Abstract

Of the methods developed (e.g., phakometry, magnetic resonance imaging, etc.) for noninvasive measurement of the geometry of the anterior segment of the human eye, Scheimpflug photography offers the best resolution and the highest precision. The primary obstacle encountered with this or any other image-based method has been in obtaining quantitative measurements directly from the images. Image enhancement (gray-scale gradient analysis) and pattern recognition methods (Hough transform and recursive least-squares algorithms) are developed so that parametric representations of lens surfaces and zone boundaries can be obtained directly from the images. Methods to correct for nonlinear Scheimpflug camera reproduction ratios and provide error estimates for geometrical parameters are also developed and will be presented separately. Combined, these techniques yield representations of lens geometry having sufficient precision, to which paraxial ray tracing can be applied to determine lens optical properties by using well-posed optical models with one unknown.

© 1998 Optical Society of America

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References

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  1. N. A. P. Brown, “The shape of the lens equator,” Exp. Eye Res. 20, 571–576 (1974).
    [CrossRef]
  2. N. A. P. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
    [CrossRef] [PubMed]
  3. N. A. P. Brown, “The change in shape and internal form of the lens of the eye on accommodation,” Exp. Eye Res. 15, 441–459 (1973).
    [CrossRef] [PubMed]
  4. A. Hachiha, S. Simon, J. Samson, K. Hanna, “The use of gray-level information and fitting techniques for precise measurement of corneal curvature,” Comput. Vis. Graph. Image Process. 47, 131–164 (1989).
    [CrossRef]
  5. J. R. Kuszak, J. G. Sivak, J. A. Weerheim, “Lens optical quality is a direct function of lens sutural architecture,” Invest. Ophthalmol. Visual Sci. 32, 2119–2129 (1991).
  6. J. R. Kuszak, C. A. Ennesser, B. A. Bertram, S. Imherr-McMannis, L. S. Jones-Rufer, R. S. Weinstein, “The contribution of cell-to-cell fusion to the ordered structure of the crystalline lens,” Lens Toxicolo. Res. 6, 639–673 (1989).
  7. J. R. Kuszak, M. S. Macsai, K. J. Bloom, J. L. Rae, R. S. Weinstein, “Cell-to-cell fusion of lens fiber cells in situ: correlative light, scanning electron microscopic, and freeze-fracture studies,” J. Ultrastruct. Res. 93, 144–160 (1985).
    [CrossRef] [PubMed]
  8. P. V. C. Hough, “A method and means for recognizing complex patterns,” U.S. patent3,069,654 (December1962).
  9. T. M. Van Veen, F. C. A. Groen, “Discretization errors in the Hough transform,” Pattern Recogn. 14, 137–145 (1981).
    [CrossRef]
  10. J. Illingworth, J. Kittler, “A survey of the Hough transform,” Comput. Vis. Graph. Image Process. 44, 87–116 (1988).
    [CrossRef]
  11. A. Rosenfeld, Picture Processing by Computer (Academic, New York, 1969).
  12. C. A. Cook, J. F. Koretz, “Acquisition of the curves of the human crystalline lens from slit-lamp images: an ap-plication of the Hough transform,” Appl. Opt. 30, 2088–2099 (1991).
    [CrossRef] [PubMed]
  13. N. A. P. Brown, “An advanced slit-lamp camera,” Br. J. Ophthamol. 56, 624–631 (1972).
    [CrossRef]
  14. J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye. 1: Evaluation of in vivo measurement techniques,” Appl. Opt. 28, 1097–1102 (1989).
    [CrossRef] [PubMed]
  15. J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
    [CrossRef]
  16. R. J. Schalkoff, Digital Image Processing and Computer Vision (Wiley, New York, 1989).
  17. J. F. Koretz, G. H. Handelman, N. A. P. Brown, “Analysis of human crystalline lens curvature as a function of accommodative state and age,” Vision Res. 24, 1141–1151 (1984).
    [CrossRef] [PubMed]
  18. R. L. Ricks, “Use of overlap in the Hough and fast Hough transforms,” in Advanced Algorithms and Architectures for Signal Processing IV, F. T. Luk, ed., Proc. SPIE1152, 225–233 (1989).
    [CrossRef]
  19. D. H. Johnson, “Application of the Hough transform to Doppler-time image processing,” in Proceedings of the International Conference on Acoustics, Speech and Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1988), pp. 1212–1215.
  20. R. O. Duda, P. E. Hart, “Use of the Hough transformation to detect lines and curves in pictures,” Commun. ACM 15, 11–15 (1972).
    [CrossRef]
  21. R. S. Conker, “A dual plane variation of the Hough transform for detecting nonconcentric circles of different radii,” Comput. Vis. Graph. Image Process. 43, 115–132 (1988).
    [CrossRef]
  22. S. Tsuji, F. Matsumoto, “Detection of elliptic and linear edges by searching two parameter spaces,” IEEE Trans. Comput. C-27, 777–781 (1979).
    [CrossRef]
  23. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

