Abstract

In making noninvasive measurements of the human cone mosaic, the task of labeling each individual cone is unavoidable. Manual labeling is a time-consuming process, setting the motivation for the development of an automated method. An automated algorithm for labeling cones in adaptive optics (AO) retinal images is implemented and tested on real data. The optical fiber properties of cones aided the design of the algorithm. Out of 2153 manually labeled cones from six different images, the automated method correctly identified 94.1% of them. The agreement between the automated and the manual labeling methods varied from 92.7% to 96.2% across the six images. Results between the two methods disagreed for 1.2% to 9.1% of the cones. Voronoi analysis of large montages of AO retinal images confirmed the general hexagonal-packing structure of retinal cones as well as the general cone density variability across portions of the retina. The consistency of our measurements demonstrates the reliability and practicality of having an automated solution to this problem.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. I. Yellott, "Spectral consequences of photoreceptor sampling in the rhesus retina," Science 221, 382-385 (1983).
    [CrossRef] [PubMed]
  2. D. R. Williams, "Topography of the foveal cone mosaic in the living human eye," Vision Res. 28, 433-454 (1988).
    [CrossRef] [PubMed]
  3. C. A. Curcio and K. R. Sloan, "Packing geometry of human cone photoreceptors--variation with eccentricity and evidence for local anisotropy," Visual Neurosci. 9, 169-180 (1992).
    [CrossRef]
  4. C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, "Human photoreceptor topography," J. Comp. Neurol. 292, 497-523 (1990).
    [CrossRef] [PubMed]
  5. D. R. Williams and R. Collier, "Consequences of spatial sampling by a human photoreceptor mosaic," Science 221, 385-387 (1983).
    [CrossRef] [PubMed]
  6. D. R. Williams and N. J. Coletta, "Cone spacing and the visual resolution limit," J. Opt. Soc. Am. A 4, 1514-1523 (1987).
    [CrossRef] [PubMed]
  7. J. Z. Liang, D. R. Williams, and D. T. Miller, "Supernormal vision and high-resolution retinal imaging through adaptive optics," J. Opt. Soc. Am. A 14, 2884-2892 (1997).
    [CrossRef]
  8. A. Roorda, A. B. Metha, P. Lennie, and D. R. Williams, "Packing arrangement of the three cone classes in primate retina," Vision Res. 41, 1291-1306 (2001).
    [CrossRef] [PubMed]
  9. A. Roorda and D. R. Williams, "Optical fiber properties of individual human cones," J. Vision 2, 404-412 (2002).
    [CrossRef]
  10. A. Roorda and K. Y. Li, "AO image processing," (2006), retrieved 2006, vision.berkeley.edu/roordalab/Kaccie/KaccieResearch.htm.
  11. D. R. Williams, "Aliasing in human foveal vision," Vision Res. 25, 195-205 (1985).
    [CrossRef] [PubMed]
  12. R. M. Mersereau, "Processing of hexagonally sampled two-dimensional signals," Proc. IEEE 67, 930-949 (1979).
    [CrossRef]
  13. J. C. Christou, A. Roorda, and D. R. Williams, "Deconvolution of adaptive optics retinal images," J. Opt. Soc. Am. A 21, 1393-1401 (2004).
    [CrossRef]
  14. R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using Matlab (Pearson Education, 2004), pp. 65-193.
  15. Image Processing Toolbox, Users Guide, Version 4 (The MathWorks, Inc., 2003).
  16. J. M. Enoch, "Optical properties of the retinal receptors," J. Opt. Soc. Am. 53, 71-85 (1963).
    [CrossRef]
  17. J. S. Lim, "Finite impulse response filters," in Two-Dimensional Signal and Image Processing, A.V.Oppenheim, ed. (Prentice Hall, 1990), pp. 195-263.
  18. R. C. Gonzalez and R. E. Woods, "Image enhancement in the frequency domain," in Digital Image Processing, 2nd ed. (Addison-Wesley, 2001), pp. 147-215.
  19. M. B. Shapiro, S. J. Schein, and F. M. Demonasterio, "Regularity and structure of the spatial pattern of blue cones of macaque retina," J. Am. Stat. Assoc. 80, 803-812 (1985).
    [CrossRef]
  20. A. Roorda, F. Romero-Borja, W. J. Donnelly, H. Queener, T. J. Hebert, and M. C. W. Campbell, "Adaptive optics scanning laser ophthalmoscopy," Opt. Express 10, 405-412 (2002).
    [PubMed]
  21. Y. H. Zhang, S. Poonja, and A. Roorda, "MEMS-based adaptive optics scanning laser ophthalmoscopy," Opt. Lett. 31, 1268-1270 (2006).
    [CrossRef] [PubMed]
  22. J. Carroll, M. Neitz, H. Hofer, J. Neitz, and D. R. Williams, "Functional photoreceptor loss revealed with adaptive optics: an alternate cause of color blindness," Proc. Natl. Acad. Sci. U.S.A. 101, 8461-8466 (2004).
    [CrossRef] [PubMed]
  23. R. L. Cook, "Stochastic sampling in computer graphics," ACM Trans. Graphics 5, 51-72 (1986).
    [CrossRef]

