Abstract

Enhanced Depth Imaging (EDI) optical coherence tomography (OCT) provides high-definition cross-sectional images of the choroid in vivo, and hence is used in many clinical studies. However, the quantification of the choroid depends on the manual labelings of two boundaries, Bruch’s membrane and the choroidal-scleral interface. This labeling process is tedious and subjective of inter-observer differences, hence, automatic segmentation of the choroid layer is highly desirable. In this paper, we present a fast and accurate algorithm that could segment the choroid automatically. Bruch’s membrane is detected by searching the pixel with the biggest gradient value above the retinal pigment epithelium (RPE) and the choroidal-scleral interface is delineated by finding the shortest path of the graph formed by valley pixels using Dijkstra’s algorithm. The experiments comparing automatic segmentation results with the manual labelings are conducted on 45 EDI-OCT images and the average of Dice’s Coefficient is 90.5%, which shows good consistency of the algorithm with the manual labelings. The processing time for each image is about 1.25 seconds.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Margolis and R. F. Spaide, “A pilot study of enhanced depth imaging optical coherence tomography of the choroid in normal eyes,” Am. J. Ophthalmol.147, 811–815 (2009).
    [CrossRef] [PubMed]
  2. H. A. Quigley, “What’s the choroid got to do with angle closure?” Arch. Ophthalmol.127(5), 693–4 (2009).
    [CrossRef] [PubMed]
  3. Y. Ikuno, K. Kawaguchi, T. Nouchi, and Y. Yasuno, “Choroidal thickness in healthy Japanese subjects,” Invest. Ophthalmol. Vis. Sci.51, 2173–2176 (2010).
    [CrossRef]
  4. X. Ding, J. Li, J. Zeng, W. Ma, R. Liu, T. Li, S. Yu, and S. Tang, “Choroidal thickness in healthy Chinese subjects,” Invest. Ophthalmol. Vis. Sci.52, 9555–9560 (2011).
    [CrossRef] [PubMed]
  5. V. Manjunath, M. Taha, J. G. Fujimoto, and J. S. Duker, “Choroidal thickness in normal eyes measured using Cirrus HD optical coherence tomography,” Am. J. Ophthalmol.150, 325–329 (2010).
    [CrossRef] [PubMed]
  6. D. L. Nickla, C. Wildsoet, and J. Wallman, “The circadian rhythm in intraocular pressure and its relation to diurnal ocular growth changes in chicks,” Exp. Eye. Res.66, 183–193 (1998).
    [CrossRef] [PubMed]
  7. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  8. R. K. Wang, “Signal degradation by multiple scattering in optical coherence tomography of dense tissue: a monte carlo study towards optical clearing of biotissues,” Phys. Med. Biol.47, 2281–2299 (2002).
    [CrossRef] [PubMed]
  9. R. F. Spaide, H. Koizumi, M. C. Pozzoni, and M. C. Pozonni, “Enhanced depth imaging spectral-domain optical coherence tomography,” Am. J. Ophthalmol.146, 496–500 (2008).
    [CrossRef] [PubMed]
  10. S. E. Chung, S. W. Kang, J. H. Lee, and Y. T. Kim, “Choroidal thickness in polypoidal choroidal vasculopathy and exudative age-related macular degeneration,” Ophthalmology118, 840–845 (2011).
    [CrossRef] [PubMed]
  11. A. H. C. Fong, K. K. W. Li, and D. Wong, “Choroidal evaluation using enhanced depth imaging spectral-domain optical coherence tomography in Vogt-Koyanagi-Harada disease,” Retina31, 502–509 (2011).
    [CrossRef] [PubMed]
  12. I. Maruko, T. Iida, Y. Sugano, A. Ojima, and T. Sekiryu, “Subfoveal choroidal thickness in fellow eyes of patients with central serous chorioretinopathy,” Retina31, 1603–1608 (2011).
    [CrossRef] [PubMed]
  13. J.-C. Mwanza, J. T. Hochberg, M. R. Banitt, W. J. Feuer, and D. L. Budenz, “Lack of association between glaucoma and macular choroidal thickness measured with enhanced depth-imaging optical coherence tomography,” Invest. Ophthalmol. Vis Sci.52, 3430–3435 (2011).
    [CrossRef] [PubMed]
  14. I. Maruko, T. Iida, Y. Sugano, A. Ojima, M. Ogasawara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of central serous chorioretinopathy,” Ophthalmology117, 1792–1799 (2010).
    [CrossRef] [PubMed]
  15. I. Maruko, T. Iida, Y. Sugano, H. Oyamada, T. Sekiryu, T. Fujiwara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of Vogt-Koyanagi-Harada disease,” Retina31, 510–517 (2011).
    [CrossRef]
  16. A. Yazdanpanah and G. Hamar, “Segmentation of intra-retinal layers from optical coherence tomgraphy images using an active contour approach,” IEEE Trans. Med. Imaging30, 484–496 (2011).
    [CrossRef]
  17. M. K. Garvin, M. D. Abramoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging27, 1495–1505 (2008).
    [CrossRef] [PubMed]
  18. S. J. Chiu, X. T. Li, P. Nicholas, C. A. Toth, J. A. Izatt, and S. Farsiu, “Automatic segmentation of seven retinal layers in SD-OCT images congruent with expert manual segmentation,” Opt. Express18, 19413–19428 (2010).
    [CrossRef] [PubMed]
  19. Q. Yang, C. A. Reisman, Z. Wang, Y. Fukuma, M. Hangai, N. Yoshimura, A. Tomidokoro, M. Araie, A. S. Raza, D. C. Hood, and K. Chan, “Automated layer segmentation of macular OCT images using dual-scale gradient information.” Opt. Express18, 21293–21307 (2010).
    [CrossRef] [PubMed]
  20. D. Koozekanani, K. Boyer, and C. Roberts, “Retinal thickness measurements from optical coherence tomgraphy using a Markov boundary model,” IEEE Trans. Med. Imaging20, 906–916 (2001).
    [CrossRef]
  21. L. Zhang, K. Lee, M. Niemeijer, R. F. Mullins, M. Sonka, and M. D. Abramoff, “Automated segmentation of the choroid from clinical SD-OCT,” Invest. Ophthalmol. Vis. Sci.53, 7510–7519 (2012).
    [CrossRef] [PubMed]
  22. V. Kajic, M. Esmaeelpour, B. Povazay, D. Marshall, P. L. Rosin, and W. Drexler, “Automated choroidal segmentation of 1060 nm OCT in healthy and pathologic eyes using a statistical mode,” Biomed. Opt. Express3, 86–103 (2012).
    [CrossRef] [PubMed]
  23. T. Torzicky, M. Pircher, S. Zotter, M. Bonesi, E. Gotzinger, and C. K. Hitzenberger, “Automated measurement of choroidal thickness in the human eye by polarization sensitive optical coherence tomography,” Opt. Express20, 7564–7574 (2012).
    [CrossRef] [PubMed]
  24. L. Duan, M. Yamanari, and Y. Yasuno, “Automated phase retardation oriented segmentation of chorio-scleral interface by polarization sensitive optical coherence tomography,” Opt. Express20, 3353–3366 (2012).
    [CrossRef] [PubMed]
  25. D. Nickla and J. Wallman, “The multifunctional choroid,” Prog. Retinal Res.29, 144–168 (2010).
    [CrossRef]
  26. E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Math.1, 269–271 (1959).
    [CrossRef]
  27. J. Tian and P. Marziliano, “Location-based graph search algorithm for boundary detection in oct images,” to be submitted to IEEE Trans. Med. Imaging.