1991 (2)

J. R. Kuszak, J. G. Sivak, J. A. Weerheim, “Lens optical quality is a direct function of lens sutural architecture,” Invest. Ophthalmol. Visual Sci. 32, 2119–2129 (1991).

C. A. Cook, J. F. Koretz, “Acquisition of the curves of the human crystalline lens from slit-lamp images: an ap-plication of the Hough transform,” Appl. Opt. 30, 2088–2099 (1991).
[CrossRef] [PubMed]

1989 (4)

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye. 1: Evaluation of in vivo measurement techniques,” Appl. Opt. 28, 1097–1102 (1989).
[CrossRef] [PubMed]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

J. R. Kuszak, C. A. Ennesser, B. A. Bertram, S. Imherr-McMannis, L. S. Jones-Rufer, R. S. Weinstein, “The contribution of cell-to-cell fusion to the ordered structure of the crystalline lens,” Lens Toxicolo. Res. 6, 639–673 (1989).

A. Hachiha, S. Simon, J. Samson, K. Hanna, “The use of gray-level information and fitting techniques for precise measurement of corneal curvature,” Comput. Vis. Graph. Image Process. 47, 131–164 (1989).
[CrossRef]

1988 (2)

J. Illingworth, J. Kittler, “A survey of the Hough transform,” Comput. Vis. Graph. Image Process. 44, 87–116 (1988).
[CrossRef]

R. S. Conker, “A dual plane variation of the Hough transform for detecting nonconcentric circles of different radii,” Comput. Vis. Graph. Image Process. 43, 115–132 (1988).
[CrossRef]

1985 (1)

J. R. Kuszak, M. S. Macsai, K. J. Bloom, J. L. Rae, R. S. Weinstein, “Cell-to-cell fusion of lens fiber cells in situ: correlative light, scanning electron microscopic, and freeze-fracture studies,” J. Ultrastruct. Res. 93, 144–160 (1985).
[CrossRef] [PubMed]

1984 (1)

J. F. Koretz, G. H. Handelman, N. A. P. Brown, “Analysis of human crystalline lens curvature as a function of accommodative state and age,” Vision Res. 24, 1141–1151 (1984).
[CrossRef] [PubMed]

1981 (1)

T. M. Van Veen, F. C. A. Groen, “Discretization errors in the Hough transform,” Pattern Recogn. 14, 137–145 (1981).
[CrossRef]

1979 (1)

S. Tsuji, F. Matsumoto, “Detection of elliptic and linear edges by searching two parameter spaces,” IEEE Trans. Comput. C-27, 777–781 (1979).
[CrossRef]

1974 (2)

N. A. P. Brown, “The shape of the lens equator,” Exp. Eye Res. 20, 571–576 (1974).
[CrossRef]

N. A. P. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
[CrossRef] [PubMed]

1973 (1)

N. A. P. Brown, “The change in shape and internal form of the lens of the eye on accommodation,” Exp. Eye Res. 15, 441–459 (1973).
[CrossRef] [PubMed]

1972 (2)

N. A. P. Brown, “An advanced slit-lamp camera,” Br. J. Ophthamol. 56, 624–631 (1972).
[CrossRef]

R. O. Duda, P. E. Hart, “Use of the Hough transformation to detect lines and curves in pictures,” Commun. ACM 15, 11–15 (1972).
[CrossRef]

Bertram, B. A.

