Abstract

We propose a joint segmentation and classification deep model for early glaucoma diagnosis using retina imaging with optical coherence tomography (OCT). Our motivation roots in the observation that ophthalmologists make the clinical decision by analyzing the retinal nerve fiber layer (RNFL) from OCT images. To simulate this process, we propose a novel deep model that joins the retinal layer segmentation and glaucoma classification. Our model consists of three parts. First, the segmentation network simultaneously predicts both six retinal layers and five boundaries between them. Then, we introduce a post processing algorithm to fuse the two results while enforcing the topology correctness. Finally, the classification network takes the RNFL thickness vector as input and outputs the probability of being glaucoma. In the classification network, we propose a carefully designed module to implement the clinical strategy to diagnose glaucoma. We validate our method both in a collected dataset of 1004 circular OCT B-Scans from 234 subjects and in a public dataset of 110 B-Scans from 10 patients with diabetic macular edema. Experimental results demonstrate that our method achieves superior segmentation performance than other state-of-the-art methods both in our collected dataset and in public dataset with severe retina pathology. For glaucoma classification, our model achieves diagnostic accuracy of 81.4% with AUC of 0.864, which clearly outperforms baseline methods.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (5)

L.-C. Chen, G. Papandreou, I. Kokkinos, K. Murphy, and A. L. Yuille, “Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs,” IEEE transactions on pattern analysis machine intelligence 40, 834–848 (2018).
[Crossref]

J. Hamwood, D. Alonso-Caneiro, S. A. Read, S. J. Vincent, and M. J. Collins, “Effect of patch size and network architecture on a convolutional neural network approach for automatic segmentation of oct retinal layers,” Biomed. Opt. Express 9, 3049–3066 (2018).
[Crossref] [PubMed]

J. Kugelman, D. Alonso-Caneiro, S. A. Read, S. J. Vincent, and M. J. Collins, “Automatic segmentation of oct retinal boundaries using recurrent neural networks and graph search,” Biomed. Opt. Express 9, 5759–5777 (2018).
[Crossref] [PubMed]

A. Chakravarty and J. Sivaswamy, “A supervised joint multi-layer segmentation framework for retinal optical coherence tomography images using conditional random field,” Comput. methods programs biomedicine 165, 235–250 (2018).
[Crossref]

J. De Fauw, J. R. Ledsam, B. Romera-Paredes, S. Nikolov, N. Tomasev, S. Blackwell, H. Askham, X. Glorot, B. O’Donoghue, D. Visentin, and et al., “Clinically applicable deep learning for diagnosis and referral in retinal disease,” Nat. medicine 24, 1342 (2018).
[Crossref]

2017 (6)

H. Muhammad, T. J. Fuchs, N. De Cuir, C. G. De Moraes, D. M. Blumberg, J. M. Liebmann, R. Ritch, and D. C. Hood, “Hybrid deep learning on single wide-field optical coherence tomography scans accurately classifies glaucoma suspects,” J. glaucoma 26, 1086–1094 (2017).
[Crossref]

K. Omodaka, G. An, S. Tsuda, Y. Shiga, N. Takada, T. Kikawa, H. Takahashi, H. Yokota, M. Akiba, and T. Nakazawa, “Classification of optic disc shape in glaucoma using machine learning based on quantified ocular parameters,” PloS one 12, e0190012 (2017).
[Crossref]

A. G. Roy, S. Conjeti, S. P. K. Karri, D. Sheet, A. Katouzian, C. Wachinger, and N. Navab, “Relaynet: retinal layer and fluid segmentation of macular optical coherence tomography using fully convolutional networks,” Biomed. optics express 8, 3627–3642 (2017).
[Crossref]

F. G. Venhuizen, B. van Ginneken, B. Liefers, M. J. van Grinsven, S. Fauser, C. Hoyng, T. Theelen, and C. I. Sánchez, “Robust total retina thickness segmentation in optical coherence tomography images using convolutional neural networks,” Biomed. optics express 8, 3292–3316 (2017).
[Crossref]

L. Fang, D. Cunefare, C. Wang, R. H. Guymer, S. Li, and S. Farsiu, “Automatic segmentation of nine retinal layer boundaries in oct images of non-exudative amd patients using deep learning and graph search,” Biomed. optics express 8, 2732–2744 (2017).
[Crossref]

M. Usman, M. M. Fraz, and S. A. Barman, “Computer vision techniques applied for diagnostic analysis of retinal oct images: a review,” Arch. Comput. Methods Eng. 24, 449–465 (2017).
[Crossref]

2015 (2)

F. Shi, X. Chen, H. Zhao, W. Zhu, D. Xiang, E. Gao, M. Sonka, and H. Chen, “Automated 3-d retinal layer segmentation of macular optical coherence tomography images with serous pigment epithelial detachments,” IEEE transactions on medical imaging 34, 441–452 (2015).
[Crossref]

S. J. Chiu, M. J. Allingham, P. S. Mettu, S. W. Cousins, J. A. Izatt, and S. Farsiu, “Kernel regression based segmentation of optical coherence tomography images with diabetic macular edema,” Biomed. optics express 6, 1172–1194 (2015).
[Crossref]

2013 (2)

J. Xu, H. Ishikawa, G. Wollstein, R. A. Bilonick, L. S. Folio, Z. Nadler, L. Kagemann, and J. S. Schuman, “Three-dimensional spectral-domain optical coherence tomography data analysis for glaucoma detection,” PloS one 8, e55476 (2013).
[Crossref] [PubMed]

A. Lang, A. Carass, M. Hauser, E. S. Sotirchos, P. A. Calabresi, H. S. Ying, and J. L. Prince, “Retinal layer segmentation of macular oct images using boundary classification,” Biomed. optics express 4, 1133–1152 (2013).
[Crossref]

2011 (1)

K. Vermeer, J. Van der Schoot, H. Lemij, and J. De Boer, “Automated segmentation by pixel classification of retinal layers in ophthalmic oct images,” Biomed. optics express 2, 1743–1756 (2011).
[Crossref]

2010 (2)

