Abstract

We present a procedure whereby the confocal laser scanning ophthalmoscope can be used to extract information about the three-dimensional structure of the central excavated area or the cup of the optic nerve head of the eye. The data are analyzed in terms of spherical harmonics. It is hypothesized that the shape of the cup of the optic nerve head for a normal eye can be parameterized by a specific set of spherical harmonic coefficients and is different from the set of coefficients describing a glaucomatous eye. The sets of coefficients are analyzed by using multivariate statistics and can in turn be used to classify new observations. Preliminary results indicate that there are significant differences in the coefficients and that the procedure might have potential as a diagnostic aid for the detection or the screening of glaucoma.

© 2000 Optical Society of America

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References

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  1. J. Caprioli, “Correlations of visual function with nerve and nerve fibre layer structure in glaucoma,” Surv. Ophthalmol. 33, 319–330 (1989).
  2. V. Cucevic, A. M. V. Brooks, N. T. Strang, A. G. Klein, K. A. Nugent, “Use of a laser confocal scanning ophthalmoscope to detect glaucomatous cupping of the optic disc,” Aust. N.Z. J. Ophthalmol. 25, 217–220 (1997).
    [CrossRef]
  3. S. M. Drance, M. Schulzer, B. Thomas, G. R. Douglas, “Multivariate analysis in glaucoma. Use of discriminant analysis in prediction glaucomatous visual field damage,” Arch. Ophthalmol. (Chicago) 99, 1019–1022 (1981).
    [CrossRef]
  4. R. O. W. Burk, J. König, K. Rohrschneider, H. Noack, H. E. Völcker, “Dreidimensionale papillentopographie mittels laser scanning tomographie: klinisches korrelat einer cluster-analyse,” Klin. Monatsbl. Augenheilkd. 204, 504–512 (1994).
    [CrossRef]
  5. P. J. Airaksinen, A. Tuulonen, H. I. Alanko, “Prediction of development of glaucoma in ocular hypertensive patients,” in Glaucoma Update IV, G. K. Krieglstein, ed. (Springer-Verlag, Berlin, 1991), pp. 183–186.
  6. S. M. Drance, M. Schulzer, G. R. Douglas, V. P. Sweeney, “Use of discriminant analysis. II. Identification of persons with glaucomatous visual field defects,” Arch. Ophthalmol. (Chicago) 96, 1571–1573 (1978).
    [CrossRef]
  7. J. Mathews, R. L. Walker, Mathematical Methods of Physics (Benjamin, New York, 1964).
  8. R. Weinreb, A. W. Dreher, J. F. Bille, “Quantitative assessment of the optic nerve head with the laser tomographic scanner,” Int. Ophthalmol. 13, 25–29 (1989).
    [CrossRef] [PubMed]
  9. W. H. Woon, F. W. Fitzke, A. C. Bird, J. Marshall, “Confocal imaging of the fundus using a scanning laser ophthalmoscope,” Br. J. Ophthamol. 76, 470–474 (1992).
    [CrossRef]
  10. G. A. Cioffi, A. L. Robin, R. D. Eastman, H. F. Perell, F. A. Sarfarazi, S. E. Kelman, “Confocal laser scanning ophthalmoscope: reproducibility of optic nerve head topographic measurements with the confocal laser scanning ophthalmoscope,” Ophthalmology 100, 57–62 (1993).
    [CrossRef] [PubMed]
  11. F. S. Mickelberg, K. Wijsman, M. Schulzer, “Reproducibility of topographic parameters obtained with the Heidelberg Retina Tomograph,” J. Glaucoma 2, 101–103 (1993).
  12. R. A. Johnson, D. W. Wichern, Applied Multivariate Statistical Analysis, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1988), p. 461; P. A. Lachenbruch, “Some misuses of discriminant analysis,” Methods Info. Med. 16, 255 (1977); M. M. Tatsouka, “Multivariate analysis of variance,” in Handbook of Multivariate Experimental Psychology, 2nd ed., J. R. Nesselroade, R. B. Cattell, eds. (Plenum, New York, 1988), p. 399.
  13. B. F. Ryan, B. L. Joiner, T. A. Ryan, Minitab Handbook, 2nd ed. (Duxbury, Boston, 1985); I. Gordon, R. Watson, Basic Statistics with Minitab (U. of Melbourne Press, Parkville, Australia, 1994).
  14. R. E. Kirsch, D. R. Anderson, “Clinical recognition of glaucomatous cupping,” Am. J. Ophthalmol. 75, 442–454 (1973).
    [PubMed]