J. R. Kuszak, C. A. Ennesser, B. A. Bertram, S. Imherr-McMannis, L. S. Jones-Rufer, R. S. Weinstein, “The contribution of cell-to-cell fusion to the ordered structure of the crystalline lens,” Lens Toxicolo. Res. 6, 639–673 (1989).

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

Bloom, K. J.

J. R. Kuszak, M. S. Macsai, K. J. Bloom, J. L. Rae, R. S. Weinstein, “Cell-to-cell fusion of lens fiber cells in situ: correlative light, scanning electron microscopic, and freeze-fracture studies,” J. Ultrastruct. Res. 93, 144–160 (1985).
[CrossRef] [PubMed]

Brown, N. A. P.

J. F. Koretz, G. H. Handelman, N. A. P. Brown, “Analysis of human crystalline lens curvature as a function of accommodative state and age,” Vision Res. 24, 1141–1151 (1984).
[CrossRef] [PubMed]

N. A. P. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
[CrossRef] [PubMed]

N. A. P. Brown, “The shape of the lens equator,” Exp. Eye Res. 20, 571–576 (1974).
[CrossRef]

N. A. P. Brown, “The change in shape and internal form of the lens of the eye on accommodation,” Exp. Eye Res. 15, 441–459 (1973).
[CrossRef] [PubMed]

N. A. P. Brown, “An advanced slit-lamp camera,” Br. J. Ophthamol. 56, 624–631 (1972).
[CrossRef]

Conker, R. S.

R. S. Conker, “A dual plane variation of the Hough transform for detecting nonconcentric circles of different radii,” Comput. Vis. Graph. Image Process. 43, 115–132 (1988).
[CrossRef]

Cook, C. A.

Duda, R. O.

R. O. Duda, P. E. Hart, “Use of the Hough transformation to detect lines and curves in pictures,” Commun. ACM 15, 11–15 (1972).
[CrossRef]

Ennesser, C. A.

J. R. Kuszak, C. A. Ennesser, B. A. Bertram, S. Imherr-McMannis, L. S. Jones-Rufer, R. S. Weinstein, “The contribution of cell-to-cell fusion to the ordered structure of the crystalline lens,” Lens Toxicolo. Res. 6, 639–673 (1989).

Goeckner, P. A.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye. 1: Evaluation of in vivo measurement techniques,” Appl. Opt. 28, 1097–1102 (1989).
[CrossRef] [PubMed]

Groen, F. C. A.

T. M. Van Veen, F. C. A. Groen, “Discretization errors in the Hough transform,” Pattern Recogn. 14, 137–145 (1981).
[CrossRef]

Hachiha, A.

A. Hachiha, S. Simon, J. Samson, K. Hanna, “The use of gray-level information and fitting techniques for precise measurement of corneal curvature,” Comput. Vis. Graph. Image Process. 47, 131–164 (1989).
[CrossRef]

Handelman, G. H.

J. F. Koretz, G. H. Handelman, N. A. P. Brown, “Analysis of human crystalline lens curvature as a function of accommodative state and age,” Vision Res. 24, 1141–1151 (1984).
[CrossRef] [PubMed]

Hanna, K.

A. Hachiha, S. Simon, J. Samson, K. Hanna, “The use of gray-level information and fitting techniques for precise measurement of corneal curvature,” Comput. Vis. Graph. Image Process. 47, 131–164 (1989).
[CrossRef]

Hart, P. E.

R. O. Duda, P. E. Hart, “Use of the Hough transformation to detect lines and curves in pictures,” Commun. ACM 15, 11–15 (1972).
[CrossRef]

Hough, P. V. C.