D. Bizios, A. Heijl, J. L. Hougaard, and B. Bengtsson, “Machine learning classifiers for glaucoma diagnosis based on classification of retinal nerve fibre layer thickness parameters measured by stratus oct,” Acta ophthalmologica 88, 44–52 (2010).
[Crossref] [PubMed]

S. J. Chiu, X. T. Li, P. Nicholas, C. A. Toth, J. A. Izatt, and S. Farsiu, “Automatic segmentation of seven retinal layers in sdoct images congruent with expert manual segmentation,” Opt. express 18, 19413–19428 (2010).
[Crossref] [PubMed]

2009 (1)

F. A. Medeiros, L. M. Zangwill, L. M. Alencar, C. Bowd, P. A. Sample, R. Susanna, and R. N. Weinreb, “Detection of glaucoma progression with stratus oct retinal nerve fiber layer, optic nerve head, and macular thickness measurements,” Investig. ophthalmology & visual science 50, 5741–5748 (2009).
[Crossref]

2006 (1)

B. Llanas and F. Sainz, “Constructive approximate interpolation by neural networks,” J. Computat. Appl. Math. 188, 283–308 (2006).
[Crossref]

1999 (1)

J. A. K. Suykens and J. Vandewalle, “Least squares support vector machine classifiers,” Neural Process. Lett. 9, 293–300 (1999).
[Crossref]

1964 (1)

P. J. Huber and et al., “Robust estimation of a location parameter,” The annals mathematical statistics 35, 73–101 (1964).
[Crossref]

Abadi, M.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, and et al., “Tensorflow: a system for large-scale machine learning,” in OSDI, vol. 16 (2016), pp. 265–283.

Abdulkadir, A.

Ö. Çiçek, A. Abdulkadir, S. S. Lienkamp, T. Brox, and O. Ronneberger, “3d u-net: learning dense volumetric segmentation from sparse annotation,” in International Conference on Medical Image Computing and Computer-Assisted Intervention, (Springer, 2016), pp. 424–432.

Akiba, M.

K. Omodaka, G. An, S. Tsuda, Y. Shiga, N. Takada, T. Kikawa, H. Takahashi, H. Yokota, M. Akiba, and T. Nakazawa, “Classification of optic disc shape in glaucoma using machine learning based on quantified ocular parameters,” PloS one 12, e0190012 (2017).
[Crossref]

Alencar, L. M.

F. A. Medeiros, L. M. Zangwill, L. M. Alencar, C. Bowd, P. A. Sample, R. Susanna, and R. N. Weinreb, “Detection of glaucoma progression with stratus oct retinal nerve fiber layer, optic nerve head, and macular thickness measurements,” Investig. ophthalmology & visual science 50, 5741–5748 (2009).
[Crossref]

Allingham, M. J.

S. J. Chiu, M. J. Allingham, P. S. Mettu, S. W. Cousins, J. A. Izatt, and S. Farsiu, “Kernel regression based segmentation of optical coherence tomography images with diabetic macular edema,” Biomed. optics express 6, 1172–1194 (2015).
[Crossref]

Alonso-Caneiro, D.

An, G.

K. Omodaka, G. An, S. Tsuda, Y. Shiga, N. Takada, T. Kikawa, H. Takahashi, H. Yokota, M. Akiba, and T. Nakazawa, “Classification of optic disc shape in glaucoma using machine learning based on quantified ocular parameters,” PloS one 12, e0190012 (2017).
[Crossref]

Askham, H.

J. De Fauw, J. R. Ledsam, B. Romera-Paredes, S. Nikolov, N. Tomasev, S. Blackwell, H. Askham, X. Glorot, B. O’Donoghue, D. Visentin, and et al., “Clinically applicable deep learning for diagnosis and referral in retinal disease,” Nat. medicine 24, 1342 (2018).
[Crossref]

Ba, J.

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).

Barham, P.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, and et al., “Tensorflow: a system for large-scale machine learning,” in OSDI, vol. 16 (2016), pp. 265–283.

Barman, S. A.

M. Usman, M. M. Fraz, and S. A. Barman, “Computer vision techniques applied for diagnostic analysis of retinal oct images: a review,” Arch. Comput. Methods Eng. 24, 449–465 (2017).
[Crossref]

Barra, V.

M. E. A. Bechar, N. Settouti, V. Barra, and M. A. Chikh, “Semi-supervised superpixel classification for medical images segmentation: application to detection of glaucoma disease,” Multidimens Syst. Signal Process. pp. 1–20 (2017).

Bechar, M. E. A.

M. E. A. Bechar, N. Settouti, V. Barra, and M. A. Chikh, “Semi-supervised superpixel classification for medical images segmentation: application to detection of glaucoma disease,” Multidimens Syst. Signal Process. pp. 1–20 (2017).

Bengtsson, B.

D. Bizios, A. Heijl, J. L. Hougaard, and B. Bengtsson, “Machine learning classifiers for glaucoma diagnosis based on classification of retinal nerve fibre layer thickness parameters measured by stratus oct,” Acta ophthalmologica 88, 44–52 (2010).
[Crossref] [PubMed]

Bilonick, R. A.

J. Xu, H. Ishikawa, G. Wollstein, R. A. Bilonick, L. S. Folio, Z. Nadler, L. Kagemann, and J. S. Schuman, “Three-dimensional spectral-domain optical coherence tomography data analysis for glaucoma detection,” PloS one 8, e55476 (2013).
[Crossref] [PubMed]

Bizios, D.

D. Bizios, A. Heijl, J. L. Hougaard, and B. Bengtsson, “Machine learning classifiers for glaucoma diagnosis based on classification of retinal nerve fibre layer thickness parameters measured by stratus oct,” Acta ophthalmologica 88, 44–52 (2010).
[Crossref] [PubMed]

Blackwell, S.

J. De Fauw, J. R. Ledsam, B. Romera-Paredes, S. Nikolov, N. Tomasev, S. Blackwell, H. Askham, X. Glorot, B. O’Donoghue, D. Visentin, and et al., “Clinically applicable deep learning for diagnosis and referral in retinal disease,” Nat. medicine 24, 1342 (2018).
[Crossref]

Blumberg, D. M.