1997 (1)

V. Cucevic, A. M. V. Brooks, N. T. Strang, A. G. Klein, K. A. Nugent, “Use of a laser confocal scanning ophthalmoscope to detect glaucomatous cupping of the optic disc,” Aust. N.Z. J. Ophthalmol. 25, 217–220 (1997).
[CrossRef]

1994 (1)

R. O. W. Burk, J. König, K. Rohrschneider, H. Noack, H. E. Völcker, “Dreidimensionale papillentopographie mittels laser scanning tomographie: klinisches korrelat einer cluster-analyse,” Klin. Monatsbl. Augenheilkd. 204, 504–512 (1994).
[CrossRef]

1993 (2)

G. A. Cioffi, A. L. Robin, R. D. Eastman, H. F. Perell, F. A. Sarfarazi, S. E. Kelman, “Confocal laser scanning ophthalmoscope: reproducibility of optic nerve head topographic measurements with the confocal laser scanning ophthalmoscope,” Ophthalmology 100, 57–62 (1993).
[CrossRef] [PubMed]

F. S. Mickelberg, K. Wijsman, M. Schulzer, “Reproducibility of topographic parameters obtained with the Heidelberg Retina Tomograph,” J. Glaucoma 2, 101–103 (1993).

1992 (1)

W. H. Woon, F. W. Fitzke, A. C. Bird, J. Marshall, “Confocal imaging of the fundus using a scanning laser ophthalmoscope,” Br. J. Ophthamol. 76, 470–474 (1992).
[CrossRef]

1989 (2)

J. Caprioli, “Correlations of visual function with nerve and nerve fibre layer structure in glaucoma,” Surv. Ophthalmol. 33, 319–330 (1989).

R. Weinreb, A. W. Dreher, J. F. Bille, “Quantitative assessment of the optic nerve head with the laser tomographic scanner,” Int. Ophthalmol. 13, 25–29 (1989).
[CrossRef] [PubMed]

1981 (1)

S. M. Drance, M. Schulzer, B. Thomas, G. R. Douglas, “Multivariate analysis in glaucoma. Use of discriminant analysis in prediction glaucomatous visual field damage,” Arch. Ophthalmol. (Chicago) 99, 1019–1022 (1981).
[CrossRef]

1978 (1)

S. M. Drance, M. Schulzer, G. R. Douglas, V. P. Sweeney, “Use of discriminant analysis. II. Identification of persons with glaucomatous visual field defects,” Arch. Ophthalmol. (Chicago) 96, 1571–1573 (1978).
[CrossRef]

1973 (1)

R. E. Kirsch, D. R. Anderson, “Clinical recognition of glaucomatous cupping,” Am. J. Ophthalmol. 75, 442–454 (1973).
[PubMed]

Airaksinen, P. J.

P. J. Airaksinen, A. Tuulonen, H. I. Alanko, “Prediction of development of glaucoma in ocular hypertensive patients,” in Glaucoma Update IV, G. K. Krieglstein, ed. (Springer-Verlag, Berlin, 1991), pp. 183–186.

Alanko, H. I.

P. J. Airaksinen, A. Tuulonen, H. I. Alanko, “Prediction of development of glaucoma in ocular hypertensive patients,” in Glaucoma Update IV, G. K. Krieglstein, ed. (Springer-Verlag, Berlin, 1991), pp. 183–186.

Anderson, D. R.

R. E. Kirsch, D. R. Anderson, “Clinical recognition of glaucomatous cupping,” Am. J. Ophthalmol. 75, 442–454 (1973).
[PubMed]

Bille, J. F.

R. Weinreb, A. W. Dreher, J. F. Bille, “Quantitative assessment of the optic nerve head with the laser tomographic scanner,” Int. Ophthalmol. 13, 25–29 (1989).
[CrossRef] [PubMed]

Bird, A. C.