2006 (1)

2004 (2)

J. C. Christou, A. Roorda, and D. R. Williams, "Deconvolution of adaptive optics retinal images," J. Opt. Soc. Am. A 21, 1393-1401 (2004).
[CrossRef]

J. Carroll, M. Neitz, H. Hofer, J. Neitz, and D. R. Williams, "Functional photoreceptor loss revealed with adaptive optics: an alternate cause of color blindness," Proc. Natl. Acad. Sci. U.S.A. 101, 8461-8466 (2004).
[CrossRef] [PubMed]

2002 (2)

2001 (1)

A. Roorda, A. B. Metha, P. Lennie, and D. R. Williams, "Packing arrangement of the three cone classes in primate retina," Vision Res. 41, 1291-1306 (2001).
[CrossRef] [PubMed]

1997 (1)

1992 (1)

C. A. Curcio and K. R. Sloan, "Packing geometry of human cone photoreceptors--variation with eccentricity and evidence for local anisotropy," Visual Neurosci. 9, 169-180 (1992).
[CrossRef]

1990 (1)

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, "Human photoreceptor topography," J. Comp. Neurol. 292, 497-523 (1990).
[CrossRef] [PubMed]

1988 (1)

D. R. Williams, "Topography of the foveal cone mosaic in the living human eye," Vision Res. 28, 433-454 (1988).
[CrossRef] [PubMed]

1987 (1)

1986 (1)

R. L. Cook, "Stochastic sampling in computer graphics," ACM Trans. Graphics 5, 51-72 (1986).
[CrossRef]

1985 (2)

M. B. Shapiro, S. J. Schein, and F. M. Demonasterio, "Regularity and structure of the spatial pattern of blue cones of macaque retina," J. Am. Stat. Assoc. 80, 803-812 (1985).
[CrossRef]

D. R. Williams, "Aliasing in human foveal vision," Vision Res. 25, 195-205 (1985).
[CrossRef] [PubMed]

1983 (2)

J. I. Yellott, "Spectral consequences of photoreceptor sampling in the rhesus retina," Science 221, 382-385 (1983).
[CrossRef] [PubMed]

D. R. Williams and R. Collier, "Consequences of spatial sampling by a human photoreceptor mosaic," Science 221, 385-387 (1983).
[CrossRef] [PubMed]

1979 (1)

R. M. Mersereau, "Processing of hexagonally sampled two-dimensional signals," Proc. IEEE 67, 930-949 (1979).
[CrossRef]

1963 (1)

Campbell, M. C. W.

Carroll, J.

J. Carroll, M. Neitz, H. Hofer, J. Neitz, and D. R. Williams, "Functional photoreceptor loss revealed with adaptive optics: an alternate cause of color blindness," Proc. Natl. Acad. Sci. U.S.A. 101, 8461-8466 (2004).
[CrossRef] [PubMed]

Christou, J. C.

Coletta, N. J.

Collier, R.

D. R. Williams and R. Collier, "Consequences of spatial sampling by a human photoreceptor mosaic," Science 221, 385-387 (1983).
[CrossRef] [PubMed]

Cook, R. L.

R. L. Cook, "Stochastic sampling in computer graphics," ACM Trans. Graphics 5, 51-72 (1986).
[CrossRef]

Curcio, C. A.

C. A. Curcio and K. R. Sloan, "Packing geometry of human cone photoreceptors--variation with eccentricity and evidence for local anisotropy," Visual Neurosci. 9, 169-180 (1992).
[CrossRef]

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, "Human photoreceptor topography," J. Comp. Neurol. 292, 497-523 (1990).
[CrossRef] [PubMed]

Demonasterio, F. M.

