Abstract

Choroidal neovascularization (CNV) generally appears in the advanced stage of age-related macular degeneration (AMD) and has more complex pathological characteristics comparing with most other retinal diseases. So far, few literatures focused on the CNV segmentation from a machine learning and computer vision perspective. Therefore, accurate CNV segmentation is a challenging problem in SD-OCT images. In this paper, a multi-scale parallel branch CNN (MPB-CNN) is proposed for CNV segmentation. First, three parallel branch networks are used for multi-scale feature extraction. In each branch, standard convolution is replaced with atrous convolution, in which wider and more powerful multi-scale information can be extracted due to the sparsity of convolutional kernels. To further improve the segmentation results, intra-branch connections are introduced to preserve signal transmission and inter-branch connections are introduced to interact multi-scale information. Then, feature maps from different branches are cascaded with low-level features computing by several convolutional layers. The combined feature is used as the input to acquire the final prediction map by stacking three convolutional layers. Besides, extra branch supervisions are applied at the end of each branch to guarantee the discrimination of feature representations from each branch and benefit the network optimization. Finally, gradient constraint is added to loss function to preserve the boundary of the CNV lesion. An effective cross validation is performed on 202 cubes from 12 patients based on patient independence with the mean dice value being 0.757 and the mean overlap ratio being 60.8%. Experiment results indicated that the proposed MPB-CNN can provide reliable segmentations for CNV from SD-OCT images.

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

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2018 (4)

T. Schlegl, S. M. Waldstein, and H. Bogunovic, “Fully Automated Detection and Quantification of Macular Fluid in OCT Using Deep Learning,” Ophthalmology 125(4), 549–558 (2018).
[Crossref]

R. Rasti, H. Rabbani, A. Mehridehnavi, and F. Hajizadeh, “Macular OCT Classification Using a Multi-Scale Convolutional Neural Network Ensemble,” IEEE Trans. Med. Imaging 37(4), 1024–1034 (2018).
[Crossref]

L. 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 Trans. Pattern Anal. Mach. Intell. 40(4), 834–848 (2018).
[Crossref]

A. Shah, , et al., “Multiple surface segmentation using convolution neural nets: application to retinal layer segmentation in OCT images,” Biomed. Opt. Express 9(9), 4509–4526 (2018).
[Crossref]

2017 (7)

X. Sui, Y. Zheng, B. Wei, H. Bi, J. Wu, X. Pan, Y. Yin, and S. Zhang, “Choroid segmentation from optical coherence tomography with graph edge weights learned from deep convolutional neural networks,” J. Neurocomput. 237, 332–341 (2017).
[Crossref]

S. Zhu, F. Shi, D. Xiang, W. Zhu, H. Chen, and X. Chen, “Choroid Neovascularization Growth Prediction With Treatment Based on Reaction-Diffusion Model in 3-D OCT Images,” IEEE J. Biomed. Health Inform. 21(6), 1667–1674 (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. Opt. Express 8(5), 2732–2744 (2017).
[Crossref]

F. Venhuizen, B. Ginneken, B. Liefers, M. Grinsven, S. Fauser, C. Hoyng C, T. Theelen, and C. Sanchez, “Robust total retina thickness segmentation in optical coherence tomography images using convolutional neural networks,” Biomed. Opt. Express 8(7), 3292–3316 (2017).
[Crossref]

C. S. Lee, A. J. Tyring, N. P. Deruyter, Y. Wu, A. Rokem, and A. Y. Lee, “Deep-learning based, automated segmentation of macular edema in optical coherence tomography,” Biomed. Opt. Express 8(7), 3440–3448 (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. Opt. Express 8(8), 3627–3642 (2017).
[Crossref]

Y. Xu, K. Yan, J. Kim, X. Wang, C. Li, L. Su, S. Yu, X. Xu, and D. D. Feng, “Dual-stage deep learning framework for pigment epithelium detachment segmentation in polypoidal choroidal vasculopathy,” Biomed. Opt. Express 8(9), 4061–4076 (2017).
[Crossref]

2016 (1)

S. S. Gao, L. Liu, and S. T. Bailey, “Quantification of choroidal neovascularization vessel length using optical coherence tomography angiography,” J. Biomed. Opt. 21(7), 076010 (2016).
[Crossref]

2015 (4)