W. H. Woon, F. W. Fitzke, A. C. Bird, J. Marshall, “Confocal imaging of the fundus using a scanning laser ophthalmoscope,” Br. J. Ophthamol. 76, 470–474 (1992).
[CrossRef]

Brooks, A. M. V.

V. Cucevic, A. M. V. Brooks, N. T. Strang, A. G. Klein, K. A. Nugent, “Use of a laser confocal scanning ophthalmoscope to detect glaucomatous cupping of the optic disc,” Aust. N.Z. J. Ophthalmol. 25, 217–220 (1997).
[CrossRef]

Burk, R. O. W.

R. O. W. Burk, J. König, K. Rohrschneider, H. Noack, H. E. Völcker, “Dreidimensionale papillentopographie mittels laser scanning tomographie: klinisches korrelat einer cluster-analyse,” Klin. Monatsbl. Augenheilkd. 204, 504–512 (1994).
[CrossRef]

Caprioli, J.

J. Caprioli, “Correlations of visual function with nerve and nerve fibre layer structure in glaucoma,” Surv. Ophthalmol. 33, 319–330 (1989).

Cioffi, G. A.

G. A. Cioffi, A. L. Robin, R. D. Eastman, H. F. Perell, F. A. Sarfarazi, S. E. Kelman, “Confocal laser scanning ophthalmoscope: reproducibility of optic nerve head topographic measurements with the confocal laser scanning ophthalmoscope,” Ophthalmology 100, 57–62 (1993).
[CrossRef] [PubMed]

Cucevic, V.

V. Cucevic, A. M. V. Brooks, N. T. Strang, A. G. Klein, K. A. Nugent, “Use of a laser confocal scanning ophthalmoscope to detect glaucomatous cupping of the optic disc,” Aust. N.Z. J. Ophthalmol. 25, 217–220 (1997).
[CrossRef]

Douglas, G. R.

S. M. Drance, M. Schulzer, B. Thomas, G. R. Douglas, “Multivariate analysis in glaucoma. Use of discriminant analysis in prediction glaucomatous visual field damage,” Arch. Ophthalmol. (Chicago) 99, 1019–1022 (1981).
[CrossRef]

S. M. Drance, M. Schulzer, G. R. Douglas, V. P. Sweeney, “Use of discriminant analysis. II. Identification of persons with glaucomatous visual field defects,” Arch. Ophthalmol. (Chicago) 96, 1571–1573 (1978).
[CrossRef]

Drance, S. M.

S. M. Drance, M. Schulzer, B. Thomas, G. R. Douglas, “Multivariate analysis in glaucoma. Use of discriminant analysis in prediction glaucomatous visual field damage,” Arch. Ophthalmol. (Chicago) 99, 1019–1022 (1981).
[CrossRef]

S. M. Drance, M. Schulzer, G. R. Douglas, V. P. Sweeney, “Use of discriminant analysis. II. Identification of persons with glaucomatous visual field defects,” Arch. Ophthalmol. (Chicago) 96, 1571–1573 (1978).
[CrossRef]

Dreher, A. W.

R. Weinreb, A. W. Dreher, J. F. Bille, “Quantitative assessment of the optic nerve head with the laser tomographic scanner,” Int. Ophthalmol. 13, 25–29 (1989).
[CrossRef] [PubMed]

Eastman, R. D.

G. A. Cioffi, A. L. Robin, R. D. Eastman, H. F. Perell, F. A. Sarfarazi, S. E. Kelman, “Confocal laser scanning ophthalmoscope: reproducibility of optic nerve head topographic measurements with the confocal laser scanning ophthalmoscope,” Ophthalmology 100, 57–62 (1993).
[CrossRef] [PubMed]

Fitzke, F. W.

W. H. Woon, F. W. Fitzke, A. C. Bird, J. Marshall, “Confocal imaging of the fundus using a scanning laser ophthalmoscope,” Br. J. Ophthamol. 76, 470–474 (1992).
[CrossRef]

Johnson, R. A.

R. A. Johnson, D. W. Wichern, Applied Multivariate Statistical Analysis, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1988), p. 461; P. A. Lachenbruch, “Some misuses of discriminant analysis,” Methods Info. Med. 16, 255 (1977); M. M. Tatsouka, “Multivariate analysis of variance,” in Handbook of Multivariate Experimental Psychology, 2nd ed., J. R. Nesselroade, R. B. Cattell, eds. (Plenum, New York, 1988), p. 399.