2012 (4)

2011 (7)

X. Ding, J. Li, J. Zeng, W. Ma, R. Liu, T. Li, S. Yu, and S. Tang, “Choroidal thickness in healthy Chinese subjects,” Invest. Ophthalmol. Vis. Sci.52, 9555–9560 (2011).
[CrossRef] [PubMed]

S. E. Chung, S. W. Kang, J. H. Lee, and Y. T. Kim, “Choroidal thickness in polypoidal choroidal vasculopathy and exudative age-related macular degeneration,” Ophthalmology118, 840–845 (2011).
[CrossRef] [PubMed]

A. H. C. Fong, K. K. W. Li, and D. Wong, “Choroidal evaluation using enhanced depth imaging spectral-domain optical coherence tomography in Vogt-Koyanagi-Harada disease,” Retina31, 502–509 (2011).
[CrossRef] [PubMed]

I. Maruko, T. Iida, Y. Sugano, A. Ojima, and T. Sekiryu, “Subfoveal choroidal thickness in fellow eyes of patients with central serous chorioretinopathy,” Retina31, 1603–1608 (2011).
[CrossRef] [PubMed]

J.-C. Mwanza, J. T. Hochberg, M. R. Banitt, W. J. Feuer, and D. L. Budenz, “Lack of association between glaucoma and macular choroidal thickness measured with enhanced depth-imaging optical coherence tomography,” Invest. Ophthalmol. Vis Sci.52, 3430–3435 (2011).
[CrossRef] [PubMed]

I. Maruko, T. Iida, Y. Sugano, H. Oyamada, T. Sekiryu, T. Fujiwara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of Vogt-Koyanagi-Harada disease,” Retina31, 510–517 (2011).
[CrossRef]

A. Yazdanpanah and G. Hamar, “Segmentation of intra-retinal layers from optical coherence tomgraphy images using an active contour approach,” IEEE Trans. Med. Imaging30, 484–496 (2011).
[CrossRef]

2010 (6)

I. Maruko, T. Iida, Y. Sugano, A. Ojima, M. Ogasawara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of central serous chorioretinopathy,” Ophthalmology117, 1792–1799 (2010).
[CrossRef] [PubMed]

V. Manjunath, M. Taha, J. G. Fujimoto, and J. S. Duker, “Choroidal thickness in normal eyes measured using Cirrus HD optical coherence tomography,” Am. J. Ophthalmol.150, 325–329 (2010).
[CrossRef] [PubMed]

Y. Ikuno, K. Kawaguchi, T. Nouchi, and Y. Yasuno, “Choroidal thickness in healthy Japanese subjects,” Invest. Ophthalmol. Vis. Sci.51, 2173–2176 (2010).
[CrossRef]

D. Nickla and J. Wallman, “The multifunctional choroid,” Prog. Retinal Res.29, 144–168 (2010).
[CrossRef]

S. J. Chiu, X. T. Li, P. Nicholas, C. A. Toth, J. A. Izatt, and S. Farsiu, “Automatic segmentation of seven retinal layers in SD-OCT images congruent with expert manual segmentation,” Opt. Express18, 19413–19428 (2010).
[CrossRef] [PubMed]

Q. Yang, C. A. Reisman, Z. Wang, Y. Fukuma, M. Hangai, N. Yoshimura, A. Tomidokoro, M. Araie, A. S. Raza, D. C. Hood, and K. Chan, “Automated layer segmentation of macular OCT images using dual-scale gradient information.” Opt. Express18, 21293–21307 (2010).
[CrossRef] [PubMed]