H. Muhammad, T. J. Fuchs, N. De Cuir, C. G. De Moraes, D. M. Blumberg, J. M. Liebmann, R. Ritch, and D. C. Hood, “Hybrid deep learning on single wide-field optical coherence tomography scans accurately classifies glaucoma suspects,” J. glaucoma 26, 1086–1094 (2017).
[Crossref]

Boer, J. De

K. Vermeer, J. Van der Schoot, H. Lemij, and J. De Boer, “Automated segmentation by pixel classification of retinal layers in ophthalmic oct images,” Biomed. optics express 2, 1743–1756 (2011).
[Crossref]

Bowd, C.

F. A. Medeiros, L. M. Zangwill, L. M. Alencar, C. Bowd, P. A. Sample, R. Susanna, and R. N. Weinreb, “Detection of glaucoma progression with stratus oct retinal nerve fiber layer, optic nerve head, and macular thickness measurements,” Investig. ophthalmology & visual science 50, 5741–5748 (2009).
[Crossref]

Brox, T.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in International Conference on Medical image computing and computer-assisted intervention, (Springer, 2015), pp. 234–241.

Ö. Çiçek, A. Abdulkadir, S. S. Lienkamp, T. Brox, and O. Ronneberger, “3d u-net: learning dense volumetric segmentation from sparse annotation,” in International Conference on Medical Image Computing and Computer-Assisted Intervention, (Springer, 2016), pp. 424–432.

Calabresi, P. A.

A. Lang, A. Carass, M. Hauser, E. S. Sotirchos, P. A. Calabresi, H. S. Ying, and J. L. Prince, “Retinal layer segmentation of macular oct images using boundary classification,” Biomed. optics express 4, 1133–1152 (2013).
[Crossref]

Y. He, A. Carass, Y. Yun, C. Zhao, B. M. Jedynak, S. D. Solomon, S. Saidha, P. A. Calabresi, and J. L. Prince, “Towards topological correct segmentation of macular oct from cascaded fcns,” in Fetal, Infant and Ophthalmic Medical Image Analysis, (Springer, 2017), pp. 202–209.
[Crossref]

Y. He, A. Carass, B. M. Jedynak, S. D. Solomon, S. Saidha, P. A. Calabresi, and J. L. Prince, “Topology guaranteed segmentation of the human retina from oct using convolutional neural networks,” arXiv preprint arXiv:1803.05120 (2018).

Carass, A.

A. Lang, A. Carass, M. Hauser, E. S. Sotirchos, P. A. Calabresi, H. S. Ying, and J. L. Prince, “Retinal layer segmentation of macular oct images using boundary classification,” Biomed. optics express 4, 1133–1152 (2013).
[Crossref]

Y. He, A. Carass, B. M. Jedynak, S. D. Solomon, S. Saidha, P. A. Calabresi, and J. L. Prince, “Topology guaranteed segmentation of the human retina from oct using convolutional neural networks,” arXiv preprint arXiv:1803.05120 (2018).

Y. He, A. Carass, Y. Yun, C. Zhao, B. M. Jedynak, S. D. Solomon, S. Saidha, P. A. Calabresi, and J. L. Prince, “Towards topological correct segmentation of macular oct from cascaded fcns,” in Fetal, Infant and Ophthalmic Medical Image Analysis, (Springer, 2017), pp. 202–209.
[Crossref]

Chakravarty, A.

A. Chakravarty and J. Sivaswamy, “A supervised joint multi-layer segmentation framework for retinal optical coherence tomography images using conditional random field,” Comput. methods programs biomedicine 165, 235–250 (2018).
[Crossref]

Chen, H.

F. Shi, X. Chen, H. Zhao, W. Zhu, D. Xiang, E. Gao, M. Sonka, and H. Chen, “Automated 3-d retinal layer segmentation of macular optical coherence tomography images with serous pigment epithelial detachments,” IEEE transactions on medical imaging 34, 441–452 (2015).
[Crossref]

H. Chen, X. Qi, L. Yu, and P.-A. Heng, “Dcan: deep contour-aware networks for accurate gland segmentation,” in Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, (2016), pp. 2487–2496.

Chen, J.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, and et al., “Tensorflow: a system for large-scale machine learning,” in OSDI, vol. 16 (2016), pp. 265–283.

Chen, L. C.

L. C. Chen, G. Papandreou, I. Kokkinos, K. Murphy, and A. L. Yuille, “Semantic image segmentation with deep convolutional nets and fully connected crfs,” Comput. Sci. pp. 357–361 (2014).

Chen, L.-C.

L.-C. Chen, G. Papandreou, I. Kokkinos, K. Murphy, and A. L. Yuille, “Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs,” IEEE transactions on pattern analysis machine intelligence 40, 834–848 (2018).
[Crossref]

Chen, X.

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Qi, X.

H. Chen, X. Qi, L. Yu, and P.-A. Heng, “Dcan: deep contour-aware networks for accurate gland segmentation,” in Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, (2016), pp. 2487–2496.

Read, S. A.

Ritch, R.

H. Muhammad, T. J. Fuchs, N. De Cuir, C. G. De Moraes, D. M. Blumberg, J. M. Liebmann, R. Ritch, and D. C. Hood, “Hybrid deep learning on single wide-field optical coherence tomography scans accurately classifies glaucoma suspects,” J. glaucoma 26, 1086–1094 (2017).
[Crossref]

Romera-Paredes, B.

J. De Fauw, J. R. Ledsam, B. Romera-Paredes, S. Nikolov, N. Tomasev, S. Blackwell, H. Askham, X. Glorot, B. O’Donoghue, D. Visentin, and et al., “Clinically applicable deep learning for diagnosis and referral in retinal disease,” Nat. medicine 24, 1342 (2018).
[Crossref]

Ronneberger, O.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in International Conference on Medical image computing and computer-assisted intervention, (Springer, 2015), pp. 234–241.

Ö. Çiçek, A. Abdulkadir, S. S. Lienkamp, T. Brox, and O. Ronneberger, “3d u-net: learning dense volumetric segmentation from sparse annotation,” in International Conference on Medical Image Computing and Computer-Assisted Intervention, (Springer, 2016), pp. 424–432.

Roy, A. G.