Joiner, B. L.

B. F. Ryan, B. L. Joiner, T. A. Ryan, Minitab Handbook, 2nd ed. (Duxbury, Boston, 1985); I. Gordon, R. Watson, Basic Statistics with Minitab (U. of Melbourne Press, Parkville, Australia, 1994).

Kelman, S. E.

G. A. Cioffi, A. L. Robin, R. D. Eastman, H. F. Perell, F. A. Sarfarazi, S. E. Kelman, “Confocal laser scanning ophthalmoscope: reproducibility of optic nerve head topographic measurements with the confocal laser scanning ophthalmoscope,” Ophthalmology 100, 57–62 (1993).
[CrossRef] [PubMed]

Kirsch, R. E.

R. E. Kirsch, D. R. Anderson, “Clinical recognition of glaucomatous cupping,” Am. J. Ophthalmol. 75, 442–454 (1973).
[PubMed]

Klein, A. G.

V. Cucevic, A. M. V. Brooks, N. T. Strang, A. G. Klein, K. A. Nugent, “Use of a laser confocal scanning ophthalmoscope to detect glaucomatous cupping of the optic disc,” Aust. N.Z. J. Ophthalmol. 25, 217–220 (1997).
[CrossRef]

König, J.

R. O. W. Burk, J. König, K. Rohrschneider, H. Noack, H. E. Völcker, “Dreidimensionale papillentopographie mittels laser scanning tomographie: klinisches korrelat einer cluster-analyse,” Klin. Monatsbl. Augenheilkd. 204, 504–512 (1994).
[CrossRef]

Marshall, J.

W. H. Woon, F. W. Fitzke, A. C. Bird, J. Marshall, “Confocal imaging of the fundus using a scanning laser ophthalmoscope,” Br. J. Ophthamol. 76, 470–474 (1992).
[CrossRef]

Mathews, J.

J. Mathews, R. L. Walker, Mathematical Methods of Physics (Benjamin, New York, 1964).

Mickelberg, F. S.

F. S. Mickelberg, K. Wijsman, M. Schulzer, “Reproducibility of topographic parameters obtained with the Heidelberg Retina Tomograph,” J. Glaucoma 2, 101–103 (1993).

Noack, H.

R. O. W. Burk, J. König, K. Rohrschneider, H. Noack, H. E. Völcker, “Dreidimensionale papillentopographie mittels laser scanning tomographie: klinisches korrelat einer cluster-analyse,” Klin. Monatsbl. Augenheilkd. 204, 504–512 (1994).
[CrossRef]

Nugent, K. A.

V. Cucevic, A. M. V. Brooks, N. T. Strang, A. G. Klein, K. A. Nugent, “Use of a laser confocal scanning ophthalmoscope to detect glaucomatous cupping of the optic disc,” Aust. N.Z. J. Ophthalmol. 25, 217–220 (1997).
[CrossRef]

Perell, H. F.

G. A. Cioffi, A. L. Robin, R. D. Eastman, H. F. Perell, F. A. Sarfarazi, S. E. Kelman, “Confocal laser scanning ophthalmoscope: reproducibility of optic nerve head topographic measurements with the confocal laser scanning ophthalmoscope,” Ophthalmology 100, 57–62 (1993).
[CrossRef] [PubMed]

Robin, A. L.

G. A. Cioffi, A. L. Robin, R. D. Eastman, H. F. Perell, F. A. Sarfarazi, S. E. Kelman, “Confocal laser scanning ophthalmoscope: reproducibility of optic nerve head topographic measurements with the confocal laser scanning ophthalmoscope,” Ophthalmology 100, 57–62 (1993).
[CrossRef] [PubMed]

Rohrschneider, K.

R. O. W. Burk, J. König, K. Rohrschneider, H. Noack, H. E. Völcker, “Dreidimensionale papillentopographie mittels laser scanning tomographie: klinisches korrelat einer cluster-analyse,” Klin. Monatsbl. Augenheilkd. 204, 504–512 (1994).
[CrossRef]

Ryan, B. F.