P. V. C. Hough, “A method and means for recognizing complex patterns,” U.S. patent3,069,654 (December1962).

Illingworth, J.

J. Illingworth, J. Kittler, “A survey of the Hough transform,” Comput. Vis. Graph. Image Process. 44, 87–116 (1988).
[CrossRef]

Imherr-McMannis, S.

J. R. Kuszak, C. A. Ennesser, B. A. Bertram, S. Imherr-McMannis, L. S. Jones-Rufer, R. S. Weinstein, “The contribution of cell-to-cell fusion to the ordered structure of the crystalline lens,” Lens Toxicolo. Res. 6, 639–673 (1989).

Johnson, D. H.

D. H. Johnson, “Application of the Hough transform to Doppler-time image processing,” in Proceedings of the International Conference on Acoustics, Speech and Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1988), pp. 1212–1215.

Jones-Rufer, L. S.

J. R. Kuszak, C. A. Ennesser, B. A. Bertram, S. Imherr-McMannis, L. S. Jones-Rufer, R. S. Weinstein, “The contribution of cell-to-cell fusion to the ordered structure of the crystalline lens,” Lens Toxicolo. Res. 6, 639–673 (1989).

Kaufman, P. L.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye. 1: Evaluation of in vivo measurement techniques,” Appl. Opt. 28, 1097–1102 (1989).
[CrossRef] [PubMed]

Kittler, J.

J. Illingworth, J. Kittler, “A survey of the Hough transform,” Comput. Vis. Graph. Image Process. 44, 87–116 (1988).
[CrossRef]

Koretz, J. F.

C. A. Cook, J. F. Koretz, “Acquisition of the curves of the human crystalline lens from slit-lamp images: an ap-plication of the Hough transform,” Appl. Opt. 30, 2088–2099 (1991).
[CrossRef] [PubMed]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye. 1: Evaluation of in vivo measurement techniques,” Appl. Opt. 28, 1097–1102 (1989).
[CrossRef] [PubMed]

J. F. Koretz, G. H. Handelman, N. A. P. Brown, “Analysis of human crystalline lens curvature as a function of accommodative state and age,” Vision Res. 24, 1141–1151 (1984).
[CrossRef] [PubMed]

Kuszak, J. R.

J. R. Kuszak, J. G. Sivak, J. A. Weerheim, “Lens optical quality is a direct function of lens sutural architecture,” Invest. Ophthalmol. Visual Sci. 32, 2119–2129 (1991).

J. R. Kuszak, C. A. Ennesser, B. A. Bertram, S. Imherr-McMannis, L. S. Jones-Rufer, R. S. Weinstein, “The contribution of cell-to-cell fusion to the ordered structure of the crystalline lens,” Lens Toxicolo. Res. 6, 639–673 (1989).

J. R. Kuszak, M. S. Macsai, K. J. Bloom, J. L. Rae, R. S. Weinstein, “Cell-to-cell fusion of lens fiber cells in situ: correlative light, scanning electron microscopic, and freeze-fracture studies,” J. Ultrastruct. Res. 93, 144–160 (1985).
[CrossRef] [PubMed]

Macsai, M. S.

J. R. Kuszak, M. S. Macsai, K. J. Bloom, J. L. Rae, R. S. Weinstein, “Cell-to-cell fusion of lens fiber cells in situ: correlative light, scanning electron microscopic, and freeze-fracture studies,” J. Ultrastruct. Res. 93, 144–160 (1985).
[CrossRef] [PubMed]

Matsumoto, F.

S. Tsuji, F. Matsumoto, “Detection of elliptic and linear edges by searching two parameter spaces,” IEEE Trans. Comput. C-27, 777–781 (1979).
[CrossRef]

Neider, M. W.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye. 1: Evaluation of in vivo measurement techniques,” Appl. Opt. 28, 1097–1102 (1989).
[CrossRef] [PubMed]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

Rae, J. L.