2009 (2)

R. Margolis and R. F. Spaide, “A pilot study of enhanced depth imaging optical coherence tomography of the choroid in normal eyes,” Am. J. Ophthalmol.147, 811–815 (2009).
[CrossRef] [PubMed]

H. A. Quigley, “What’s the choroid got to do with angle closure?” Arch. Ophthalmol.127(5), 693–4 (2009).
[CrossRef] [PubMed]

2008 (2)

M. K. Garvin, M. D. Abramoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging27, 1495–1505 (2008).
[CrossRef] [PubMed]

R. F. Spaide, H. Koizumi, M. C. Pozzoni, and M. C. Pozonni, “Enhanced depth imaging spectral-domain optical coherence tomography,” Am. J. Ophthalmol.146, 496–500 (2008).
[CrossRef] [PubMed]

2002 (1)

R. K. Wang, “Signal degradation by multiple scattering in optical coherence tomography of dense tissue: a monte carlo study towards optical clearing of biotissues,” Phys. Med. Biol.47, 2281–2299 (2002).
[CrossRef] [PubMed]

2001 (1)

D. Koozekanani, K. Boyer, and C. Roberts, “Retinal thickness measurements from optical coherence tomgraphy using a Markov boundary model,” IEEE Trans. Med. Imaging20, 906–916 (2001).
[CrossRef]

1998 (1)

D. L. Nickla, C. Wildsoet, and J. Wallman, “The circadian rhythm in intraocular pressure and its relation to diurnal ocular growth changes in chicks,” Exp. Eye. Res.66, 183–193 (1998).
[CrossRef] [PubMed]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

1959 (1)

E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Math.1, 269–271 (1959).
[CrossRef]

Abramoff, M. D.

L. Zhang, K. Lee, M. Niemeijer, R. F. Mullins, M. Sonka, and M. D. Abramoff, “Automated segmentation of the choroid from clinical SD-OCT,” Invest. Ophthalmol. Vis. Sci.53, 7510–7519 (2012).
[CrossRef] [PubMed]

M. K. Garvin, M. D. Abramoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging27, 1495–1505 (2008).
[CrossRef] [PubMed]

Araie, M.

Banitt, M. R.

J.-C. Mwanza, J. T. Hochberg, M. R. Banitt, W. J. Feuer, and D. L. Budenz, “Lack of association between glaucoma and macular choroidal thickness measured with enhanced depth-imaging optical coherence tomography,” Invest. Ophthalmol. Vis Sci.52, 3430–3435 (2011).
[CrossRef] [PubMed]

Bonesi, M.

Boyer, K.

D. Koozekanani, K. Boyer, and C. Roberts, “Retinal thickness measurements from optical coherence tomgraphy using a Markov boundary model,” IEEE Trans. Med. Imaging20, 906–916 (2001).
[CrossRef]

Budenz, D. L.

J.-C. Mwanza, J. T. Hochberg, M. R. Banitt, W. J. Feuer, and D. L. Budenz, “Lack of association between glaucoma and macular choroidal thickness measured with enhanced depth-imaging optical coherence tomography,” Invest. Ophthalmol. Vis Sci.52, 3430–3435 (2011).
[CrossRef] [PubMed]

Chan, K.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Chiu, S. J.

Chung, S. E.

S. E. Chung, S. W. Kang, J. H. Lee, and Y. T. Kim, “Choroidal thickness in polypoidal choroidal vasculopathy and exudative age-related macular degeneration,” Ophthalmology118, 840–845 (2011).
[CrossRef] [PubMed]

Dijkstra, E. W.

E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Math.1, 269–271 (1959).
[CrossRef]

Ding, X.

X. Ding, J. Li, J. Zeng, W. Ma, R. Liu, T. Li, S. Yu, and S. Tang, “Choroidal thickness in healthy Chinese subjects,” Invest. Ophthalmol. Vis. Sci.52, 9555–9560 (2011).
[CrossRef] [PubMed]

Drexler, W.

Duan, L.

Duker, J. S.

V. Manjunath, M. Taha, J. G. Fujimoto, and J. S. Duker, “Choroidal thickness in normal eyes measured using Cirrus HD optical coherence tomography,” Am. J. Ophthalmol.150, 325–329 (2010).
[CrossRef] [PubMed]

Esmaeelpour, M.

Farsiu, S.

Feuer, W. J.

J.-C. Mwanza, J. T. Hochberg, M. R. Banitt, W. J. Feuer, and D. L. Budenz, “Lack of association between glaucoma and macular choroidal thickness measured with enhanced depth-imaging optical coherence tomography,” Invest. Ophthalmol. Vis Sci.52, 3430–3435 (2011).
[CrossRef] [PubMed]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fong, A. H. C.

A. H. C. Fong, K. K. W. Li, and D. Wong, “Choroidal evaluation using enhanced depth imaging spectral-domain optical coherence tomography in Vogt-Koyanagi-Harada disease,” Retina31, 502–509 (2011).
[CrossRef] [PubMed]

Fujimoto, J. G.

V. Manjunath, M. Taha, J. G. Fujimoto, and J. S. Duker, “Choroidal thickness in normal eyes measured using Cirrus HD optical coherence tomography,” Am. J. Ophthalmol.150, 325–329 (2010).
[CrossRef] [PubMed]

Fujiwara, T.