R. S. Sulaiman, J. Quigley, X. Qi, M. N. O’Hare, M. B. Grant, and M. E. Boulton, “A simple optical coherence tomography quantification method for choroidal neovascularization,” J. Ocul. Pharmacol. Ther. 31(8), 447–454 (2015).
[Crossref]

T. E. de Carlo, M. A. Bonini Filho, A. T. Chin, M. Adhi, and D. Ferrara, “Spectral-Domain Optical Coherence Tomography Angiography of Choroidal Neovascularization,” Ophthalmology 122(6), 1228–1238 (2015).
[Crossref]

E. Bruyère, V. Caillaux, S. Y. Cohen, and D. Martiano, “Spectral-Domain Optical Coherence Tomography of Subretinal Hyperreflective Exudation in Myopic Choroidal Neovascularization,” Am. J. Ophthalmol. 160(4), 749–758 (2015).
[Crossref]

L. Liu, S. S. Gao, S. T. Bailey, and D. Huang, “Automated choroidal neovascularization detection algorithm for optical coherence tomography angiography,” Biomed. Opt. Express 6(9), 3564–3576 (2015).
[Crossref]

2014 (2)

Y. Jia, S. T. Bailey, D. J. Wilson, and O. Tan, “Quantitative Optical Coherence Tomography Angiography of Choroidal Neovascularization in Age-Related Macular Degeneration,” Ophthalmology 121(7), 1435–1444 (2014).
[Crossref]

S. Niu, Q. Chen, L. de Sisternes, and D. L. Rubin, “Automated retinal layers segmentation and quantitative evaluation in SD-OCT images,” Comput. Biol. Med. 54, 116–128 (2014).
[Crossref]

2013 (1)

W. M. Abdelmoula, S. M. Shah, and A. S. Fahmy, “Segmentation of Choroidal Neovascularization in Fundus Fluorescein Angiograms,” IEEE Trans. Biomed. Eng. 60(5), 1439–1445 (2013).
[Crossref]

2011 (1)

C. L. Tsai, Y. L. Yang, S. J. Chen, K. S. Lin, C. H. Chan, and W. Y. Lin, “Automatic Characterization of Classic Choroidal Neovascularization using AdaBoost for Supervised Learning,” Invest. Ophthalmol. Visual Sci. 52(5), 2767–2774 (2011).
[Crossref]

2010 (1)

C. Framme, G. Panagakis, and R. Birngruber, “Effects on choroidal neovascularization after anti-VEGF Upload using intravitreal ranibizumab, as determined by spectral domain-optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 51(3), 1671–1676 (2010).
[Crossref]

2007 (1)

U. Schmidt-Erfurth, K. Kriechbaum, and A. Oldag, “Three-dimensional angiography of classic and occult lesion types in choroidal neovascularization,” Invest. Ophthalmol. Visual Sci. 48(4), 1751–1760 (2007).
[Crossref]

2001 (1)

T. Fukuchi, K. Takahashi, M. Uyama, and M. Matsumura, “Comparative Study of Experimental Choroidal Neovascularization by Optical Coherence Tomography and Histopathology,” Jpn. J. Ophthalmol. 45(3), 252–258 (2001).
[Crossref]

Abdelmoula, W. M.

W. M. Abdelmoula, S. M. Shah, and A. S. Fahmy, “Segmentation of Choroidal Neovascularization in Fundus Fluorescein Angiograms,” IEEE Trans. Biomed. Eng. 60(5), 1439–1445 (2013).
[Crossref]

Abdulkadir, A.

O. Cicek, 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, 424–432, (2016).

Abramoff, M. D.

A. Shah, M. D. Abramoff, and X. Wu, “Simultaneous multiple surface segmentation using deep learning,” in Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support, 3–11, (2017).

Adam, H.

L. Chen, G. Papandreou, F. Schroff, and H. Adam, “Rethinking Atrous Convolution for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

L. Chen, Y. Zhu, G. Papandreou, F. Schroff, and H. Adam, “Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2018).

Adhi, M.

T. E. de Carlo, M. A. Bonini Filho, A. T. Chin, M. Adhi, and D. Ferrara, “Spectral-Domain Optical Coherence Tomography Angiography of Choroidal Neovascularization,” Ophthalmology 122(6), 1228–1238 (2015).
[Crossref]

Bailey, S. T.