M. B. Shapiro, S. J. Schein, and F. M. Demonasterio, "Regularity and structure of the spatial pattern of blue cones of macaque retina," J. Am. Stat. Assoc. 80, 803-812 (1985).
[CrossRef]

Donnelly, W. J.

Eddins, S. L.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using Matlab (Pearson Education, 2004), pp. 65-193.

Enoch, J. M.

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using Matlab (Pearson Education, 2004), pp. 65-193.

R. C. Gonzalez and R. E. Woods, "Image enhancement in the frequency domain," in Digital Image Processing, 2nd ed. (Addison-Wesley, 2001), pp. 147-215.

Hebert, T. J.

Hendrickson, A. E.

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, "Human photoreceptor topography," J. Comp. Neurol. 292, 497-523 (1990).
[CrossRef] [PubMed]

Hofer, H.

J. Carroll, M. Neitz, H. Hofer, J. Neitz, and D. R. Williams, "Functional photoreceptor loss revealed with adaptive optics: an alternate cause of color blindness," Proc. Natl. Acad. Sci. U.S.A. 101, 8461-8466 (2004).
[CrossRef] [PubMed]

Kalina, R. E.

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, "Human photoreceptor topography," J. Comp. Neurol. 292, 497-523 (1990).
[CrossRef] [PubMed]

Lennie, P.

A. Roorda, A. B. Metha, P. Lennie, and D. R. Williams, "Packing arrangement of the three cone classes in primate retina," Vision Res. 41, 1291-1306 (2001).
[CrossRef] [PubMed]

Li, K. Y.

A. Roorda and K. Y. Li, "AO image processing," (2006), retrieved 2006, vision.berkeley.edu/roordalab/Kaccie/KaccieResearch.htm.

Liang, J. Z.

Lim, J. S.

J. S. Lim, "Finite impulse response filters," in Two-Dimensional Signal and Image Processing, A.V.Oppenheim, ed. (Prentice Hall, 1990), pp. 195-263.

Mersereau, R. M.

R. M. Mersereau, "Processing of hexagonally sampled two-dimensional signals," Proc. IEEE 67, 930-949 (1979).
[CrossRef]

Metha, A. B.

A. Roorda, A. B. Metha, P. Lennie, and D. R. Williams, "Packing arrangement of the three cone classes in primate retina," Vision Res. 41, 1291-1306 (2001).
[CrossRef] [PubMed]

Miller, D. T.

Neitz, J.

J. Carroll, M. Neitz, H. Hofer, J. Neitz, and D. R. Williams, "Functional photoreceptor loss revealed with adaptive optics: an alternate cause of color blindness," Proc. Natl. Acad. Sci. U.S.A. 101, 8461-8466 (2004).
[CrossRef] [PubMed]

Neitz, M.

J. Carroll, M. Neitz, H. Hofer, J. Neitz, and D. R. Williams, "Functional photoreceptor loss revealed with adaptive optics: an alternate cause of color blindness," Proc. Natl. Acad. Sci. U.S.A. 101, 8461-8466 (2004).
[CrossRef] [PubMed]

Poonja, S.

Queener, H.

Romero-Borja, F.

Roorda, A.

Y. H. Zhang, S. Poonja, and A. Roorda, "MEMS-based adaptive optics scanning laser ophthalmoscopy," Opt. Lett. 31, 1268-1270 (2006).
[CrossRef] [PubMed]

J. C. Christou, A. Roorda, and D. R. Williams, "Deconvolution of adaptive optics retinal images," J. Opt. Soc. Am. A 21, 1393-1401 (2004).
[CrossRef]

A. Roorda and D. R. Williams, "Optical fiber properties of individual human cones," J. Vision 2, 404-412 (2002).
[CrossRef]

A. Roorda, F. Romero-Borja, W. J. Donnelly, H. Queener, T. J. Hebert, and M. C. W. Campbell, "Adaptive optics scanning laser ophthalmoscopy," Opt. Express 10, 405-412 (2002).
[PubMed]

A. Roorda, A. B. Metha, P. Lennie, and D. R. Williams, "Packing arrangement of the three cone classes in primate retina," Vision Res. 41, 1291-1306 (2001).
[CrossRef] [PubMed]

A. Roorda and K. Y. Li, "AO image processing," (2006), retrieved 2006, vision.berkeley.edu/roordalab/Kaccie/KaccieResearch.htm.