I. Maruko, T. Iida, Y. Sugano, H. Oyamada, T. Sekiryu, T. Fujiwara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of Vogt-Koyanagi-Harada disease,” Retina31, 510–517 (2011).
[CrossRef]

Fukuma, Y.

Garvin, M. K.

M. K. Garvin, M. D. Abramoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging27, 1495–1505 (2008).
[CrossRef] [PubMed]

Gotzinger, E.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hamar, G.

A. Yazdanpanah and G. Hamar, “Segmentation of intra-retinal layers from optical coherence tomgraphy images using an active contour approach,” IEEE Trans. Med. Imaging30, 484–496 (2011).
[CrossRef]

Hangai, M.

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hitzenberger, C. K.

Hochberg, J. T.

J.-C. Mwanza, J. T. Hochberg, M. R. Banitt, W. J. Feuer, and D. L. Budenz, “Lack of association between glaucoma and macular choroidal thickness measured with enhanced depth-imaging optical coherence tomography,” Invest. Ophthalmol. Vis Sci.52, 3430–3435 (2011).
[CrossRef] [PubMed]

Hood, D. C.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Iida, T.

I. Maruko, T. Iida, Y. Sugano, H. Oyamada, T. Sekiryu, T. Fujiwara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of Vogt-Koyanagi-Harada disease,” Retina31, 510–517 (2011).
[CrossRef]

I. Maruko, T. Iida, Y. Sugano, A. Ojima, and T. Sekiryu, “Subfoveal choroidal thickness in fellow eyes of patients with central serous chorioretinopathy,” Retina31, 1603–1608 (2011).
[CrossRef] [PubMed]

I. Maruko, T. Iida, Y. Sugano, A. Ojima, M. Ogasawara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of central serous chorioretinopathy,” Ophthalmology117, 1792–1799 (2010).
[CrossRef] [PubMed]

Ikuno, Y.

Y. Ikuno, K. Kawaguchi, T. Nouchi, and Y. Yasuno, “Choroidal thickness in healthy Japanese subjects,” Invest. Ophthalmol. Vis. Sci.51, 2173–2176 (2010).
[CrossRef]

Izatt, J. A.

Kajic, V.

Kang, S. W.

S. E. Chung, S. W. Kang, J. H. Lee, and Y. T. Kim, “Choroidal thickness in polypoidal choroidal vasculopathy and exudative age-related macular degeneration,” Ophthalmology118, 840–845 (2011).
[CrossRef] [PubMed]

Kardon, R.

M. K. Garvin, M. D. Abramoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging27, 1495–1505 (2008).
[CrossRef] [PubMed]

Kawaguchi, K.

Y. Ikuno, K. Kawaguchi, T. Nouchi, and Y. Yasuno, “Choroidal thickness in healthy Japanese subjects,” Invest. Ophthalmol. Vis. Sci.51, 2173–2176 (2010).
[CrossRef]

Kim, Y. T.

S. E. Chung, S. W. Kang, J. H. Lee, and Y. T. Kim, “Choroidal thickness in polypoidal choroidal vasculopathy and exudative age-related macular degeneration,” Ophthalmology118, 840–845 (2011).
[CrossRef] [PubMed]

Koizumi, H.

R. F. Spaide, H. Koizumi, M. C. Pozzoni, and M. C. Pozonni, “Enhanced depth imaging spectral-domain optical coherence tomography,” Am. J. Ophthalmol.146, 496–500 (2008).
[CrossRef] [PubMed]

Koozekanani, D.

D. Koozekanani, K. Boyer, and C. Roberts, “Retinal thickness measurements from optical coherence tomgraphy using a Markov boundary model,” IEEE Trans. Med. Imaging20, 906–916 (2001).
[CrossRef]

Lee, J. H.

S. E. Chung, S. W. Kang, J. H. Lee, and Y. T. Kim, “Choroidal thickness in polypoidal choroidal vasculopathy and exudative age-related macular degeneration,” Ophthalmology118, 840–845 (2011).
[CrossRef] [PubMed]

Lee, K.

L. Zhang, K. Lee, M. Niemeijer, R. F. Mullins, M. Sonka, and M. D. Abramoff, “Automated segmentation of the choroid from clinical SD-OCT,” Invest. Ophthalmol. Vis. Sci.53, 7510–7519 (2012).
[CrossRef] [PubMed]

Li, J.

X. Ding, J. Li, J. Zeng, W. Ma, R. Liu, T. Li, S. Yu, and S. Tang, “Choroidal thickness in healthy Chinese subjects,” Invest. Ophthalmol. Vis. Sci.52, 9555–9560 (2011).
[CrossRef] [PubMed]

Li, K. K. W.

A. H. C. Fong, K. K. W. Li, and D. Wong, “Choroidal evaluation using enhanced depth imaging spectral-domain optical coherence tomography in Vogt-Koyanagi-Harada disease,” Retina31, 502–509 (2011).
[CrossRef] [PubMed]

Li, T.

X. Ding, J. Li, J. Zeng, W. Ma, R. Liu, T. Li, S. Yu, and S. Tang, “Choroidal thickness in healthy Chinese subjects,” Invest. Ophthalmol. Vis. Sci.52, 9555–9560 (2011).
[CrossRef] [PubMed]

Li, X. T.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Liu, R.

X. Ding, J. Li, J. Zeng, W. Ma, R. Liu, T. Li, S. Yu, and S. Tang, “Choroidal thickness in healthy Chinese subjects,” Invest. Ophthalmol. Vis. Sci.52, 9555–9560 (2011).
[CrossRef] [PubMed]

Ma, W.