S. S. Gao, L. Liu, and S. T. Bailey, “Quantification of choroidal neovascularization vessel length using optical coherence tomography angiography,” J. Biomed. Opt. 21(7), 076010 (2016).
[Crossref]

L. Liu, S. S. Gao, S. T. Bailey, and D. Huang, “Automated choroidal neovascularization detection algorithm for optical coherence tomography angiography,” Biomed. Opt. Express 6(9), 3564–3576 (2015).
[Crossref]

Y. Jia, S. T. Bailey, D. J. Wilson, and O. Tan, “Quantitative Optical Coherence Tomography Angiography of Choroidal Neovascularization in Age-Related Macular Degeneration,” Ophthalmology 121(7), 1435–1444 (2014).
[Crossref]

Bi, H.

X. Sui, Y. Zheng, B. Wei, H. Bi, J. Wu, X. Pan, Y. Yin, and S. Zhang, “Choroid segmentation from optical coherence tomography with graph edge weights learned from deep convolutional neural networks,” J. Neurocomput. 237, 332–341 (2017).
[Crossref]

Birngruber, R.

C. Framme, G. Panagakis, and R. Birngruber, “Effects on choroidal neovascularization after anti-VEGF Upload using intravitreal ranibizumab, as determined by spectral domain-optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 51(3), 1671–1676 (2010).
[Crossref]

Black, N.

E. Brankin, P. McCuIlagh, N. Black, W. Patton, and A. Muldrew, “The optimisation of thresholding techniques for the identification of choroidal neovascular membranes in exudative age-related macular degeneration,” In Proc. 19th IEEE Symp. Comput.-Based Med. Syst, 430–435, (2006).

E. Brankin, P. McCullagh, W. Patton, A. Muldrew, and N. Black, “Identification of choroidal neovascularisation on fluorescein angiograms using gradient vector flow active contours,” In Proc. Int. Mach. Vis. Imag. Process. Conf, 165–169, (2008).

Bogunovic, H.

T. Schlegl, S. M. Waldstein, and H. Bogunovic, “Fully Automated Detection and Quantification of Macular Fluid in OCT Using Deep Learning,” Ophthalmology 125(4), 549–558 (2018).
[Crossref]

Bonini Filho, M. A.

T. E. de Carlo, M. A. Bonini Filho, A. T. Chin, M. Adhi, and D. Ferrara, “Spectral-Domain Optical Coherence Tomography Angiography of Choroidal Neovascularization,” Ophthalmology 122(6), 1228–1238 (2015).
[Crossref]

Boulton, M. E.

R. S. Sulaiman, J. Quigley, X. Qi, M. N. O’Hare, M. B. Grant, and M. E. Boulton, “A simple optical coherence tomography quantification method for choroidal neovascularization,” J. Ocul. Pharmacol. Ther. 31(8), 447–454 (2015).
[Crossref]

Brankin, E.

E. Brankin, P. McCullagh, W. Patton, A. Muldrew, and N. Black, “Identification of choroidal neovascularisation on fluorescein angiograms using gradient vector flow active contours,” In Proc. Int. Mach. Vis. Imag. Process. Conf, 165–169, (2008).

E. Brankin, P. McCuIlagh, N. Black, W. Patton, and A. Muldrew, “The optimisation of thresholding techniques for the identification of choroidal neovascular membranes in exudative age-related macular degeneration,” In Proc. 19th IEEE Symp. Comput.-Based Med. Syst, 430–435, (2006).

Brox, T.

O. Ronneberger, P. Fischer, and T. Brox, “U-Net: Convolutional Networks for Biomedical Image Segmentation,” International Conference on Medical Image Computing and Computer Assisted Intervention, (2015).

O. Cicek, 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, 424–432, (2016).

Bruyère, E.

E. Bruyère, V. Caillaux, S. Y. Cohen, and D. Martiano, “Spectral-Domain Optical Coherence Tomography of Subretinal Hyperreflective Exudation in Myopic Choroidal Neovascularization,” Am. J. Ophthalmol. 160(4), 749–758 (2015).
[Crossref]

Caillaux, V.

E. Bruyère, V. Caillaux, S. Y. Cohen, and D. Martiano, “Spectral-Domain Optical Coherence Tomography of Subretinal Hyperreflective Exudation in Myopic Choroidal Neovascularization,” Am. J. Ophthalmol. 160(4), 749–758 (2015).
[Crossref]

Chan, C. H.