A. G. Roy, S. Conjeti, S. P. K. Karri, D. Sheet, A. Katouzian, C. Wachinger, and N. Navab, “Relaynet: retinal layer and fluid segmentation of macular optical coherence tomography using fully convolutional networks,” Biomed. optics express 8, 3627–3642 (2017).
[Crossref]

Sahin, Y. H.

S. Olut, Y. H. Sahin, U. Demir, and G. Unal, “Generative adversarial training for mra image synthesis using multi-contrast mri,” arXiv preprint arXiv:1804.04366 (2018).

Saidha, S.

Y. He, A. Carass, B. M. Jedynak, S. D. Solomon, S. Saidha, P. A. Calabresi, and J. L. Prince, “Topology guaranteed segmentation of the human retina from oct using convolutional neural networks,” arXiv preprint arXiv:1803.05120 (2018).

Y. He, A. Carass, Y. Yun, C. Zhao, B. M. Jedynak, S. D. Solomon, S. Saidha, P. A. Calabresi, and J. L. Prince, “Towards topological correct segmentation of macular oct from cascaded fcns,” in Fetal, Infant and Ophthalmic Medical Image Analysis, (Springer, 2017), pp. 202–209.
[Crossref]

Sainz, F.

B. Llanas and F. Sainz, “Constructive approximate interpolation by neural networks,” J. Computat. Appl. Math. 188, 283–308 (2006).
[Crossref]

Sample, P. A.

F. A. Medeiros, L. M. Zangwill, L. M. Alencar, C. Bowd, P. A. Sample, R. Susanna, and R. N. Weinreb, “Detection of glaucoma progression with stratus oct retinal nerve fiber layer, optic nerve head, and macular thickness measurements,” Investig. ophthalmology & visual science 50, 5741–5748 (2009).
[Crossref]

Sánchez, C. I.

F. G. Venhuizen, B. van Ginneken, B. Liefers, M. J. van Grinsven, S. Fauser, C. Hoyng, T. Theelen, and C. I. Sánchez, “Robust total retina thickness segmentation in optical coherence tomography images using convolutional neural networks,” Biomed. optics express 8, 3292–3316 (2017).
[Crossref]

Schuman, J. S.

J. Xu, H. Ishikawa, G. Wollstein, R. A. Bilonick, L. S. Folio, Z. Nadler, L. Kagemann, and J. S. Schuman, “Three-dimensional spectral-domain optical coherence tomography data analysis for glaucoma detection,” PloS one 8, e55476 (2013).
[Crossref] [PubMed]

Settouti, N.

M. E. A. Bechar, N. Settouti, V. Barra, and M. A. Chikh, “Semi-supervised superpixel classification for medical images segmentation: application to detection of glaucoma disease,” Multidimens Syst. Signal Process. pp. 1–20 (2017).

Sheet, D.

A. G. Roy, S. Conjeti, S. P. K. Karri, D. Sheet, A. Katouzian, C. Wachinger, and N. Navab, “Relaynet: retinal layer and fluid segmentation of macular optical coherence tomography using fully convolutional networks,” Biomed. optics express 8, 3627–3642 (2017).
[Crossref]

Shelhamer, E.

J. Long, E. Shelhamer, and T. Darrell, “Fully convolutional networks for semantic segmentation,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2015), pp. 3431–3440.

Shi, F.

F. Shi, X. Chen, H. Zhao, W. Zhu, D. Xiang, E. Gao, M. Sonka, and H. Chen, “Automated 3-d retinal layer segmentation of macular optical coherence tomography images with serous pigment epithelial detachments,” IEEE transactions on medical imaging 34, 441–452 (2015).
[Crossref]

Shiga, Y.

K. Omodaka, G. An, S. Tsuda, Y. Shiga, N. Takada, T. Kikawa, H. Takahashi, H. Yokota, M. Akiba, and T. Nakazawa, “Classification of optic disc shape in glaucoma using machine learning based on quantified ocular parameters,” PloS one 12, e0190012 (2017).
[Crossref]

Simonyan, K.

K. Simonyan and A. Zisserman, “Very deep convolutional networks for large-scale image recognition,” Comput. Sci. (2014).

Sivaswamy, J.

A. Chakravarty and J. Sivaswamy, “A supervised joint multi-layer segmentation framework for retinal optical coherence tomography images using conditional random field,” Comput. methods programs biomedicine 165, 235–250 (2018).
[Crossref]

Solomon, S. D.

Y. He, A. Carass, Y. Yun, C. Zhao, B. M. Jedynak, S. D. Solomon, S. Saidha, P. A. Calabresi, and J. L. Prince, “Towards topological correct segmentation of macular oct from cascaded fcns,” in Fetal, Infant and Ophthalmic Medical Image Analysis, (Springer, 2017), pp. 202–209.
[Crossref]

Y. He, A. Carass, B. M. Jedynak, S. D. Solomon, S. Saidha, P. A. Calabresi, and J. L. Prince, “Topology guaranteed segmentation of the human retina from oct using convolutional neural networks,” arXiv preprint arXiv:1803.05120 (2018).

Sonka, M.

F. Shi, X. Chen, H. Zhao, W. Zhu, D. Xiang, E. Gao, M. Sonka, and H. Chen, “Automated 3-d retinal layer segmentation of macular optical coherence tomography images with serous pigment epithelial detachments,” IEEE transactions on medical imaging 34, 441–452 (2015).
[Crossref]

Sorkine-Hornung, A.

F. Perazzi, J. Pont-Tuset, B. McWilliams, L. Van Gool, M. Gross, and A. Sorkine-Hornung, “A benchmark dataset and evaluation methodology for video object segmentation,” in The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2016).

Sotirchos, E. S.

A. Lang, A. Carass, M. Hauser, E. S. Sotirchos, P. A. Calabresi, H. S. Ying, and J. L. Prince, “Retinal layer segmentation of macular oct images using boundary classification,” Biomed. optics express 4, 1133–1152 (2013).
[Crossref]

Susanna, R.

F. A. Medeiros, L. M. Zangwill, L. M. Alencar, C. Bowd, P. A. Sample, R. Susanna, and R. N. Weinreb, “Detection of glaucoma progression with stratus oct retinal nerve fiber layer, optic nerve head, and macular thickness measurements,” Investig. ophthalmology & visual science 50, 5741–5748 (2009).
[Crossref]

Sutskever, I.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” in Advances in neural information processing systems, (2012), pp. 1097–1105.