X. Ding, J. Li, J. Zeng, W. Ma, R. Liu, T. Li, S. Yu, and S. Tang, “Choroidal thickness in healthy Chinese subjects,” Invest. Ophthalmol. Vis. Sci.52, 9555–9560 (2011).
[CrossRef] [PubMed]

Manjunath, V.

V. Manjunath, M. Taha, J. G. Fujimoto, and J. S. Duker, “Choroidal thickness in normal eyes measured using Cirrus HD optical coherence tomography,” Am. J. Ophthalmol.150, 325–329 (2010).
[CrossRef] [PubMed]

Margolis, R.

R. Margolis and R. F. Spaide, “A pilot study of enhanced depth imaging optical coherence tomography of the choroid in normal eyes,” Am. J. Ophthalmol.147, 811–815 (2009).
[CrossRef] [PubMed]

Marshall, D.

Maruko, I.

I. Maruko, T. Iida, Y. Sugano, H. Oyamada, T. Sekiryu, T. Fujiwara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of Vogt-Koyanagi-Harada disease,” Retina31, 510–517 (2011).
[CrossRef]

I. Maruko, T. Iida, Y. Sugano, A. Ojima, and T. Sekiryu, “Subfoveal choroidal thickness in fellow eyes of patients with central serous chorioretinopathy,” Retina31, 1603–1608 (2011).
[CrossRef] [PubMed]

I. Maruko, T. Iida, Y. Sugano, A. Ojima, M. Ogasawara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of central serous chorioretinopathy,” Ophthalmology117, 1792–1799 (2010).
[CrossRef] [PubMed]

Marziliano, P.

J. Tian and P. Marziliano, “Location-based graph search algorithm for boundary detection in oct images,” to be submitted to IEEE Trans. Med. Imaging.

Mullins, R. F.

L. Zhang, K. Lee, M. Niemeijer, R. F. Mullins, M. Sonka, and M. D. Abramoff, “Automated segmentation of the choroid from clinical SD-OCT,” Invest. Ophthalmol. Vis. Sci.53, 7510–7519 (2012).
[CrossRef] [PubMed]

Mwanza, J.-C.

J.-C. Mwanza, J. T. Hochberg, M. R. Banitt, W. J. Feuer, and D. L. Budenz, “Lack of association between glaucoma and macular choroidal thickness measured with enhanced depth-imaging optical coherence tomography,” Invest. Ophthalmol. Vis Sci.52, 3430–3435 (2011).
[CrossRef] [PubMed]

Nicholas, P.

Nickla, D.

D. Nickla and J. Wallman, “The multifunctional choroid,” Prog. Retinal Res.29, 144–168 (2010).
[CrossRef]

Nickla, D. L.

D. L. Nickla, C. Wildsoet, and J. Wallman, “The circadian rhythm in intraocular pressure and its relation to diurnal ocular growth changes in chicks,” Exp. Eye. Res.66, 183–193 (1998).
[CrossRef] [PubMed]

Niemeijer, M.

L. Zhang, K. Lee, M. Niemeijer, R. F. Mullins, M. Sonka, and M. D. Abramoff, “Automated segmentation of the choroid from clinical SD-OCT,” Invest. Ophthalmol. Vis. Sci.53, 7510–7519 (2012).
[CrossRef] [PubMed]

Nouchi, T.

Y. Ikuno, K. Kawaguchi, T. Nouchi, and Y. Yasuno, “Choroidal thickness in healthy Japanese subjects,” Invest. Ophthalmol. Vis. Sci.51, 2173–2176 (2010).
[CrossRef]

Ogasawara, M.

I. Maruko, T. Iida, Y. Sugano, A. Ojima, M. Ogasawara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of central serous chorioretinopathy,” Ophthalmology117, 1792–1799 (2010).
[CrossRef] [PubMed]

Ojima, A.

I. Maruko, T. Iida, Y. Sugano, A. Ojima, and T. Sekiryu, “Subfoveal choroidal thickness in fellow eyes of patients with central serous chorioretinopathy,” Retina31, 1603–1608 (2011).
[CrossRef] [PubMed]

I. Maruko, T. Iida, Y. Sugano, A. Ojima, M. Ogasawara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of central serous chorioretinopathy,” Ophthalmology117, 1792–1799 (2010).
[CrossRef] [PubMed]

Oyamada, H.

I. Maruko, T. Iida, Y. Sugano, H. Oyamada, T. Sekiryu, T. Fujiwara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of Vogt-Koyanagi-Harada disease,” Retina31, 510–517 (2011).
[CrossRef]

Pircher, M.

Povazay, B.

Pozonni, M. C.

R. F. Spaide, H. Koizumi, M. C. Pozzoni, and M. C. Pozonni, “Enhanced depth imaging spectral-domain optical coherence tomography,” Am. J. Ophthalmol.146, 496–500 (2008).
[CrossRef] [PubMed]

Pozzoni, M. C.

R. F. Spaide, H. Koizumi, M. C. Pozzoni, and M. C. Pozonni, “Enhanced depth imaging spectral-domain optical coherence tomography,” Am. J. Ophthalmol.146, 496–500 (2008).
[CrossRef] [PubMed]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Quigley, H. A.

H. A. Quigley, “What’s the choroid got to do with angle closure?” Arch. Ophthalmol.127(5), 693–4 (2009).
[CrossRef] [PubMed]

Raza, A. S.

Reisman, C. A.

Roberts, C.