C. L. Tsai, Y. L. Yang, S. J. Chen, K. S. Lin, C. H. Chan, and W. Y. Lin, “Automatic Characterization of Classic Choroidal Neovascularization using AdaBoost for Supervised Learning,” Invest. Ophthalmol. Visual Sci. 52(5), 2767–2774 (2011).
[Crossref]

Chavane, F.

S. Takerkart, R. Fenouil, J. Piovano, A. Reynaud, L. Hoffart, F. Chavane, T. Papadopoulo, J. Conrath, and G. S. Masson, “A quantification framework for post-lesion neovascularization in retinal angiography,” In Proc. IEEE Int. Symp. Biomed. Imag, 1457–1460, (2008).

Chen, H.

S. Zhu, F. Shi, D. Xiang, W. Zhu, H. Chen, and X. Chen, “Choroid Neovascularization Growth Prediction With Treatment Based on Reaction-Diffusion Model in 3-D OCT Images,” IEEE J. Biomed. Health Inform. 21(6), 1667–1674 (2017).
[Crossref]

X. Yang, H. Chen, and J. Qin, “Automatic 3D Cardiovascular MR Segmentation with Densely-Connected Volumetric ConvNets,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

Chen, L.

L. 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 Trans. Pattern Anal. Mach. Intell. 40(4), 834–848 (2018).
[Crossref]

L. Chen, G. Papandreou, F. Schroff, and H. Adam, “Rethinking Atrous Convolution for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

L. Chen, Y. Zhu, G. Papandreou, F. Schroff, and H. Adam, “Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2018).

Chen, M.

M. Chen, J. Wang, I. Oguz, B. L. VanderBeek, and J. C. Gee, “Automated segmentation of the choroid in edi-oct images with retinal pathology using convolution neural networks,” in Fetal, Infant and Ophthalmic Medical Image Analysis, 177–184, (2017).

Chen, Q.

S. Niu, Q. Chen, L. de Sisternes, and D. L. Rubin, “Automated retinal layers segmentation and quantitative evaluation in SD-OCT images,” Comput. Biol. Med. 54, 116–128 (2014).
[Crossref]

Chen, S. J.

C. L. Tsai, Y. L. Yang, S. J. Chen, K. S. Lin, C. H. Chan, and W. Y. Lin, “Automatic Characterization of Classic Choroidal Neovascularization using AdaBoost for Supervised Learning,” Invest. Ophthalmol. Visual Sci. 52(5), 2767–2774 (2011).
[Crossref]

Chen, X.

S. Zhu, F. Shi, D. Xiang, W. Zhu, H. Chen, and X. Chen, “Choroid Neovascularization Growth Prediction With Treatment Based on Reaction-Diffusion Model in 3-D OCT Images,” IEEE J. Biomed. Health Inform. 21(6), 1667–1674 (2017).
[Crossref]

S. Zhu, X. Chen, F. Shi, D. Xiang, and W. Zhu, “3D choroid neovascularization growth prediction based on reaction-diffusion model,” Proceedings of the SPIE, (2016).

Chin, A. T.

T. E. de Carlo, M. A. Bonini Filho, A. T. Chin, M. Adhi, and D. Ferrara, “Spectral-Domain Optical Coherence Tomography Angiography of Choroidal Neovascularization,” Ophthalmology 122(6), 1228–1238 (2015).
[Crossref]

Cicek, O.

O. Cicek, 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, 424–432, (2016).

Cohen, S. Y.

E. Bruyère, V. Caillaux, S. Y. Cohen, and D. Martiano, “Spectral-Domain Optical Coherence Tomography of Subretinal Hyperreflective Exudation in Myopic Choroidal Neovascularization,” Am. J. Ophthalmol. 160(4), 749–758 (2015).
[Crossref]

Conjeti, S.

Conrath, J.

S. Takerkart, R. Fenouil, J. Piovano, A. Reynaud, L. Hoffart, F. Chavane, T. Papadopoulo, J. Conrath, and G. S. Masson, “A quantification framework for post-lesion neovascularization in retinal angiography,” In Proc. IEEE Int. Symp. Biomed. Imag, 1457–1460, (2008).

Cunefare, D.

Darrell, T.

E. Shelhamer, J. Long, and T. Darrell, “Fully Convolutional Networks for Semantic Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2015).

Dasgupta, A.

A. Dasgupta and S. Singh, “A fully convolutional neural network based structured prediction approach towards the retinal vessel segmentation,” IEEE International Symposium on Biomedical Imaging (ISBI), (2017).

de Carlo, T. E.