B. F. Ryan, B. L. Joiner, T. A. Ryan, Minitab Handbook, 2nd ed. (Duxbury, Boston, 1985); I. Gordon, R. Watson, Basic Statistics with Minitab (U. of Melbourne Press, Parkville, Australia, 1994).

Ryan, T. A.

B. F. Ryan, B. L. Joiner, T. A. Ryan, Minitab Handbook, 2nd ed. (Duxbury, Boston, 1985); I. Gordon, R. Watson, Basic Statistics with Minitab (U. of Melbourne Press, Parkville, Australia, 1994).

Sarfarazi, F. A.

G. A. Cioffi, A. L. Robin, R. D. Eastman, H. F. Perell, F. A. Sarfarazi, S. E. Kelman, “Confocal laser scanning ophthalmoscope: reproducibility of optic nerve head topographic measurements with the confocal laser scanning ophthalmoscope,” Ophthalmology 100, 57–62 (1993).
[CrossRef] [PubMed]

Schulzer, M.

F. S. Mickelberg, K. Wijsman, M. Schulzer, “Reproducibility of topographic parameters obtained with the Heidelberg Retina Tomograph,” J. Glaucoma 2, 101–103 (1993).

S. M. Drance, M. Schulzer, B. Thomas, G. R. Douglas, “Multivariate analysis in glaucoma. Use of discriminant analysis in prediction glaucomatous visual field damage,” Arch. Ophthalmol. (Chicago) 99, 1019–1022 (1981).
[CrossRef]

S. M. Drance, M. Schulzer, G. R. Douglas, V. P. Sweeney, “Use of discriminant analysis. II. Identification of persons with glaucomatous visual field defects,” Arch. Ophthalmol. (Chicago) 96, 1571–1573 (1978).
[CrossRef]

Strang, N. T.

V. Cucevic, A. M. V. Brooks, N. T. Strang, A. G. Klein, K. A. Nugent, “Use of a laser confocal scanning ophthalmoscope to detect glaucomatous cupping of the optic disc,” Aust. N.Z. J. Ophthalmol. 25, 217–220 (1997).
[CrossRef]

Sweeney, V. P.

S. M. Drance, M. Schulzer, G. R. Douglas, V. P. Sweeney, “Use of discriminant analysis. II. Identification of persons with glaucomatous visual field defects,” Arch. Ophthalmol. (Chicago) 96, 1571–1573 (1978).
[CrossRef]

Thomas, B.

S. M. Drance, M. Schulzer, B. Thomas, G. R. Douglas, “Multivariate analysis in glaucoma. Use of discriminant analysis in prediction glaucomatous visual field damage,” Arch. Ophthalmol. (Chicago) 99, 1019–1022 (1981).
[CrossRef]

Tuulonen, A.

P. J. Airaksinen, A. Tuulonen, H. I. Alanko, “Prediction of development of glaucoma in ocular hypertensive patients,” in Glaucoma Update IV, G. K. Krieglstein, ed. (Springer-Verlag, Berlin, 1991), pp. 183–186.

Völcker, H. E.

R. O. W. Burk, J. König, K. Rohrschneider, H. Noack, H. E. Völcker, “Dreidimensionale papillentopographie mittels laser scanning tomographie: klinisches korrelat einer cluster-analyse,” Klin. Monatsbl. Augenheilkd. 204, 504–512 (1994).
[CrossRef]

Walker, R. L.

J. Mathews, R. L. Walker, Mathematical Methods of Physics (Benjamin, New York, 1964).

Weinreb, R.

R. Weinreb, A. W. Dreher, J. F. Bille, “Quantitative assessment of the optic nerve head with the laser tomographic scanner,” Int. Ophthalmol. 13, 25–29 (1989).
[CrossRef] [PubMed]

Wichern, D. W.

R. A. Johnson, D. W. Wichern, Applied Multivariate Statistical Analysis, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1988), p. 461; P. A. Lachenbruch, “Some misuses of discriminant analysis,” Methods Info. Med. 16, 255 (1977); M. M. Tatsouka, “Multivariate analysis of variance,” in Handbook of Multivariate Experimental Psychology, 2nd ed., J. R. Nesselroade, R. B. Cattell, eds. (Plenum, New York, 1988), p. 399.