D. Koozekanani, K. Boyer, and C. Roberts, “Retinal thickness measurements from optical coherence tomgraphy using a Markov boundary model,” IEEE Trans. Med. Imaging20, 906–916 (2001).
[CrossRef]

Rosin, P. L.

Russell, S. R.

M. K. Garvin, M. D. Abramoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging27, 1495–1505 (2008).
[CrossRef] [PubMed]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Sekiryu, T.

I. Maruko, T. Iida, Y. Sugano, H. Oyamada, T. Sekiryu, T. Fujiwara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of Vogt-Koyanagi-Harada disease,” Retina31, 510–517 (2011).
[CrossRef]

I. Maruko, T. Iida, Y. Sugano, A. Ojima, and T. Sekiryu, “Subfoveal choroidal thickness in fellow eyes of patients with central serous chorioretinopathy,” Retina31, 1603–1608 (2011).
[CrossRef] [PubMed]

Sonka, M.

L. Zhang, K. Lee, M. Niemeijer, R. F. Mullins, M. Sonka, and M. D. Abramoff, “Automated segmentation of the choroid from clinical SD-OCT,” Invest. Ophthalmol. Vis. Sci.53, 7510–7519 (2012).
[CrossRef] [PubMed]

M. K. Garvin, M. D. Abramoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging27, 1495–1505 (2008).
[CrossRef] [PubMed]

Spaide, R. F.

I. Maruko, T. Iida, Y. Sugano, H. Oyamada, T. Sekiryu, T. Fujiwara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of Vogt-Koyanagi-Harada disease,” Retina31, 510–517 (2011).
[CrossRef]

I. Maruko, T. Iida, Y. Sugano, A. Ojima, M. Ogasawara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of central serous chorioretinopathy,” Ophthalmology117, 1792–1799 (2010).
[CrossRef] [PubMed]

R. Margolis and R. F. Spaide, “A pilot study of enhanced depth imaging optical coherence tomography of the choroid in normal eyes,” Am. J. Ophthalmol.147, 811–815 (2009).
[CrossRef] [PubMed]

R. F. Spaide, H. Koizumi, M. C. Pozzoni, and M. C. Pozonni, “Enhanced depth imaging spectral-domain optical coherence tomography,” Am. J. Ophthalmol.146, 496–500 (2008).
[CrossRef] [PubMed]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Sugano, Y.

I. Maruko, T. Iida, Y. Sugano, H. Oyamada, T. Sekiryu, T. Fujiwara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of Vogt-Koyanagi-Harada disease,” Retina31, 510–517 (2011).
[CrossRef]

I. Maruko, T. Iida, Y. Sugano, A. Ojima, and T. Sekiryu, “Subfoveal choroidal thickness in fellow eyes of patients with central serous chorioretinopathy,” Retina31, 1603–1608 (2011).
[CrossRef] [PubMed]

I. Maruko, T. Iida, Y. Sugano, A. Ojima, M. Ogasawara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of central serous chorioretinopathy,” Ophthalmology117, 1792–1799 (2010).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Taha, M.

V. Manjunath, M. Taha, J. G. Fujimoto, and J. S. Duker, “Choroidal thickness in normal eyes measured using Cirrus HD optical coherence tomography,” Am. J. Ophthalmol.150, 325–329 (2010).
[CrossRef] [PubMed]

Tang, S.

X. Ding, J. Li, J. Zeng, W. Ma, R. Liu, T. Li, S. Yu, and S. Tang, “Choroidal thickness in healthy Chinese subjects,” Invest. Ophthalmol. Vis. Sci.52, 9555–9560 (2011).
[CrossRef] [PubMed]

Tian, J.

J. Tian and P. Marziliano, “Location-based graph search algorithm for boundary detection in oct images,” to be submitted to IEEE Trans. Med. Imaging.

Tomidokoro, A.

Torzicky, T.

Toth, C. A.

Wallman, J.

D. Nickla and J. Wallman, “The multifunctional choroid,” Prog. Retinal Res.29, 144–168 (2010).
[CrossRef]

D. L. Nickla, C. Wildsoet, and J. Wallman, “The circadian rhythm in intraocular pressure and its relation to diurnal ocular growth changes in chicks,” Exp. Eye. Res.66, 183–193 (1998).
[CrossRef] [PubMed]

Wang, R. K.

R. K. Wang, “Signal degradation by multiple scattering in optical coherence tomography of dense tissue: a monte carlo study towards optical clearing of biotissues,” Phys. Med. Biol.47, 2281–2299 (2002).
[CrossRef] [PubMed]

Wang, Z.

Wildsoet, C.

D. L. Nickla, C. Wildsoet, and J. Wallman, “The circadian rhythm in intraocular pressure and its relation to diurnal ocular growth changes in chicks,” Exp. Eye. Res.66, 183–193 (1998).
[CrossRef] [PubMed]

Wong, D.

A. H. C. Fong, K. K. W. Li, and D. Wong, “Choroidal evaluation using enhanced depth imaging spectral-domain optical coherence tomography in Vogt-Koyanagi-Harada disease,” Retina31, 502–509 (2011).
[CrossRef] [PubMed]

Wu, X.

M. K. Garvin, M. D. Abramoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging27, 1495–1505 (2008).
[CrossRef] [PubMed]

Yamanari, M.

Yang, Q.

Yasuno, Y.

Yazdanpanah, A.

A. Yazdanpanah and G. Hamar, “Segmentation of intra-retinal layers from optical coherence tomgraphy images using an active contour approach,” IEEE Trans. Med. Imaging30, 484–496 (2011).
[CrossRef]

Yoshimura, N.