T. E. de Carlo, M. A. Bonini Filho, A. T. Chin, M. Adhi, and D. Ferrara, “Spectral-Domain Optical Coherence Tomography Angiography of Choroidal Neovascularization,” Ophthalmology 122(6), 1228–1238 (2015).
[Crossref]

de Sisternes, L.

S. Niu, Q. Chen, L. de Sisternes, and D. L. Rubin, “Automated retinal layers segmentation and quantitative evaluation in SD-OCT images,” Comput. Biol. Med. 54, 116–128 (2014).
[Crossref]

Deruyter, N. P.

Fahmy, A. S.

W. M. Abdelmoula, S. M. Shah, and A. S. Fahmy, “Segmentation of Choroidal Neovascularization in Fundus Fluorescein Angiograms,” IEEE Trans. Biomed. Eng. 60(5), 1439–1445 (2013).
[Crossref]

Fang, L.

Farsiu, S.

Fauser, S.

Feng, D. D.

Fenouil, R.

S. Takerkart, R. Fenouil, J. Piovano, A. Reynaud, L. Hoffart, F. Chavane, T. Papadopoulo, J. Conrath, and G. S. Masson, “A quantification framework for post-lesion neovascularization in retinal angiography,” In Proc. IEEE Int. Symp. Biomed. Imag, 1457–1460, (2008).

Ferrante, E.

K. Kamnitsas, E. Ferrante, S. Parisot, and C. Ledig, “DeepMedic for Brain Tumor Segmentation,” International Conference on Medical Image Computing and Computer Assisted Intervention, (2016).

Ferrara, D.

T. E. de Carlo, M. A. Bonini Filho, A. T. Chin, M. Adhi, and D. Ferrara, “Spectral-Domain Optical Coherence Tomography Angiography of Choroidal Neovascularization,” Ophthalmology 122(6), 1228–1238 (2015).
[Crossref]

Fischer, P.

O. Ronneberger, P. Fischer, and T. Brox, “U-Net: Convolutional Networks for Biomedical Image Segmentation,” International Conference on Medical Image Computing and Computer Assisted Intervention, (2015).

Framme, C.

C. Framme, G. Panagakis, and R. Birngruber, “Effects on choroidal neovascularization after anti-VEGF Upload using intravitreal ranibizumab, as determined by spectral domain-optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 51(3), 1671–1676 (2010).
[Crossref]

Fu, J.

J. Fu, J. Liu, Y. Member, H. Wang, and Lu, “Stacked Deconvolutional Network for Semantic Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

Fukuchi, T.

T. Fukuchi, K. Takahashi, M. Uyama, and M. Matsumura, “Comparative Study of Experimental Choroidal Neovascularization by Optical Coherence Tomography and Histopathology,” Jpn. J. Ophthalmol. 45(3), 252–258 (2001).
[Crossref]

Gao, S. S.

S. S. Gao, L. Liu, and S. T. Bailey, “Quantification of choroidal neovascularization vessel length using optical coherence tomography angiography,” J. Biomed. Opt. 21(7), 076010 (2016).
[Crossref]

L. Liu, S. S. Gao, S. T. Bailey, and D. Huang, “Automated choroidal neovascularization detection algorithm for optical coherence tomography angiography,” Biomed. Opt. Express 6(9), 3564–3576 (2015).
[Crossref]

Gee, J. C.

M. Chen, J. Wang, I. Oguz, B. L. VanderBeek, and J. C. Gee, “Automated segmentation of the choroid in edi-oct images with retinal pathology using convolution neural networks,” in Fetal, Infant and Ophthalmic Medical Image Analysis, 177–184, (2017).

Ginneken, B.

Grant, M. B.

R. S. Sulaiman, J. Quigley, X. Qi, M. N. O’Hare, M. B. Grant, and M. E. Boulton, “A simple optical coherence tomography quantification method for choroidal neovascularization,” J. Ocul. Pharmacol. Ther. 31(8), 447–454 (2015).
[Crossref]

Grinsven, M.

Guymer, R. H.

Hajizadeh, F.

R. Rasti, H. Rabbani, A. Mehridehnavi, and F. Hajizadeh, “Macular OCT Classification Using a Multi-Scale Convolutional Neural Network Ensemble,” IEEE Trans. Med. Imaging 37(4), 1024–1034 (2018).
[Crossref]

He, K.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep Residual Learning for Image Recognition,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2016).