J. R. Kuszak, M. S. Macsai, K. J. Bloom, J. L. Rae, R. S. Weinstein, “Cell-to-cell fusion of lens fiber cells in situ: correlative light, scanning electron microscopic, and freeze-fracture studies,” J. Ultrastruct. Res. 93, 144–160 (1985).
[CrossRef] [PubMed]

Ricks, R. L.

R. L. Ricks, “Use of overlap in the Hough and fast Hough transforms,” in Advanced Algorithms and Architectures for Signal Processing IV, F. T. Luk, ed., Proc. SPIE1152, 225–233 (1989).
[CrossRef]

Rosenfeld, A.

A. Rosenfeld, Picture Processing by Computer (Academic, New York, 1969).

Samson, J.

A. Hachiha, S. Simon, J. Samson, K. Hanna, “The use of gray-level information and fitting techniques for precise measurement of corneal curvature,” Comput. Vis. Graph. Image Process. 47, 131–164 (1989).
[CrossRef]

Schalkoff, R. J.

R. J. Schalkoff, Digital Image Processing and Computer Vision (Wiley, New York, 1989).

Simon, S.

A. Hachiha, S. Simon, J. Samson, K. Hanna, “The use of gray-level information and fitting techniques for precise measurement of corneal curvature,” Comput. Vis. Graph. Image Process. 47, 131–164 (1989).
[CrossRef]

Sivak, J. G.

J. R. Kuszak, J. G. Sivak, J. A. Weerheim, “Lens optical quality is a direct function of lens sutural architecture,” Invest. Ophthalmol. Visual Sci. 32, 2119–2129 (1991).

Tsuji, S.

S. Tsuji, F. Matsumoto, “Detection of elliptic and linear edges by searching two parameter spaces,” IEEE Trans. Comput. C-27, 777–781 (1979).
[CrossRef]

Van Veen, T. M.

T. M. Van Veen, F. C. A. Groen, “Discretization errors in the Hough transform,” Pattern Recogn. 14, 137–145 (1981).
[CrossRef]

Weerheim, J. A.

J. R. Kuszak, J. G. Sivak, J. A. Weerheim, “Lens optical quality is a direct function of lens sutural architecture,” Invest. Ophthalmol. Visual Sci. 32, 2119–2129 (1991).

Weinstein, R. S.

J. R. Kuszak, C. A. Ennesser, B. A. Bertram, S. Imherr-McMannis, L. S. Jones-Rufer, R. S. Weinstein, “The contribution of cell-to-cell fusion to the ordered structure of the crystalline lens,” Lens Toxicolo. Res. 6, 639–673 (1989).

J. R. Kuszak, M. S. Macsai, K. J. Bloom, J. L. Rae, R. S. Weinstein, “Cell-to-cell fusion of lens fiber cells in situ: correlative light, scanning electron microscopic, and freeze-fracture studies,” J. Ultrastruct. Res. 93, 144–160 (1985).
[CrossRef] [PubMed]

Appl. Opt. (2)

Br. J. Ophthamol. (1)

N. A. P. Brown, “An advanced slit-lamp camera,” Br. J. Ophthamol. 56, 624–631 (1972).
[CrossRef]

Commun. ACM (1)

R. O. Duda, P. E. Hart, “Use of the Hough transformation to detect lines and curves in pictures,” Commun. ACM 15, 11–15 (1972).
[CrossRef]

Comput. Vis. Graph. Image Process. (3)

R. S. Conker, “A dual plane variation of the Hough transform for detecting nonconcentric circles of different radii,” Comput. Vis. Graph. Image Process. 43, 115–132 (1988).
[CrossRef]

A. Hachiha, S. Simon, J. Samson, K. Hanna, “The use of gray-level information and fitting techniques for precise measurement of corneal curvature,” Comput. Vis. Graph. Image Process. 47, 131–164 (1989).
[CrossRef]

J. Illingworth, J. Kittler, “A survey of the Hough transform,” Comput. Vis. Graph. Image Process. 44, 87–116 (1988).
[CrossRef]