Suykens, J. A. K.

J. A. K. Suykens and J. Vandewalle, “Least squares support vector machine classifiers,” Neural Process. Lett. 9, 293–300 (1999).
[Crossref]

Szegedy, C.

S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” arXiv preprint arXiv:1502.03167 (2015).

Takada, N.

K. Omodaka, G. An, S. Tsuda, Y. Shiga, N. Takada, T. Kikawa, H. Takahashi, H. Yokota, M. Akiba, and T. Nakazawa, “Classification of optic disc shape in glaucoma using machine learning based on quantified ocular parameters,” PloS one 12, e0190012 (2017).
[Crossref]

Takahashi, H.

K. Omodaka, G. An, S. Tsuda, Y. Shiga, N. Takada, T. Kikawa, H. Takahashi, H. Yokota, M. Akiba, and T. Nakazawa, “Classification of optic disc shape in glaucoma using machine learning based on quantified ocular parameters,” PloS one 12, e0190012 (2017).
[Crossref]

Theelen, T.

F. G. Venhuizen, B. van Ginneken, B. Liefers, M. J. van Grinsven, S. Fauser, C. Hoyng, T. Theelen, and C. I. Sánchez, “Robust total retina thickness segmentation in optical coherence tomography images using convolutional neural networks,” Biomed. optics express 8, 3292–3316 (2017).
[Crossref]

Tomasev, N.

J. De Fauw, J. R. Ledsam, B. Romera-Paredes, S. Nikolov, N. Tomasev, S. Blackwell, H. Askham, X. Glorot, B. O’Donoghue, D. Visentin, and et al., “Clinically applicable deep learning for diagnosis and referral in retinal disease,” Nat. medicine 24, 1342 (2018).
[Crossref]

Toth, C. A.

Tsuda, S.

K. Omodaka, G. An, S. Tsuda, Y. Shiga, N. Takada, T. Kikawa, H. Takahashi, H. Yokota, M. Akiba, and T. Nakazawa, “Classification of optic disc shape in glaucoma using machine learning based on quantified ocular parameters,” PloS one 12, e0190012 (2017).
[Crossref]

Tu, Z.

S. Xie and Z. Tu, “Holistically-nested edge detection,” in Proceedings of the IEEE international conference on computer vision, (2015), pp. 1395–1403.

Unal, G.

S. Olut, Y. H. Sahin, U. Demir, and G. Unal, “Generative adversarial training for mra image synthesis using multi-contrast mri,” arXiv preprint arXiv:1804.04366 (2018).

Usman, M.

M. Usman, M. M. Fraz, and S. A. Barman, “Computer vision techniques applied for diagnostic analysis of retinal oct images: a review,” Arch. Comput. Methods Eng. 24, 449–465 (2017).
[Crossref]

Van der Schoot, J.

K. Vermeer, J. Van der Schoot, H. Lemij, and J. De Boer, “Automated segmentation by pixel classification of retinal layers in ophthalmic oct images,” Biomed. optics express 2, 1743–1756 (2011).
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van Ginneken, B.

F. G. Venhuizen, B. van Ginneken, B. Liefers, M. J. van Grinsven, S. Fauser, C. Hoyng, T. Theelen, and C. I. Sánchez, “Robust total retina thickness segmentation in optical coherence tomography images using convolutional neural networks,” Biomed. optics express 8, 3292–3316 (2017).
[Crossref]

Van Gool, L.

F. Perazzi, J. Pont-Tuset, B. McWilliams, L. Van Gool, M. Gross, and A. Sorkine-Hornung, “A benchmark dataset and evaluation methodology for video object segmentation,” in The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2016).

van Grinsven, M. J.

F. G. Venhuizen, B. van Ginneken, B. Liefers, M. J. van Grinsven, S. Fauser, C. Hoyng, T. Theelen, and C. I. Sánchez, “Robust total retina thickness segmentation in optical coherence tomography images using convolutional neural networks,” Biomed. optics express 8, 3292–3316 (2017).
[Crossref]

Vandewalle, J.

J. A. K. Suykens and J. Vandewalle, “Least squares support vector machine classifiers,” Neural Process. Lett. 9, 293–300 (1999).
[Crossref]

Venhuizen, F. G.

F. G. Venhuizen, B. van Ginneken, B. Liefers, M. J. van Grinsven, S. Fauser, C. Hoyng, T. Theelen, and C. I. Sánchez, “Robust total retina thickness segmentation in optical coherence tomography images using convolutional neural networks,” Biomed. optics express 8, 3292–3316 (2017).
[Crossref]

Vermeer, K.

K. Vermeer, J. Van der Schoot, H. Lemij, and J. De Boer, “Automated segmentation by pixel classification of retinal layers in ophthalmic oct images,” Biomed. optics express 2, 1743–1756 (2011).
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Vincent, S. J.

Visentin, D.

J. De Fauw, J. R. Ledsam, B. Romera-Paredes, S. Nikolov, N. Tomasev, S. Blackwell, H. Askham, X. Glorot, B. O’Donoghue, D. Visentin, and et al., “Clinically applicable deep learning for diagnosis and referral in retinal disease,” Nat. medicine 24, 1342 (2018).
[Crossref]

Wachinger, C.

A. G. Roy, S. Conjeti, S. P. K. Karri, D. Sheet, A. Katouzian, C. Wachinger, and N. Navab, “Relaynet: retinal layer and fluid segmentation of macular optical coherence tomography using fully convolutional networks,” Biomed. optics express 8, 3627–3642 (2017).
[Crossref]

Wang, C.

L. Fang, D. Cunefare, C. Wang, R. H. Guymer, S. Li, and S. Farsiu, “Automatic segmentation of nine retinal layer boundaries in oct images of non-exudative amd patients using deep learning and graph search,” Biomed. optics express 8, 2732–2744 (2017).
[Crossref]

Weinreb, R. N.

F. A. Medeiros, L. M. Zangwill, L. M. Alencar, C. Bowd, P. A. Sample, R. Susanna, and R. N. Weinreb, “Detection of glaucoma progression with stratus oct retinal nerve fiber layer, optic nerve head, and macular thickness measurements,” Investig. ophthalmology & visual science 50, 5741–5748 (2009).
[Crossref]

Wollstein, G.