Hoffart, L.

S. Takerkart, R. Fenouil, J. Piovano, A. Reynaud, L. Hoffart, F. Chavane, T. Papadopoulo, J. Conrath, and G. S. Masson, “A quantification framework for post-lesion neovascularization in retinal angiography,” In Proc. IEEE Int. Symp. Biomed. Imag, 1457–1460, (2008).

Hoyng C, C.

Huang, D.

Jia, Y.

Y. Jia, S. T. Bailey, D. J. Wilson, and O. Tan, “Quantitative Optical Coherence Tomography Angiography of Choroidal Neovascularization in Age-Related Macular Degeneration,” Ophthalmology 121(7), 1435–1444 (2014).
[Crossref]

Kamnitsas, K.

K. Kamnitsas, E. Ferrante, S. Parisot, and C. Ledig, “DeepMedic for Brain Tumor Segmentation,” International Conference on Medical Image Computing and Computer Assisted Intervention, (2016).

Karri, S. P. K.

Katouzian, A.

Kim, J.

Kokkinos, I.

L. 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 Trans. Pattern Anal. Mach. Intell. 40(4), 834–848 (2018).
[Crossref]

Kriechbaum, K.

U. Schmidt-Erfurth, K. Kriechbaum, and A. Oldag, “Three-dimensional angiography of classic and occult lesion types in choroidal neovascularization,” Invest. Ophthalmol. Visual Sci. 48(4), 1751–1760 (2007).
[Crossref]

Ledig, C.

K. Kamnitsas, E. Ferrante, S. Parisot, and C. Ledig, “DeepMedic for Brain Tumor Segmentation,” International Conference on Medical Image Computing and Computer Assisted Intervention, (2016).

Lee, A. Y.

Lee, C. S.

Li, C.

Li, S.

Liefers, B.

Lienkamp, S. S.

O. Cicek, 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, 424–432, (2016).

Lin, K. S.

C. L. Tsai, Y. L. Yang, S. J. Chen, K. S. Lin, C. H. Chan, and W. Y. Lin, “Automatic Characterization of Classic Choroidal Neovascularization using AdaBoost for Supervised Learning,” Invest. Ophthalmol. Visual Sci. 52(5), 2767–2774 (2011).
[Crossref]

Lin, L.

P. Luo, G. Wang, L. Lin, and X. Wang, “Deep Dual Learning for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

G. Wang, P. Luo, L. Lin, and X. Wang, “Learning Object Interactions and Descriptions for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

Lin, W. Y.

C. L. Tsai, Y. L. Yang, S. J. Chen, K. S. Lin, C. H. Chan, and W. Y. Lin, “Automatic Characterization of Classic Choroidal Neovascularization using AdaBoost for Supervised Learning,” Invest. Ophthalmol. Visual Sci. 52(5), 2767–2774 (2011).
[Crossref]

Liu, J.

J. Fu, J. Liu, Y. Member, H. Wang, and Lu, “Stacked Deconvolutional Network for Semantic Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

Liu, L.

S. S. Gao, L. Liu, and S. T. Bailey, “Quantification of choroidal neovascularization vessel length using optical coherence tomography angiography,” J. Biomed. Opt. 21(7), 076010 (2016).
[Crossref]

L. Liu, S. S. Gao, S. T. Bailey, and D. Huang, “Automated choroidal neovascularization detection algorithm for optical coherence tomography angiography,” Biomed. Opt. Express 6(9), 3564–3576 (2015).
[Crossref]

Liu, X.

Y. Tai, J. Yang, and X. Liu, “Image Super-Resolution via Deep Recursive Residual Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

Long, J.

E. Shelhamer, J. Long, and T. Darrell, “Fully Convolutional Networks for Semantic Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2015).

Lu,

J. Fu, J. Liu, Y. Member, H. Wang, and Lu, “Stacked Deconvolutional Network for Semantic Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

Luo, P.

P. Luo, G. Wang, L. Lin, and X. Wang, “Deep Dual Learning for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

G. Wang, P. Luo, L. Lin, and X. Wang, “Learning Object Interactions and Descriptions for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

Martiano, D.

E. Bruyère, V. Caillaux, S. Y. Cohen, and D. Martiano, “Spectral-Domain Optical Coherence Tomography of Subretinal Hyperreflective Exudation in Myopic Choroidal Neovascularization,” Am. J. Ophthalmol. 160(4), 749–758 (2015).
[Crossref]

Masson, G. S.