Schein, S. J.

M. B. Shapiro, S. J. Schein, and F. M. Demonasterio, "Regularity and structure of the spatial pattern of blue cones of macaque retina," J. Am. Stat. Assoc. 80, 803-812 (1985).
[CrossRef]

Shapiro, M. B.

M. B. Shapiro, S. J. Schein, and F. M. Demonasterio, "Regularity and structure of the spatial pattern of blue cones of macaque retina," J. Am. Stat. Assoc. 80, 803-812 (1985).
[CrossRef]

Sloan, K. R.

C. A. Curcio and K. R. Sloan, "Packing geometry of human cone photoreceptors--variation with eccentricity and evidence for local anisotropy," Visual Neurosci. 9, 169-180 (1992).
[CrossRef]

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, "Human photoreceptor topography," J. Comp. Neurol. 292, 497-523 (1990).
[CrossRef] [PubMed]

Williams, D. R.

J. C. Christou, A. Roorda, and D. R. Williams, "Deconvolution of adaptive optics retinal images," J. Opt. Soc. Am. A 21, 1393-1401 (2004).
[CrossRef]

J. Carroll, M. Neitz, H. Hofer, J. Neitz, and D. R. Williams, "Functional photoreceptor loss revealed with adaptive optics: an alternate cause of color blindness," Proc. Natl. Acad. Sci. U.S.A. 101, 8461-8466 (2004).
[CrossRef] [PubMed]

A. Roorda and D. R. Williams, "Optical fiber properties of individual human cones," J. Vision 2, 404-412 (2002).
[CrossRef]

A. Roorda, A. B. Metha, P. Lennie, and D. R. Williams, "Packing arrangement of the three cone classes in primate retina," Vision Res. 41, 1291-1306 (2001).
[CrossRef] [PubMed]

J. Z. Liang, D. R. Williams, and D. T. Miller, "Supernormal vision and high-resolution retinal imaging through adaptive optics," J. Opt. Soc. Am. A 14, 2884-2892 (1997).
[CrossRef]

D. R. Williams, "Topography of the foveal cone mosaic in the living human eye," Vision Res. 28, 433-454 (1988).
[CrossRef] [PubMed]

D. R. Williams and N. J. Coletta, "Cone spacing and the visual resolution limit," J. Opt. Soc. Am. A 4, 1514-1523 (1987).
[CrossRef] [PubMed]

D. R. Williams, "Aliasing in human foveal vision," Vision Res. 25, 195-205 (1985).
[CrossRef] [PubMed]

D. R. Williams and R. Collier, "Consequences of spatial sampling by a human photoreceptor mosaic," Science 221, 385-387 (1983).
[CrossRef] [PubMed]

Woods, R. E.

R. C. Gonzalez and R. E. Woods, "Image enhancement in the frequency domain," in Digital Image Processing, 2nd ed. (Addison-Wesley, 2001), pp. 147-215.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using Matlab (Pearson Education, 2004), pp. 65-193.

Yellott, J. I.

J. I. Yellott, "Spectral consequences of photoreceptor sampling in the rhesus retina," Science 221, 382-385 (1983).
[CrossRef] [PubMed]

Zhang, Y. H.

ACM Trans. Graphics (1)

R. L. Cook, "Stochastic sampling in computer graphics," ACM Trans. Graphics 5, 51-72 (1986).
[CrossRef]

J. Am. Stat. Assoc. (1)

M. B. Shapiro, S. J. Schein, and F. M. Demonasterio, "Regularity and structure of the spatial pattern of blue cones of macaque retina," J. Am. Stat. Assoc. 80, 803-812 (1985).
[CrossRef]

J. Comp. Neurol. (1)

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, "Human photoreceptor topography," J. Comp. Neurol. 292, 497-523 (1990).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Vision (1)

A. Roorda and D. R. Williams, "Optical fiber properties of individual human cones," J. Vision 2, 404-412 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. IEEE (1)

R. M. Mersereau, "Processing of hexagonally sampled two-dimensional signals," Proc. IEEE 67, 930-949 (1979).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