J. Xu, H. Ishikawa, G. Wollstein, R. A. Bilonick, L. S. Folio, Z. Nadler, L. Kagemann, and J. S. Schuman, “Three-dimensional spectral-domain optical coherence tomography data analysis for glaucoma detection,” PloS one 8, e55476 (2013).
[Crossref] [PubMed]

Xiang, D.

F. Shi, X. Chen, H. Zhao, W. Zhu, D. Xiang, E. Gao, M. Sonka, and H. Chen, “Automated 3-d retinal layer segmentation of macular optical coherence tomography images with serous pigment epithelial detachments,” IEEE transactions on medical imaging 34, 441–452 (2015).
[Crossref]

Xie, S.

S. Xie and Z. Tu, “Holistically-nested edge detection,” in Proceedings of the IEEE international conference on computer vision, (2015), pp. 1395–1403.

Xu, J.

J. Xu, H. Ishikawa, G. Wollstein, R. A. Bilonick, L. S. Folio, Z. Nadler, L. Kagemann, and J. S. Schuman, “Three-dimensional spectral-domain optical coherence tomography data analysis for glaucoma detection,” PloS one 8, e55476 (2013).
[Crossref] [PubMed]

Ying, H. S.

A. Lang, A. Carass, M. Hauser, E. S. Sotirchos, P. A. Calabresi, H. S. Ying, and J. L. Prince, “Retinal layer segmentation of macular oct images using boundary classification,” Biomed. optics express 4, 1133–1152 (2013).
[Crossref]

Yokota, H.

K. Omodaka, G. An, S. Tsuda, Y. Shiga, N. Takada, T. Kikawa, H. Takahashi, H. Yokota, M. Akiba, and T. Nakazawa, “Classification of optic disc shape in glaucoma using machine learning based on quantified ocular parameters,” PloS one 12, e0190012 (2017).
[Crossref]

Yu, L.

H. Chen, X. Qi, L. Yu, and P.-A. Heng, “Dcan: deep contour-aware networks for accurate gland segmentation,” in Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, (2016), pp. 2487–2496.

Yuille, A. L.

L.-C. Chen, G. Papandreou, I. Kokkinos, K. Murphy, and A. L. Yuille, “Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs,” IEEE transactions on pattern analysis machine intelligence 40, 834–848 (2018).
[Crossref]

L. C. Chen, G. Papandreou, I. Kokkinos, K. Murphy, and A. L. Yuille, “Semantic image segmentation with deep convolutional nets and fully connected crfs,” Comput. Sci. pp. 357–361 (2014).

Yun, Y.

Y. He, A. Carass, Y. Yun, C. Zhao, B. M. Jedynak, S. D. Solomon, S. Saidha, P. A. Calabresi, and J. L. Prince, “Towards topological correct segmentation of macular oct from cascaded fcns,” in Fetal, Infant and Ophthalmic Medical Image Analysis, (Springer, 2017), pp. 202–209.
[Crossref]

Zangwill, L. M.

F. A. Medeiros, L. M. Zangwill, L. M. Alencar, C. Bowd, P. A. Sample, R. Susanna, and R. N. Weinreb, “Detection of glaucoma progression with stratus oct retinal nerve fiber layer, optic nerve head, and macular thickness measurements,” Investig. ophthalmology & visual science 50, 5741–5748 (2009).
[Crossref]

Zhao, C.

Y. He, A. Carass, Y. Yun, C. Zhao, B. M. Jedynak, S. D. Solomon, S. Saidha, P. A. Calabresi, and J. L. Prince, “Towards topological correct segmentation of macular oct from cascaded fcns,” in Fetal, Infant and Ophthalmic Medical Image Analysis, (Springer, 2017), pp. 202–209.
[Crossref]

Zhao, H.

F. Shi, X. Chen, H. Zhao, W. Zhu, D. Xiang, E. Gao, M. Sonka, and H. Chen, “Automated 3-d retinal layer segmentation of macular optical coherence tomography images with serous pigment epithelial detachments,” IEEE transactions on medical imaging 34, 441–452 (2015).
[Crossref]

Zhu, W.

F. Shi, X. Chen, H. Zhao, W. Zhu, D. Xiang, E. Gao, M. Sonka, and H. Chen, “Automated 3-d retinal layer segmentation of macular optical coherence tomography images with serous pigment epithelial detachments,” IEEE transactions on medical imaging 34, 441–452 (2015).
[Crossref]

Zisserman, A.

K. Simonyan and A. Zisserman, “Very deep convolutional networks for large-scale image recognition,” Comput. Sci. (2014).

Acta ophthalmologica (1)

D. Bizios, A. Heijl, J. L. Hougaard, and B. Bengtsson, “Machine learning classifiers for glaucoma diagnosis based on classification of retinal nerve fibre layer thickness parameters measured by stratus oct,” Acta ophthalmologica 88, 44–52 (2010).
[Crossref] [PubMed]

Arch. Comput. Methods Eng. (1)

M. Usman, M. M. Fraz, and S. A. Barman, “Computer vision techniques applied for diagnostic analysis of retinal oct images: a review,” Arch. Comput. Methods Eng. 24, 449–465 (2017).
[Crossref]

Biomed. Opt. Express (2)

Biomed. optics express (6)

A. G. Roy, S. Conjeti, S. P. K. Karri, D. Sheet, A. Katouzian, C. Wachinger, and N. Navab, “Relaynet: retinal layer and fluid segmentation of macular optical coherence tomography using fully convolutional networks,” Biomed. optics express 8, 3627–3642 (2017).
[Crossref]

F. G. Venhuizen, B. van Ginneken, B. Liefers, M. J. van Grinsven, S. Fauser, C. Hoyng, T. Theelen, and C. I. Sánchez, “Robust total retina thickness segmentation in optical coherence tomography images using convolutional neural networks,” Biomed. optics express 8, 3292–3316 (2017).
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S. J. Chiu, M. J. Allingham, P. S. Mettu, S. W. Cousins, J. A. Izatt, and S. Farsiu, “Kernel regression based segmentation of optical coherence tomography images with diabetic macular edema,” Biomed. optics express 6, 1172–1194 (2015).
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A. Lang, A. Carass, M. Hauser, E. S. Sotirchos, P. A. Calabresi, H. S. Ying, and J. L. Prince, “Retinal layer segmentation of macular oct images using boundary classification,” Biomed. optics express 4, 1133–1152 (2013).
[Crossref]