Wijsman, K.

F. S. Mickelberg, K. Wijsman, M. Schulzer, “Reproducibility of topographic parameters obtained with the Heidelberg Retina Tomograph,” J. Glaucoma 2, 101–103 (1993).

Woon, W. H.

W. H. Woon, F. W. Fitzke, A. C. Bird, J. Marshall, “Confocal imaging of the fundus using a scanning laser ophthalmoscope,” Br. J. Ophthamol. 76, 470–474 (1992).
[CrossRef]

Am. J. Ophthalmol. (1)

R. E. Kirsch, D. R. Anderson, “Clinical recognition of glaucomatous cupping,” Am. J. Ophthalmol. 75, 442–454 (1973).
[PubMed]

Arch. Ophthalmol. (Chicago) (2)

S. M. Drance, M. Schulzer, B. Thomas, G. R. Douglas, “Multivariate analysis in glaucoma. Use of discriminant analysis in prediction glaucomatous visual field damage,” Arch. Ophthalmol. (Chicago) 99, 1019–1022 (1981).
[CrossRef]

S. M. Drance, M. Schulzer, G. R. Douglas, V. P. Sweeney, “Use of discriminant analysis. II. Identification of persons with glaucomatous visual field defects,” Arch. Ophthalmol. (Chicago) 96, 1571–1573 (1978).
[CrossRef]

Aust. N.Z. J. Ophthalmol. (1)

V. Cucevic, A. M. V. Brooks, N. T. Strang, A. G. Klein, K. A. Nugent, “Use of a laser confocal scanning ophthalmoscope to detect glaucomatous cupping of the optic disc,” Aust. N.Z. J. Ophthalmol. 25, 217–220 (1997).
[CrossRef]

Br. J. Ophthamol. (1)

W. H. Woon, F. W. Fitzke, A. C. Bird, J. Marshall, “Confocal imaging of the fundus using a scanning laser ophthalmoscope,” Br. J. Ophthamol. 76, 470–474 (1992).
[CrossRef]

Int. Ophthalmol. (1)

R. Weinreb, A. W. Dreher, J. F. Bille, “Quantitative assessment of the optic nerve head with the laser tomographic scanner,” Int. Ophthalmol. 13, 25–29 (1989).
[CrossRef] [PubMed]

J. Glaucoma (1)

F. S. Mickelberg, K. Wijsman, M. Schulzer, “Reproducibility of topographic parameters obtained with the Heidelberg Retina Tomograph,” J. Glaucoma 2, 101–103 (1993).

Klin. Monatsbl. Augenheilkd. (1)

R. O. W. Burk, J. König, K. Rohrschneider, H. Noack, H. E. Völcker, “Dreidimensionale papillentopographie mittels laser scanning tomographie: klinisches korrelat einer cluster-analyse,” Klin. Monatsbl. Augenheilkd. 204, 504–512 (1994).
[CrossRef]

Ophthalmology (1)

G. A. Cioffi, A. L. Robin, R. D. Eastman, H. F. Perell, F. A. Sarfarazi, S. E. Kelman, “Confocal laser scanning ophthalmoscope: reproducibility of optic nerve head topographic measurements with the confocal laser scanning ophthalmoscope,” Ophthalmology 100, 57–62 (1993).
[CrossRef] [PubMed]

Surv. Ophthalmol. (1)

J. Caprioli, “Correlations of visual function with nerve and nerve fibre layer structure in glaucoma,” Surv. Ophthalmol. 33, 319–330 (1989).

Other (4)

P. J. Airaksinen, A. Tuulonen, H. I. Alanko, “Prediction of development of glaucoma in ocular hypertensive patients,” in Glaucoma Update IV, G. K. Krieglstein, ed. (Springer-Verlag, Berlin, 1991), pp. 183–186.

J. Mathews, R. L. Walker, Mathematical Methods of Physics (Benjamin, New York, 1964).

R. A. Johnson, D. W. Wichern, Applied Multivariate Statistical Analysis, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1988), p. 461; P. A. Lachenbruch, “Some misuses of discriminant analysis,” Methods Info. Med. 16, 255 (1977); M. M. Tatsouka, “Multivariate analysis of variance,” in Handbook of Multivariate Experimental Psychology, 2nd ed., J. R. Nesselroade, R. B. Cattell, eds. (Plenum, New York, 1988), p. 399.