Exp. Eye Res. (3)

N. A. P. Brown, “The shape of the lens equator,” Exp. Eye Res. 20, 571–576 (1974).
[CrossRef]

N. A. P. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
[CrossRef] [PubMed]

N. A. P. Brown, “The change in shape and internal form of the lens of the eye on accommodation,” Exp. Eye Res. 15, 441–459 (1973).
[CrossRef] [PubMed]

IEEE Trans. Comput. (1)

S. Tsuji, F. Matsumoto, “Detection of elliptic and linear edges by searching two parameter spaces,” IEEE Trans. Comput. C-27, 777–781 (1979).
[CrossRef]

Invest. Ophthalmol. Visual Sci. (1)

J. R. Kuszak, J. G. Sivak, J. A. Weerheim, “Lens optical quality is a direct function of lens sutural architecture,” Invest. Ophthalmol. Visual Sci. 32, 2119–2129 (1991).

J. Ultrastruct. Res. (1)

J. R. Kuszak, M. S. Macsai, K. J. Bloom, J. L. Rae, R. S. Weinstein, “Cell-to-cell fusion of lens fiber cells in situ: correlative light, scanning electron microscopic, and freeze-fracture studies,” J. Ultrastruct. Res. 93, 144–160 (1985).
[CrossRef] [PubMed]

Lens Toxicolo. Res. (1)

J. R. Kuszak, C. A. Ennesser, B. A. Bertram, S. Imherr-McMannis, L. S. Jones-Rufer, R. S. Weinstein, “The contribution of cell-to-cell fusion to the ordered structure of the crystalline lens,” Lens Toxicolo. Res. 6, 639–673 (1989).

Pattern Recogn. (1)

T. M. Van Veen, F. C. A. Groen, “Discretization errors in the Hough transform,” Pattern Recogn. 14, 137–145 (1981).
[CrossRef]

Vision Res. (2)

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

J. F. Koretz, G. H. Handelman, N. A. P. Brown, “Analysis of human crystalline lens curvature as a function of accommodative state and age,” Vision Res. 24, 1141–1151 (1984).
[CrossRef] [PubMed]

Other (6)

R. L. Ricks, “Use of overlap in the Hough and fast Hough transforms,” in Advanced Algorithms and Architectures for Signal Processing IV, F. T. Luk, ed., Proc. SPIE1152, 225–233 (1989).
[CrossRef]

D. H. Johnson, “Application of the Hough transform to Doppler-time image processing,” in Proceedings of the International Conference on Acoustics, Speech and Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1988), pp. 1212–1215.

R. J. Schalkoff, Digital Image Processing and Computer Vision (Wiley, New York, 1989).

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

P. V. C. Hough, “A method and means for recognizing complex patterns,” U.S. patent3,069,654 (December1962).

A. Rosenfeld, Picture Processing by Computer (Academic, New York, 1969).

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Figures (10)

Fig. 1
Fig. 1

Reproduction of digitized CL section of a Scheimpflug image of an 18-year-old lens at 6.25-Dpt accommodation.

Fig. 2
Fig. 2

Same as Fig. 1, but for the digitized WL section.

Fig. 3
Fig. 3

Example set of 5×5 gradient scanning kernels.

Fig. 4
Fig. 4

Results from image in Fig. 1 after gradient scanning on cornea (upper) and lens (lower).

Fig. 5
Fig. 5

Results from image in Fig. 4. Angular separation is shown by crosses (upper); the pairs representing the curve selected by the first Hough algorithm are shown by crosses (lower).

Fig. 6
Fig. 6

Geometry of epsilon search for corresponding points.

Fig. 7
Fig. 7

Final curves from image in Fig. 5, showing anterior corneal (upper) and lens (lower) surfaces.

Fig. 8
Fig. 8

Results from image in Fig. 2. Angular separation is shown by crosses (upper); the pairs representing the curve selected by the second Hough algorithm are shown by crosses (lower).