L. Fang, D. Cunefare, C. Wang, R. H. Guymer, S. Li, and S. Farsiu, “Automatic segmentation of nine retinal layer boundaries in oct images of non-exudative amd patients using deep learning and graph search,” Biomed. optics express 8, 2732–2744 (2017).
[Crossref]

K. Vermeer, J. Van der Schoot, H. Lemij, and J. De Boer, “Automated segmentation by pixel classification of retinal layers in ophthalmic oct images,” Biomed. optics express 2, 1743–1756 (2011).
[Crossref]

Comput. methods programs biomedicine (1)

A. Chakravarty and J. Sivaswamy, “A supervised joint multi-layer segmentation framework for retinal optical coherence tomography images using conditional random field,” Comput. methods programs biomedicine 165, 235–250 (2018).
[Crossref]

IEEE transactions on medical imaging (1)

F. Shi, X. Chen, H. Zhao, W. Zhu, D. Xiang, E. Gao, M. Sonka, and H. Chen, “Automated 3-d retinal layer segmentation of macular optical coherence tomography images with serous pigment epithelial detachments,” IEEE transactions on medical imaging 34, 441–452 (2015).
[Crossref]

IEEE transactions on pattern analysis machine intelligence (1)

L.-C. Chen, G. Papandreou, I. Kokkinos, K. Murphy, and A. L. Yuille, “Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs,” IEEE transactions on pattern analysis machine intelligence 40, 834–848 (2018).
[Crossref]

Investig. ophthalmology & visual science (1)

F. A. Medeiros, L. M. Zangwill, L. M. Alencar, C. Bowd, P. A. Sample, R. Susanna, and R. N. Weinreb, “Detection of glaucoma progression with stratus oct retinal nerve fiber layer, optic nerve head, and macular thickness measurements,” Investig. ophthalmology & visual science 50, 5741–5748 (2009).
[Crossref]

J. Computat. Appl. Math. (1)

B. Llanas and F. Sainz, “Constructive approximate interpolation by neural networks,” J. Computat. Appl. Math. 188, 283–308 (2006).
[Crossref]

J. glaucoma (1)

H. Muhammad, T. J. Fuchs, N. De Cuir, C. G. De Moraes, D. M. Blumberg, J. M. Liebmann, R. Ritch, and D. C. Hood, “Hybrid deep learning on single wide-field optical coherence tomography scans accurately classifies glaucoma suspects,” J. glaucoma 26, 1086–1094 (2017).
[Crossref]

Nat. medicine (1)

J. De Fauw, J. R. Ledsam, B. Romera-Paredes, S. Nikolov, N. Tomasev, S. Blackwell, H. Askham, X. Glorot, B. O’Donoghue, D. Visentin, and et al., “Clinically applicable deep learning for diagnosis and referral in retinal disease,” Nat. medicine 24, 1342 (2018).
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Neural Process. Lett. (1)

J. A. K. Suykens and J. Vandewalle, “Least squares support vector machine classifiers,” Neural Process. Lett. 9, 293–300 (1999).
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Opt. express (1)

PloS one (2)

K. Omodaka, G. An, S. Tsuda, Y. Shiga, N. Takada, T. Kikawa, H. Takahashi, H. Yokota, M. Akiba, and T. Nakazawa, “Classification of optic disc shape in glaucoma using machine learning based on quantified ocular parameters,” PloS one 12, e0190012 (2017).
[Crossref]

J. Xu, H. Ishikawa, G. Wollstein, R. A. Bilonick, L. S. Folio, Z. Nadler, L. Kagemann, and J. S. Schuman, “Three-dimensional spectral-domain optical coherence tomography data analysis for glaucoma detection,” PloS one 8, e55476 (2013).
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The annals mathematical statistics (1)

P. J. Huber and et al., “Robust estimation of a location parameter,” The annals mathematical statistics 35, 73–101 (1964).
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S. Olut, Y. H. Sahin, U. Demir, and G. Unal, “Generative adversarial training for mra image synthesis using multi-contrast mri,” arXiv preprint arXiv:1804.04366 (2018).

K. Simonyan and A. Zisserman, “Very deep convolutional networks for large-scale image recognition,” Comput. Sci. (2014).

F. Perazzi, J. Pont-Tuset, B. McWilliams, L. Van Gool, M. Gross, and A. Sorkine-Hornung, “A benchmark dataset and evaluation methodology for video object segmentation,” in The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2016).

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, and et al., “Tensorflow: a system for large-scale machine learning,” in OSDI, vol. 16 (2016), pp. 265–283.

M. E. A. Bechar, N. Settouti, V. Barra, and M. A. Chikh, “Semi-supervised superpixel classification for medical images segmentation: application to detection of glaucoma disease,” Multidimens Syst. Signal Process. pp. 1–20 (2017).

H. Chen, X. Qi, L. Yu, and P.-A. Heng, “Dcan: deep contour-aware networks for accurate gland segmentation,” in Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, (2016), pp. 2487–2496.

S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” arXiv preprint arXiv:1502.03167 (2015).

S. Xie and Z. Tu, “Holistically-nested edge detection,” in Proceedings of the IEEE international conference on computer vision, (2015), pp. 1395–1403.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” in Advances in neural information processing systems, (2012), pp. 1097–1105.

R. Girshick, J. Donahue, T. Darrell, and J. Malik, “Rich feature hierarchies for accurate object detection and semantic segmentation,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2014), pp. 580–587.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in International Conference on Medical image computing and computer-assisted intervention, (Springer, 2015), pp. 234–241.

Ö. Çiçek, A. Abdulkadir, S. S. Lienkamp, T. Brox, and O. Ronneberger, “3d u-net: learning dense volumetric segmentation from sparse annotation,” in International Conference on Medical Image Computing and Computer-Assisted Intervention, (Springer, 2016), pp. 424–432.