Yu, S.

X. Ding, J. Li, J. Zeng, W. Ma, R. Liu, T. Li, S. Yu, and S. Tang, “Choroidal thickness in healthy Chinese subjects,” Invest. Ophthalmol. Vis. Sci.52, 9555–9560 (2011).
[CrossRef] [PubMed]

Zeng, J.

X. Ding, J. Li, J. Zeng, W. Ma, R. Liu, T. Li, S. Yu, and S. Tang, “Choroidal thickness in healthy Chinese subjects,” Invest. Ophthalmol. Vis. Sci.52, 9555–9560 (2011).
[CrossRef] [PubMed]

Zhang, L.

L. Zhang, K. Lee, M. Niemeijer, R. F. Mullins, M. Sonka, and M. D. Abramoff, “Automated segmentation of the choroid from clinical SD-OCT,” Invest. Ophthalmol. Vis. Sci.53, 7510–7519 (2012).
[CrossRef] [PubMed]

Zotter, S.

Am. J. Ophthalmol. (3)

R. Margolis and R. F. Spaide, “A pilot study of enhanced depth imaging optical coherence tomography of the choroid in normal eyes,” Am. J. Ophthalmol.147, 811–815 (2009).
[CrossRef] [PubMed]

R. F. Spaide, H. Koizumi, M. C. Pozzoni, and M. C. Pozonni, “Enhanced depth imaging spectral-domain optical coherence tomography,” Am. J. Ophthalmol.146, 496–500 (2008).
[CrossRef] [PubMed]

V. Manjunath, M. Taha, J. G. Fujimoto, and J. S. Duker, “Choroidal thickness in normal eyes measured using Cirrus HD optical coherence tomography,” Am. J. Ophthalmol.150, 325–329 (2010).
[CrossRef] [PubMed]

Arch. Ophthalmol. (1)

H. A. Quigley, “What’s the choroid got to do with angle closure?” Arch. Ophthalmol.127(5), 693–4 (2009).
[CrossRef] [PubMed]

Biomed. Opt. Express (1)

Exp. Eye. Res. (1)

D. L. Nickla, C. Wildsoet, and J. Wallman, “The circadian rhythm in intraocular pressure and its relation to diurnal ocular growth changes in chicks,” Exp. Eye. Res.66, 183–193 (1998).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging (3)

A. Yazdanpanah and G. Hamar, “Segmentation of intra-retinal layers from optical coherence tomgraphy images using an active contour approach,” IEEE Trans. Med. Imaging30, 484–496 (2011).
[CrossRef]

M. K. Garvin, M. D. Abramoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging27, 1495–1505 (2008).
[CrossRef] [PubMed]

D. Koozekanani, K. Boyer, and C. Roberts, “Retinal thickness measurements from optical coherence tomgraphy using a Markov boundary model,” IEEE Trans. Med. Imaging20, 906–916 (2001).
[CrossRef]

Invest. Ophthalmol. Vis Sci. (1)

J.-C. Mwanza, J. T. Hochberg, M. R. Banitt, W. J. Feuer, and D. L. Budenz, “Lack of association between glaucoma and macular choroidal thickness measured with enhanced depth-imaging optical coherence tomography,” Invest. Ophthalmol. Vis Sci.52, 3430–3435 (2011).
[CrossRef] [PubMed]

Invest. Ophthalmol. Vis. Sci. (3)

L. Zhang, K. Lee, M. Niemeijer, R. F. Mullins, M. Sonka, and M. D. Abramoff, “Automated segmentation of the choroid from clinical SD-OCT,” Invest. Ophthalmol. Vis. Sci.53, 7510–7519 (2012).
[CrossRef] [PubMed]

Y. Ikuno, K. Kawaguchi, T. Nouchi, and Y. Yasuno, “Choroidal thickness in healthy Japanese subjects,” Invest. Ophthalmol. Vis. Sci.51, 2173–2176 (2010).
[CrossRef]

X. Ding, J. Li, J. Zeng, W. Ma, R. Liu, T. Li, S. Yu, and S. Tang, “Choroidal thickness in healthy Chinese subjects,” Invest. Ophthalmol. Vis. Sci.52, 9555–9560 (2011).
[CrossRef] [PubMed]

Numerische Math. (1)

E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Math.1, 269–271 (1959).
[CrossRef]

Ophthalmology (2)

S. E. Chung, S. W. Kang, J. H. Lee, and Y. T. Kim, “Choroidal thickness in polypoidal choroidal vasculopathy and exudative age-related macular degeneration,” Ophthalmology118, 840–845 (2011).
[CrossRef] [PubMed]

I. Maruko, T. Iida, Y. Sugano, A. Ojima, M. Ogasawara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of central serous chorioretinopathy,” Ophthalmology117, 1792–1799 (2010).
[CrossRef] [PubMed]

Opt. Express (4)

Phys. Med. Biol. (1)

R. K. Wang, “Signal degradation by multiple scattering in optical coherence tomography of dense tissue: a monte carlo study towards optical clearing of biotissues,” Phys. Med. Biol.47, 2281–2299 (2002).
[CrossRef] [PubMed]

Prog. Retinal Res. (1)

D. Nickla and J. Wallman, “The multifunctional choroid,” Prog. Retinal Res.29, 144–168 (2010).
[CrossRef]

Retina (3)

I. Maruko, T. Iida, Y. Sugano, H. Oyamada, T. Sekiryu, T. Fujiwara, and R. F. Spaide, “Subfoveal choroidal thickness after treatment of Vogt-Koyanagi-Harada disease,” Retina31, 510–517 (2011).
[CrossRef]

A. H. C. Fong, K. K. W. Li, and D. Wong, “Choroidal evaluation using enhanced depth imaging spectral-domain optical coherence tomography in Vogt-Koyanagi-Harada disease,” Retina31, 502–509 (2011).
[CrossRef] [PubMed]

I. Maruko, T. Iida, Y. Sugano, A. Ojima, and T. Sekiryu, “Subfoveal choroidal thickness in fellow eyes of patients with central serous chorioretinopathy,” Retina31, 1603–1608 (2011).
[CrossRef] [PubMed]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Other (1)

J. Tian and P. Marziliano, “Location-based graph search algorithm for boundary detection in oct images,” to be submitted to IEEE Trans. Med. Imaging.