S. Takerkart, R. Fenouil, J. Piovano, A. Reynaud, L. Hoffart, F. Chavane, T. Papadopoulo, J. Conrath, and G. S. Masson, “A quantification framework for post-lesion neovascularization in retinal angiography,” In Proc. IEEE Int. Symp. Biomed. Imag, 1457–1460, (2008).

Matsumura, M.

T. Fukuchi, K. Takahashi, M. Uyama, and M. Matsumura, “Comparative Study of Experimental Choroidal Neovascularization by Optical Coherence Tomography and Histopathology,” Jpn. J. Ophthalmol. 45(3), 252–258 (2001).
[Crossref]

McCuIlagh, P.

E. Brankin, P. McCuIlagh, N. Black, W. Patton, and A. Muldrew, “The optimisation of thresholding techniques for the identification of choroidal neovascular membranes in exudative age-related macular degeneration,” In Proc. 19th IEEE Symp. Comput.-Based Med. Syst, 430–435, (2006).

McCullagh, P.

E. Brankin, P. McCullagh, W. Patton, A. Muldrew, and N. Black, “Identification of choroidal neovascularisation on fluorescein angiograms using gradient vector flow active contours,” In Proc. Int. Mach. Vis. Imag. Process. Conf, 165–169, (2008).

Mehridehnavi, A.

R. Rasti, H. Rabbani, A. Mehridehnavi, and F. Hajizadeh, “Macular OCT Classification Using a Multi-Scale Convolutional Neural Network Ensemble,” IEEE Trans. Med. Imaging 37(4), 1024–1034 (2018).
[Crossref]

Member, Y.

J. Fu, J. Liu, Y. Member, H. Wang, and Lu, “Stacked Deconvolutional Network for Semantic Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

Muldrew, A.

E. Brankin, P. McCuIlagh, N. Black, W. Patton, and A. Muldrew, “The optimisation of thresholding techniques for the identification of choroidal neovascular membranes in exudative age-related macular degeneration,” In Proc. 19th IEEE Symp. Comput.-Based Med. Syst, 430–435, (2006).

E. Brankin, P. McCullagh, W. Patton, A. Muldrew, and N. Black, “Identification of choroidal neovascularisation on fluorescein angiograms using gradient vector flow active contours,” In Proc. Int. Mach. Vis. Imag. Process. Conf, 165–169, (2008).

Murphy, K.

L. 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 Trans. Pattern Anal. Mach. Intell. 40(4), 834–848 (2018).
[Crossref]

Navab, N.

Niu, S.

S. Niu, Q. Chen, L. de Sisternes, and D. L. Rubin, “Automated retinal layers segmentation and quantitative evaluation in SD-OCT images,” Comput. Biol. Med. 54, 116–128 (2014).
[Crossref]

O’Hare, M. N.

R. S. Sulaiman, J. Quigley, X. Qi, M. N. O’Hare, M. B. Grant, and M. E. Boulton, “A simple optical coherence tomography quantification method for choroidal neovascularization,” J. Ocul. Pharmacol. Ther. 31(8), 447–454 (2015).
[Crossref]

Oguz, I.

M. Chen, J. Wang, I. Oguz, B. L. VanderBeek, and J. C. Gee, “Automated segmentation of the choroid in edi-oct images with retinal pathology using convolution neural networks,” in Fetal, Infant and Ophthalmic Medical Image Analysis, 177–184, (2017).

Oldag, A.

U. Schmidt-Erfurth, K. Kriechbaum, and A. Oldag, “Three-dimensional angiography of classic and occult lesion types in choroidal neovascularization,” Invest. Ophthalmol. Visual Sci. 48(4), 1751–1760 (2007).
[Crossref]

Pan, X.

X. Sui, Y. Zheng, B. Wei, H. Bi, J. Wu, X. Pan, Y. Yin, and S. Zhang, “Choroid segmentation from optical coherence tomography with graph edge weights learned from deep convolutional neural networks,” J. Neurocomput. 237, 332–341 (2017).
[Crossref]

Panagakis, G.

C. Framme, G. Panagakis, and R. Birngruber, “Effects on choroidal neovascularization after anti-VEGF Upload using intravitreal ranibizumab, as determined by spectral domain-optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 51(3), 1671–1676 (2010).
[Crossref]

Papadopoulo, T.