Y. He, A. Carass, Y. Yun, C. Zhao, B. M. Jedynak, S. D. Solomon, S. Saidha, P. A. Calabresi, and J. L. Prince, “Towards topological correct segmentation of macular oct from cascaded fcns,” in Fetal, Infant and Ophthalmic Medical Image Analysis, (Springer, 2017), pp. 202–209.
[Crossref]

Y. He, A. Carass, B. M. Jedynak, S. D. Solomon, S. Saidha, P. A. Calabresi, and J. L. Prince, “Topology guaranteed segmentation of the human retina from oct using convolutional neural networks,” arXiv preprint arXiv:1803.05120 (2018).

A. Mosinska, P. Marquez Neila, M. Kozinski, and P. Fua, “Beyond the pixel-wise loss for topology-aware delineation,” in Conference on Computer Vision and Pattern Recognition (CVPR), (2018), CONF.

J. Long, E. Shelhamer, and T. Darrell, “Fully convolutional networks for semantic segmentation,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (2015), pp. 3431–3440.

L. C. Chen, G. Papandreou, I. Kokkinos, K. Murphy, and A. L. Yuille, “Semantic image segmentation with deep convolutional nets and fully connected crfs,” Comput. Sci. pp. 357–361 (2014).

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Figures (9)

Fig. 1
Fig. 1 Our collected data are circular B-Scans performed in a 3.4mm diameter circle centered at the optic nerve head with depth of 1.9mm. (a) Current clinical RNFL thickness report uses sectoral-based RNFL thickness obtained from automatic segmentation of OCT machine; (b) Entire RNFL thickness vector is adopted in this paper calculated from segmentation results by our proposed approach. We segment the whole circular B-Scan into six layers (from top to bottom): vitreous, NFL (nerve fiber layer), GCL + IPL (ganglion cell layer and inner plexiform layer), INL-RPE (from inner nuclear layer to retinal pigment epithelium), choroid and sclera.
Fig. 2
Fig. 2 The workflow of segmentation-diagnosis pipeline: BL-net for segmentation, refinement process and classification net.
Fig. 3
Fig. 3 The architecture of BL-net.
Fig. 4
Fig. 4 Network for combination strategy. Mb is the boundary location matrix from coarse predicted boundary mask of B-part, and Ml is the one from the predicted layer mask of L-part refined by bi-decision. This network outputs the final learned location matrix M taking Mb and Ml as inputs.
Fig. 5
Fig. 5 Common fully connected layer (a) versus proposed unit layer (b).
Fig. 6
Fig. 6 Qualitative results of segmentation on our collected dataset. (a) shows examples of segmentations from BL-net and refinement strategies. (b) shows the refinement process of a bad case’s detected boundaries and segmented layers. U-net and S-net are two baseline models, bi-decision is proposed to refine outputs of the l-part of BL-net, interpolation is proposed to refine outputs of the b-part of BL-net and combination strategy is to fuse the two refined results. Refinement strategies correct topology error of bad segmentations.
Fig. 7
Fig. 7 Illustrations of bi-decision strategy removing the topology error. Take the third boundary for example. The third boundary is the down-boundary of layer 3 and the top-boundary of layer 4. The matched of these two boundaries is assured as the true boundary which is followed by interpolation to produce the final complete one.
Fig. 8
Fig. 8 Examples of seven retinal layers and total retina segmentation on public dataset. (a) For seven retina layers, the first column shows segmented layers, and the second column shows computed boundaries. (b) shows segmentation results for total retina. All segmentations are from l-part of BL-net combined with bi-decision strategy.
Fig. 9
Fig. 9 ROC curves for glaucoma classification. (a) shows the performance of different models. (b) shows the performance of our classification net using RNFL thickness vector when covering a specific region. S1, S2 .. S8 sequentially denote each of the region of eight splitting on the vector.

Tables (7)

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Algorithm 1 Bi-decision strategy

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Table 1 Average segmentation results using 3-fold cross-validation on our collected dataset. Jaccard index J is used as the region-based metric and Dice coefficient is used as the contour-based metric. ‡: Boundary masks are transformed from predicted layer segmentation. †: Layer masks are transformed from predicted boundaries. *: Statistically significant improvement compared with S-net+T-net (pvalue ≤ 0.1).

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Table 2 Dice coefficient for each retinal layer and unsigned boundary localization errors (mean ± standard deviation in pixels) for each retinal boundary of bi-decision.

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Table 3 Comparison of Dice coefficient for each retinal layer on a public dataset. The best performance is shown by bold and the second best is shown by * .

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Table 4 Comparison of unsigned boundary localization errors (in pixels) for each retinal boundary on a public dataset. The best performance is shown by bold.

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Table 5 Diagnosing results (testing set). †: Initialization of bias of the unit layer of classification net. *: Average RNFL thickness in training.

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Table 6 Classification results using the RNFL thickness vector covering a specific region.

Equations (9)

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L o s s _ s e g = x χ log p b ( x , g b ( x ) ; w b ) x χ log p l ( x , g l ( x ) ; w b , w l ) + α | | w | | 2
f ( x ) = j = 0 n 1 ( y j y j + 1 ) σ ( ( β α ) A x x j + 1 x j + ( α x j + 1 β x j ) x j + 1 x j ) + y n σ ( ( β α ) A x x n x n 1 + ( 2 α β x n α x n 1 ) x n x n 1 A )
M b _ l = [ M b m a s k _ b ;   M l m a s k _ l ]
M = conv ( M b _ l )
L o s s _ l o c = { 1 2 ( y f ( x ; w i ) ) 2 , | y f ( x ) | < δ δ | y f ( x ; w i ) | 1 2 δ 2 , otherwise
u n i t _ l a y e r _ o u t p u t = max ( t h r e s h o l d t h i c k n e s s I , 0 )
L o s s _ c l a s s = i = 0 n log p ( t i , g ( t i ) ; w c )
J = 1 l l = 1 l L i L _ G i L i L _ G i = 1 l l = 1 n T P i T P i + F P i + F N i
D i c e = 1 b j = 1 b 2 P j R j P j + R j , P j = T P j T P j + F P j , R j = T P j T P j + F N j

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