B. F. Ryan, B. L. Joiner, T. A. Ryan, Minitab Handbook, 2nd ed. (Duxbury, Boston, 1985); I. Gordon, R. Watson, Basic Statistics with Minitab (U. of Melbourne Press, Parkville, Australia, 1994).

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Figures (3)

Fig. 1
Fig. 1

Extended focus (left) and depth (right) images of a glaucomatous eye, obtained from the CLSO.

Fig. 2
Fig. 2

Contour plot of the depth image in Fig. 1.

Fig. 3
Fig. 3

Contour plot of spherical harmonic reconstruction of the depth image in Fig. 1.

Tables (2)

Tables Icon

Table 1 Linear Discriminant Function (LDF) Coefficients for Glaucomatous (G) and Normal (N) Groups with lmax=4a

Tables Icon

Table 2 Summary of Results with the Use of Multivariate Analysis based on LDF’s and Comparison with Clinical Diagnosis

Equations (27)

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

r(θ, ϕ)=l=0m=-llClmYlm*(θ, ϕ),
Ylm(θ, ϕ)=12ll!2l+14π(l-m)!(l+m)!1/2exp(imϕ)×(-sin θ)mdl+md(cos θ)l+m(cos2 θ-1)l
Yl, -m(θ, ϕ)=(-1)mYlm*(θ, ϕ),
0πdθ sin θ02πdϕYlm(θ, ϕ)Ylm*(θ, ϕ)=δllδmm.
Clm=02πdϕ0πdθ(sin θ)r(θ, ϕ)Ylm(θ, ϕ).
r(π-θ, ϕ)=r(θ, ϕ),
0πdθ(sin θ)f(θ, ϕ)=0π/2dθ(sin θ)f(θ, ϕ)+π/2πdθ(sin θ)f(θ, ϕ).
π/2πdθ(sin θ)f(θ, ϕ)=0π/2dθ sin(π-θ)f(π-θ, ϕ),
f(π-θ,ϕ)=r(π-θ, ϕ)Ylm(π-θ, ϕ),
Ylm(π-θ, ϕ)=(-1)l+mYlm(θ, ϕ).
Clm=[1+(-1)l+m]×02πdϕ0π/2dθ(sin θ)r(θ, ϕ)Ylm(θ, ϕ),
Clm=0ifl+misodd.
r(θ, ϕ)=[r(θ, ϕ)]*,
Cl,-m=(-1)mClm*.
C00=2πr,
r(θ, ϕ, lmax)=l=0lmaxm=-llClmYlm*(θ, ϕ)=l=0lmaxm=1l2 Re[Clm*Ylm(θ, ϕ)]+Cl0Yl0(θ, ϕ).
σ2(lmax)=i=0θstepsj=0ϕsteps[rdata(θi, ϕj)-r(θi, ϕj, lmax)]2θstepsϕsteps,
rL(θ, ϕ)=rR(θ, π-ϕ)for0ϕ<πrR(θ, 3π-ϕ)forπϕ<2π,
ClmL=ClmR*.
C=(C00, C11r, C11i, C20, C31r, C31i ,,Clmaxlmaxr, Clmaxlmaxi),
Σj=(C-Cj)(C-Cj)
Σ=(nN-1)ΣN+(nG-1)ΣGnN+nG-2,
dj2(Cnew)=(Cnew-Cj)Σ-1(Cnew-Cj)=-2(CjΣ-1Cnew-0.5CjΣ-1Cj)+CnewΣ-1Cnew=-2LDFj(Cnew)+CnewΣ-1Cnew,
LDFj(Cnew)=CjΣ-1Cnew-0.5CjΣ-1Cj.
LDFj(Cnew)=KjCnew+Kjconst,
Kj=(Kj00, Kj11r, Kj11i, Kj20, Kj31r, Kj31i ,, Kjlmaxlmaxr, Kjlmaxlmaxi)=CjΣ-1,
Kjconst=-0.5CjΣ-1Cj

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