detection," IEEE Trans. Pattern Anal. Mach. Intell. 8, 679-698 (1986).
[CrossRef] [PubMed]

V. S. Nalwa and T. O. Binford, "On detecting edges," IEEE Trans. Pattern Anal. Mach. Intell. 8, 699-714 (1986).
[CrossRef] [PubMed]

IEEE Trans. Syst. Man Cybern.

S. Peleg, "Iterative histogram modification, 2," IEEE Trans. Syst. Man Cybern. 8, 555-556 (1978).

Int. J. Comput. Vision

S. M. Smith and J. M. Brady, "SUSAN--A new approach to low level image processing," Int. J. Comput. Vision 23, 45-78 (1997).
[CrossRef]

J. App. Meteorol.

T. J. Schuur and A. V. Rhyzhkov, "Drop size distributions measured by a 2D video disdrometer: comparison with dual-polarization radar data," J. App. Meteorol. 40, 1019-1034 (2001).
[CrossRef]

J. Appl. Meteorol.

R. G. Knollenberg, "The optical array: an alternative to scattering or extinction for airborne particle size determination," J. Appl. Meteorol. 9, 86-103 (1970).
[CrossRef]

J. Joss and A. Waldvogel, "Comments on 'Some observations on the Joss-Waldvogel rainfall disdrometer'," J. Appl. Meteorol. 16, 112-113 (1977).
[CrossRef]

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]

G. Donnadieu, "Comparison of results obtained with the VIDIAZ spectropluviometer and the Joss-Waldvogel rainfall disdrometer in a 'rain of a thundery type'," J. Appl. Meteorol. 19, 593-597 (1980).
[CrossRef]

J. Assoc. Comput. Mach.

M. H. Hueckel, "An operator which locates edges in digitized pictures," J. Assoc. Comput. Mach. 18, 113-125 (1971).
[CrossRef]

M. H. Hueckel, "A local visual operator which recognizes edges and lines," J. Assoc. Comput. Mach. 20, 634-647 (1973).
[CrossRef]

J. Atmos. Ocean. Technol.

M. Grossklaus, K. Uhlig, and L. Hasse, "An optical disdrometer for use in high wind speeds," J. Atmos. Ocean. Technol. 15, 1051-1059 (1998).
[CrossRef]

S. Borrmann and R. Jaenicke, "Application of microholography for ground-based in situ measurements in stratus cloud layers: a case study," J. Atmos. Ocean. Technol. 10, 277-293 (1993).
[CrossRef]

D. Hauser, P. Amayenc, and B. Nutten, "A new optical instrument for simultaneous measurement of raindrop diameter and fall speed distributions," J. Atmos. Ocean. Technol. 1, 256-269 (1984).
[CrossRef]

M. Löffler-Mang and J. Joss, "An optical disdrometer for measuring size and velocity of hydrometeors," J. Atmos. Ocean. Technol. 17, 130-139 (2000).
[CrossRef]

A. Kruger and W. F. Krajewski, "Two-dimensional video disdrometer: a description," J. Atmos. Ocean. Technol. 19, 602-617 (2002).
[CrossRef]

V. Nĕspor, W. F. Krajewski, and A. Kruger, "Wind-induced error of raindrop size distribution measurement using a two-dimensional video disdrometer," J. Atmos. Ocean. Technol. 17, 1483-1492 (2000).
[CrossRef]

J. Atmos. Sci.

R. A. Black and J. Hallett, "Observations of the distribution of ice in hurricanes," J. Atmos. Sci. 43, 802-822 (1986).
[CrossRef]

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

K. V. Beard, R. J. Kubesh, and H. T. Ochs, "Laboratory measurements of small raindrop distortion, Pt. 1: axis ratios and fall behavior," J. Atmos. Sci. 48, 698-710 (1991).
[CrossRef]

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

J. Fluorine Chem.

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

J. Hydrol.

J.-Y. Delahaye, L. Barthès, P. Golé, J. Lavergnat, and J. P. Vinson, "A dual-beam spectropluviometer concept," J. Hydrol. 328, 110-120 (2006).
[CrossRef]

J. Rech. Atmos.

G. Donnadieu, "Mesure de la vitesse terminale des gouttes du pluie au sol à l'aide du spectropluviomètre VIDIAZ," J. Rech. Atmos. 12, 245-259 (1978).

Man Cybern.

M. C. Shin, D. B. Goldgof, K. W. Bowyer, and S. Nikiforou, "Comparison of edge detection algorithms using a structure from motion task," IEEE Trans. Syst. Man Cybern. 31, 589-601 (2001).
[CrossRef]

Pattern Recogn.