J. Carroll, M. Neitz, H. Hofer, J. Neitz, and D. R. Williams, "Functional photoreceptor loss revealed with adaptive optics: an alternate cause of color blindness," Proc. Natl. Acad. Sci. U.S.A. 101, 8461-8466 (2004).
[CrossRef] [PubMed]

Science (2)

D. R. Williams and R. Collier, "Consequences of spatial sampling by a human photoreceptor mosaic," Science 221, 385-387 (1983).
[CrossRef] [PubMed]

J. I. Yellott, "Spectral consequences of photoreceptor sampling in the rhesus retina," Science 221, 382-385 (1983).
[CrossRef] [PubMed]

Vision Res. (3)

D. R. Williams, "Topography of the foveal cone mosaic in the living human eye," Vision Res. 28, 433-454 (1988).
[CrossRef] [PubMed]

A. Roorda, A. B. Metha, P. Lennie, and D. R. Williams, "Packing arrangement of the three cone classes in primate retina," Vision Res. 41, 1291-1306 (2001).
[CrossRef] [PubMed]

D. R. Williams, "Aliasing in human foveal vision," Vision Res. 25, 195-205 (1985).
[CrossRef] [PubMed]

Visual Neurosci. (1)

C. A. Curcio and K. R. Sloan, "Packing geometry of human cone photoreceptors--variation with eccentricity and evidence for local anisotropy," Visual Neurosci. 9, 169-180 (1992).
[CrossRef]

Other (5)

J. S. Lim, "Finite impulse response filters," in Two-Dimensional Signal and Image Processing, A.V.Oppenheim, ed. (Prentice Hall, 1990), pp. 195-263.

R. C. Gonzalez and R. E. Woods, "Image enhancement in the frequency domain," in Digital Image Processing, 2nd ed. (Addison-Wesley, 2001), pp. 147-215.

A. Roorda and K. Y. Li, "AO image processing," (2006), retrieved 2006, vision.berkeley.edu/roordalab/Kaccie/KaccieResearch.htm.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using Matlab (Pearson Education, 2004), pp. 65-193.

Image Processing Toolbox, Users Guide, Version 4 (The MathWorks, Inc., 2003).

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 (8)

Fig. 1
Fig. 1

Power spectrum of an AO retinal image (enhanced by log scale) generated using the fast Fourier transform. The shape and size of the band region indicate the hexagonal arrangement and sampling limits of the cones in the image. The periodicity of the tightest packed cones is about 145   cycles per degree (cpd).

Fig. 2
Fig. 2

Output of IPT function imregionalmax is a (a) binary sequence whose values are nonzero at all identified local maxima in the input sequence. (b) This sequence is dilated with a disk-shaped structuring element, and (c) cone locations are computed by computing the center of mass of each object in the sequence after dilation.

Fig. 3
Fig. 3

Every marker in these six grayscale images is manually placed by the authors. Each image is 8   bits and 128 × 128   pixels , and each marker is accurate to the nearest pixel.

Fig. 4
Fig. 4

Voronoi diagrams corresponding to the mosaic of Fig. 3d computed from cone locations acquired by (a) the automated method and (b)–(f) the five experienced human observers.

Fig. 5
Fig. 5

Montage image of the monkey retina acquired by the AO flood-illuminated system at the University of Rochester and labeled with the proposed algorithm.

Fig. 6
Fig. 6

Voronoi diagrams generated for the montage given in Fig. 4 at the eccentricities specified above each diagram. Hexagonal regions are shaded in light gray.

Fig. 7
Fig. 7

Topography map of retinal cone density for the montage given in Fig. 4.

Fig. 8
Fig. 8

Percentages of hexagonal Voronoi regions plotted over eccentricity for all seven montages analyzed in this study.

Tables (2)

Tables Icon

Table 1 Sources for Cone Photoreceptor Images a

Tables Icon

Table 2 Performance Comparison between Manual and Automated Methods

Equations (4)

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

I ( x 1 , x 2 ) = I ( x 1 , x 2 ) β ( x 1 , x 2 ) ,
I ( n 1 , n 2 ) = I ( x 1 T 1 , x 2 T 2 ) + η ( n 1 , n 2 ) ,
f ( n 1 , n 2 ) = h ( n 1 , n 2 ) I ( n 1 , n 2 ) ,
f ( n 1 , n 2 ) = W ( n 1 , n 2 ) [ h ( n 1 , n 2 ) I ( n 1 , n 2 ) ] ,

Metrics