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 (12)

Fig. 1
Fig. 1

Anatomy of the human eye: the choroid is the vascular layer between the sclera and the retina. Image courtesy of the National Eye Institute, National Institute of Health.

Fig. 2
Fig. 2

(a) EDI-OCT image in the macular region of the human eye. (b) The Bruch’s Membrane and the choroidal-scleral interface are manually labeled by the ophthalmologists.

Fig. 3
Fig. 3

The overview of the automatic segmentation of the choroid in EDI-OCT images.

Fig. 4
Fig. 4

BM detection algorithm. (a) Part of the EDI-OCT image, (b) The detected RPE (CRPE in red dotted line) and Bruch’s membrane (CBM in blue solid line). (c) The new image Îs has the flat Bruch’s membrane.

Fig. 5
Fig. 5

The valleys (local minimums) of the A-scans are used as the feature to detect the choroidal-scleral interface. However, there are also valleys caused by the speckle noise and the blood vessels in the choroid region.

Fig. 6
Fig. 6

Construction of graph G, each valley pixel is a vertex of the graph and is connected to the vertices in the next Nnh columns.

Fig. 7
Fig. 7

(a) A straighted EDI-OCT image. (b) The choroidal-scleral interface is sometimes invisible and the missing boundary is refereed as gaps (circles), where the valley pixels (cross) do not appear near the manual labeled choroidal-scleral interface (dashed lines). (c) The delineation result of the proposed algorithm by setting Nnh = 10 and Nnh = 20. When Nnh = 20, the value 3Nnh (60 pixels) is greater than the horizontal distance of the largest gap (57 pixels). Therefore, vs and ve is connected and the result agrees well with the manual labeling in (b);

Fig. 8
Fig. 8

(a) Construction of graph G, each valley pixel is a vertex of the graph and is connected to the vertex in the next Nnh columns; (b) Hard and soft thresholding methods for assigning penalty weights.

Fig. 9
Fig. 9

The Dice’s coefficient of the choroid segmentation between the output of the proposed algorithm and the manual labelings.

Fig. 10
Fig. 10

The ratio between the error and the manual labelings in estimating the choroidal thickness of 45 EDI-OCT images.

Fig. 11
Fig. 11

(a) A part of non-inverted image I43. (b) The comparison between the results of the proposed algorithm(indicated by the dash lines) and the ground truth labeled by the ophthalmologists (drawn in solid lines). (c) The enlarged major discrepancy region.

Fig. 12
Fig. 12

(a) A part of the inverted image I6. (b) The comparison between the results of the proposed algorithm(indicated by the dash lines) and the ground truth labeled by the ophthalmologists (drawn in solid lines). (c)The enlarged major discrepancy region.

Tables (2)

Tables Icon

Algorithm 1 V = ValleyDet(g, δ)

Tables Icon

Table 1 The parameter settings in the experiments

Equations (13)

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

C R P E = { ( x , y R P E ) | x [ 1 , N c ] , y R P E = argmax u [ 1 , N r ] f x ( u ) } ,
B M = { ( x , y B M ) | x [ 1 , N c ] , y B M = argmax u [ y R P E Δ , y R P E ] g * f x ( u ) } ,
( p ˜ 4 , p ˜ 3 , p ˜ 2 , p ˜ 1 , p ˜ 0 ) = argmin ( p 4 , p 3 , p 2 , p 1 , p 0 ) x = 1 N c ( y B M p 4 x 4 p 3 x 3 p 2 x 2 p 1 x p 0 ) 2 .
V 1 = V 1 V 4 V 7 V N c ,
V x = { ( x , y ) | y ValleyDet ( f s x , δ ) } .
w ( a , b ) = w ( Δ x , Δ y , w M , T p , α ) = ( Δ x 2 + Δ y 2 ) w c + w M H ( Δ y T p ) | Δ y T p | 1 + exp ( α ( Δ y T p ) ) w p ,
( v 2 v 1 ) ( v 3 v 2 ) > 0.
w ( v 1 , v 2 , v 3 ) = w ( v 1 , v 2 ) + w ( v 2 , v l 3 ) = v 2 v 1 2 + v 3 v 2 2 < v 1 v 3 2 = w ( v 1 , v 3 ) .
w p = w M H ( Δ y T p ) .
C H T = { ( x , y ) | x [ 1 , N c ] , y [ y C S I , y B M ] } ,
f C H T ( x ) = σ a × | { y | ( x , y ) C H T } | ,
Dice C H T = 2 | C H T C H T 0 | | C H T | + | C H T 0 | .
r = 1 N c x = 1 N c f C H T ( x ) f C H T 0 ( x ) 1 N c x = 1 N c f C H T 0 ( x ) .

Metrics