K. S. Fu and J. K. Mui, "A survey on image segmentation," Pattern Recogn. 13, 3-16 (1981).
[CrossRef]

Proc. IEEE

A. Rosenfeld, "A nonlinear edge detection technique," Proc. IEEE 58, 814-816 (1970).
[CrossRef]

I. E. Abdou and W. Pratt, "Quantitative design and evaluation of enhancement/thresholding edge detectors," Proc. IEEE 67, 753-763 (1979).
[CrossRef]

I. D. G. Macleod, "Comments on techniques of edge detection," Proc. IEEE 60, 344 (1972).
[CrossRef]

Pure Appl. Geophys.

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

Radio Sci.

K. V. Beard, "Oscillation models for predicting raindrop axis and backscatter ratios," Radio Sci. 19, 67-74 (1984).
[CrossRef]

Rev. Sci. Instrum.

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]

submitted to Opt. Eng.

N. A. Sivasubramanian and J. R. Saylor, "Application of a histogram modification algorithm to thresholding of raindrop images," submitted to Opt. Eng.

Technical Report TR-569

R. A. Hummel, "Edge detection using basis functions," Technical Report TR-569 (University of Maryland, 1977).

Other

J. M. S. Prewitt, "Object enhancement and extraction," in Picture Processing and Psychopictorics, B. S. Lipkin and A. Rosenfeld, eds. (Academic, 1970).

K. C. Hayes and A. Rosenfeld, "Efficient edge detectors and applications," Technical Report TR-207 (University of Maryland, 1972).

I. D. G. Macleod, "On finding structure in pictures," in Picture Language Machines, S. Kaneff, ed. (Academic, 1970), pp. 231-256.

M. Sonka, V. Hlavac, and R. Boyle, Image Processing Analysis and Machine Vision (Thomson-Engineering, 1999).

D. Vernon, Machine Vision (Prentice Hall, 1991).

E. Trucco and A. Verri, Introductory Techniques for 3-D Computer Vision (Prentice Hall, 1998).

I. E. Sobel, Camera Models and Machine Perception (Stanford U. Press, 1970).

L. Mero and Z. Vassy, "A simplified and fast version of the Hueckel operator for finding optimal edges in pictures," in Proceedings of the 4th International Joint Conference on Artificial Intelligence (ASCE, 1975), pp. 650-655.

L. Rosenthaler, F. Heitger, O. Kübler, and R. von der Heydt, "Detection of general edges and keypoints," in Proceedings of the European Conference on Computer Vision, (1992), pp. 78-86.

C. A. Rothwell, J. L. Mundy, W. Hoffman, and V.-D. Nguyen, "Driving vision by topology," in IEEE International Symposium on Computer Vision (IEEE, 1995), pp. 395-400.

L. G. Roberts, "Machine perception of three-dimensional solids," in Optical and Electro-optical Information Processing, J. T. Tippet, D. A. Berkowitz, L. C. Clapp, C. J. Koester and A. Vanderburgh, eds. (MIT Press, 1965), pp. 159-197.

J. H. G. Hale, "Dectection of elementary features in a picture by non-linear local numerical processing," in Proceedings of the 3rd International Joint Conference on Pattern Recognition (1976), pp. 764-768.

K. R. Castleman, Digital Image Processing (Prentice Hall, 1996).

L. Bliven (personal communication, 2001).

R. G. Knollenberg, Clouds: Their Formation, Optical Properties, and Effects (Academic, 1981), pp. 15-89.

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

V. N. Bringi and V. Chandrasekar, Polarimetric Doppler Weather Radar (Cambridge U. Press, 2001).

P. Meischner, Weather Radar (Springer, 2004).

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).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Raindrop imaging setup.

Fig. 2
Fig. 2

Sample gray scale images taken by the system illustrated in Fig. 1: (a) In-focus drop, (b) out-of-focus drop.

Fig. 3
Fig. 3

(a) Edge-enhanced version of the sample gray scale image presented in Fig. 2(a). The Sobel operator was used in this case. (b) Binary image obtained after thresholding the edge enhanced image in (a). The slightly oval shape of the white portion in the center of the image is due to a difference in the x and y-direction pixel resolutions, discussed in Section 4.

Fig. 4
Fig. 4

Sample gray scale images of an M g F 2 sphere. (a) In-focus and (b) out-of-focus.

Fig. 5
Fig. 5

Laboratory setup used to collect images of M g F 2 spheres of different diameters and at different z-locations.