Fig. 9
Fig. 9

Final curve for anterior lens nuclear boundary from images in Fig. 8.

Fig. 10
Fig. 10

(a) Curves obtained for corneal surfaces, lens surfaces, and zones of discontinuity from the illustrative subject at -3-Dpt refractive error (0-Dpt accommodation), (b) those for the same subject at -12.25-Dpt refractive error (9.25-Dpt accommodation). Units are in screen coordinates (pixels).

Tables (2)

Tables Icon

Table 1 Coefficients τ, υ, and R, Along with Their Error Estimates, for the Parabolic Curves Shown in Fig. 10(a) for the Subject at 0-Dpt Accommodationa

Tables Icon

Table 2 Same as Table 1, but for the Parabolic Curves Shown in Fig. 10(b)a

Equations (43)

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

|Gi|=[(Gi(x))2+(Gi(y))2]1/2,
arg(Gi)=tan-1(Gi(y)/Gi(x))+π,
y=υ+(x-τ)2ϑ.
h: (xi, yi)=(τ, υ, ϑ)τ×υ×ϑϑ=(xi-τ)2yi-υ.
Ω={τ-p, τ-p+1, , τp|τ-p<τ-p+1<<τ0<<τp},
Ξ={υ-q, υ-q+1, , υq|υ-q<υ-q+1<<υ0<<υq},
{ϑ1, ϑ2, , ϑrRr|ϑ1<ϑ2<<ϑr},
τi=xc+Sτ(i-p-1),i=1, 2, , 2p+1,
υi=yc+Sυ(i-q-1),i=1, 2, , 2q+1,
g(xi, yi)=(dj, τk, υl)d×Ω×Ξj=[ϑ(τk, υl)-ϑmin]/δϑ(ϑ|ϑmin<ϑ<ϑmax),k=1, , 2p+1,l=1, , 2q+1,
ϑ(τk, υl)=(xi-τk)2yi-υl.
τ=xc+Sτ(k-p-1),
υ=yc+Sυ(l-q-1),
ϑ=ϑmin+δϑ(j-1).
Nov=11-%ov,
Nov=2nov+1.
g(xi, yi)=(dj, τk, υl)j-novjj+nov,j=[ϑ(τk, υl)-ϑmin]/δϑ(ϑ|ϑmin<ϑ<ϑmax),k=1, , 2p+1,l=1, , 2q+1.
yi=tanarg(Gi)-π2.
ϑ=2yi(xi-τ),
υ=yi-yi2(xi-τ).
{(xi, yi; yi)R3|i=1, , n2}.
m=yi2,b=yi-xiyi2.
{υ-q, υ-q+1, , υqR2q+1|υ-q<υ-q+1<<υ0<<υq},
g:(xi, yi; yi)=(bk, τl)b×Ωk-novkk+nov,k=q+Sυ(υ(τl)-yc)(ϑmin<ϑ(τl)<ϑmax)l=1, , 2p+1,
Bk,l(i+1)=ϑ(τl)+(Ak,l-1)Bk,l(i)Ak,l.
τ=xc+Sτ(l-p-1),
υ=yc+Sυ(k-q-1),
ϑ=m=-novnovn=-novnovAm+k,n+lBm+k,n+lm=-novnovn=-novnovAm+k,n+l.
p=(x-τ)2,
q=y-υ
=|ϑ(yi-υ)-(xi-τ)2|1+ϑ2.
y=1-y240,
x=1-x320
τ=160 β+2γγ,
υ=240(1-α-β-γ)+60 (β+2γ)2γ,
ϑ=-32022401γ.
αjk=i1σi2X(xj)X(xk).
σi=σ2s2=1N-4j=1N(yj-a1-a2xj-a3xj2)2.
σaks2kk(σi=1).
αjk=i=1NxiN2/(j+k-2)j+k-2.
στ2=σa2212a32+σa32a22a322,
συ2=σa12+σa22a22a32+σa32a224a322,
σϑ2=σa32a322.

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