Fig. 6
Fig. 6

Sample gray scale images of a 5 mm sphere at three different z-locations.

Fig. 7
Fig. 7

Sample binary images of a 5 mm sphere after the application of the edge detection algorithms.

Fig. 8
Fig. 8

Variation of D m with z using the Canny algorithm for actual diameters of (a) 3 mm, (b) 4 mm, (c) 5 mm, (d) 6 mm, (e) 7 mm, and (f) 8 mm.

Fig. 9
Fig. 9

Variation of D m with z using the Hueckel algorithm for sphere diameters of (a) 3 mm, (b) 4 mm, (c) 5 mm, (d) 6 mm, (e) 7 mm, and (f) 8 mm.

Fig. 10
Fig. 10

Plot of d o f versus D for each edge detection algorithm. The line through each data is a simple linear interpolation between each point.

Fig. 11
Fig. 11

Plot of D versus D (the actual diameter) for each of the edge detection algorithms.

Fig. 12
Fig. 12

Plots of D m versus z for two of the edge detection methods presented here: (a) Hueckel and (b) Roberts. Also included is (c) a histogram modification method due to Peleg [70]. While there are differences in the D m versus z behavior for the edge detection algorithms presented in this work, the behavior among these algorithms is quite similar when compared to different algorithmic approaches. (plot (c) obtained from Sivasubramanian and Saylor [35]).

Fig. 13
Fig. 13

Plot of d o f versus D for the Hueckel algorithm with quadratic fit.

Fig. 14
Fig. 14

Plot of E versus D, both in mm.

Tables (3)

Tables Icon

Table 1 Depth of Field dof (cm) for the Different Edge Detection Algorithms for Each Sphere Diameter

Tables Icon

Table 2 Average Measured Diameter D (mm) for the Different Edge Detection Algorithms for Each Sphere Diameter

Tables Icon

Table 3 Slope and Intercept of the Linear Fits to the D versus D Data Presented in Fig. 11

Equations (25)

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

Z = 0 D 6 N ( D ) d D ,
R = π 6 0 D 3 N ( D ) w t ( D ) d D ,
N ( D ) = N 0 e Λ D ,
Z = N 0 ( 6 ! ) Λ 7 .
e = ( 1 α 2 ) 1 / 2 ,
α = v / h ,
d o f = z e z s ,
H 1 = [ 1 0 0 1 ] ,     H 2 = [ 0 1 1 0 ] .
g ( i , j ) = [ g 1 2 ( i , j ) + g 2 2 ( i , j ) ] 1 / 2 ,
        f ( r ) ( i , j ) = [ m = i r i + r n = j r j + r f ( m , n ) ] ( 2 r + 1 ) 2 .
L ( d ) ( i , j ) = L ( r 1 , d ) ( i , j ) × L ( r 1 + 1 , d ) ( i , j ) × × L ( r 2 , d ) .
L ( i , j ) = m a x [ L ( d ) ( i , j ) ] .
S ( x , y , b , h , ρ , θ ) = { b ( x c o s θ + y s i n θ ) < ρ b + h ( x c o s θ + y s i n θ ) ρ ,
G ( i , j ) = e ( i 2 + j 2 2 σ 2 ) ,
θ ( i , j ) = t a n 1 ( g j ( i , j ) g i ( i , j ) ) ,
H ( i , j ) = e x p ( i 2 + j 2 d r 2 ) [ e x p ( ( d i j + d p k d p k ) 2 ) e x p ( ( d i j d p k d p k ) 2 ) ] ,
[ 1 1 1 0 0 0 1 1 1 ] [ 1 1 0 1 0 1 0 1 1 ] [ 1 0 1 1 0 1 1 0 1 ] [ 0 1 1 1 0 1 1 1 0 ]
[ 1 1 1 0 0 0 1 1 1 ] [ 1 1 0 1 0 1 0 1 1 ] [ 1 0 1 1 0 1 1 0 1 ] [ 0 1 1 1 0 1 1 1 0 ] .
H 1 = [ 1 0 1 2 0 2 1 0 1 ] ,     H 2 = [ 1 2 1 0 0 0 1 2 1 ] .
H 1 = [ 1 0 1 1 0 1 1 0 1 ] ,     H 2 = [ 1 1 1 0 0 0 1 1 1 ] ,
D m = 2 × A d π ,
A d = n p × 0.05 × 0.1 ,
D = 1 d o f z s z e P ( z ) d z ,
E m = | D m D | .
E = 1 d o f z s z e Q ( z ) d z .

Metrics