S. Takerkart, R. Fenouil, J. Piovano, A. Reynaud, L. Hoffart, F. Chavane, T. Papadopoulo, J. Conrath, and G. S. Masson, “A quantification framework for post-lesion neovascularization in retinal angiography,” In Proc. IEEE Int. Symp. Biomed. Imag, 1457–1460, (2008).

Papandreou, G.

L. 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 Trans. Pattern Anal. Mach. Intell. 40(4), 834–848 (2018).
[Crossref]

L. Chen, G. Papandreou, F. Schroff, and H. Adam, “Rethinking Atrous Convolution for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

L. Chen, Y. Zhu, G. Papandreou, F. Schroff, and H. Adam, “Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2018).

Parisot, S.

K. Kamnitsas, E. Ferrante, S. Parisot, and C. Ledig, “DeepMedic for Brain Tumor Segmentation,” International Conference on Medical Image Computing and Computer Assisted Intervention, (2016).

Patton, W.

E. Brankin, P. McCullagh, W. Patton, A. Muldrew, and N. Black, “Identification of choroidal neovascularisation on fluorescein angiograms using gradient vector flow active contours,” In Proc. Int. Mach. Vis. Imag. Process. Conf, 165–169, (2008).

E. Brankin, P. McCuIlagh, N. Black, W. Patton, and A. Muldrew, “The optimisation of thresholding techniques for the identification of choroidal neovascular membranes in exudative age-related macular degeneration,” In Proc. 19th IEEE Symp. Comput.-Based Med. Syst, 430–435, (2006).

Piovano, J.

S. Takerkart, R. Fenouil, J. Piovano, A. Reynaud, L. Hoffart, F. Chavane, T. Papadopoulo, J. Conrath, and G. S. Masson, “A quantification framework for post-lesion neovascularization in retinal angiography,” In Proc. IEEE Int. Symp. Biomed. Imag, 1457–1460, (2008).

Qi, X.

R. S. Sulaiman, J. Quigley, X. Qi, M. N. O’Hare, M. B. Grant, and M. E. Boulton, “A simple optical coherence tomography quantification method for choroidal neovascularization,” J. Ocul. Pharmacol. Ther. 31(8), 447–454 (2015).
[Crossref]

Qin, J.

X. Yang, H. Chen, and J. Qin, “Automatic 3D Cardiovascular MR Segmentation with Densely-Connected Volumetric ConvNets,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

Quigley, J.

R. S. Sulaiman, J. Quigley, X. Qi, M. N. O’Hare, M. B. Grant, and M. E. Boulton, “A simple optical coherence tomography quantification method for choroidal neovascularization,” J. Ocul. Pharmacol. Ther. 31(8), 447–454 (2015).
[Crossref]

Rabbani, H.

R. Rasti, H. Rabbani, A. Mehridehnavi, and F. Hajizadeh, “Macular OCT Classification Using a Multi-Scale Convolutional Neural Network Ensemble,” IEEE Trans. Med. Imaging 37(4), 1024–1034 (2018).
[Crossref]

Rasti, R.

R. Rasti, H. Rabbani, A. Mehridehnavi, and F. Hajizadeh, “Macular OCT Classification Using a Multi-Scale Convolutional Neural Network Ensemble,” IEEE Trans. Med. Imaging 37(4), 1024–1034 (2018).
[Crossref]

Ren, S.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep Residual Learning for Image Recognition,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2016).

Reynaud, A.

S. Takerkart, R. Fenouil, J. Piovano, A. Reynaud, L. Hoffart, F. Chavane, T. Papadopoulo, J. Conrath, and G. S. Masson, “A quantification framework for post-lesion neovascularization in retinal angiography,” In Proc. IEEE Int. Symp. Biomed. Imag, 1457–1460, (2008).

Rokem, A.

Ronneberger, O.

O. Cicek, 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, 424–432, (2016).

O. Ronneberger, P. Fischer, and T. Brox, “U-Net: Convolutional Networks for Biomedical Image Segmentation,” International Conference on Medical Image Computing and Computer Assisted Intervention, (2015).

Roy, A. G.

Rubin, D. L.

S. Niu, Q. Chen, L. de Sisternes, and D. L. Rubin, “Automated retinal layers segmentation and quantitative evaluation in SD-OCT images,” Comput. Biol. Med. 54, 116–128 (2014).
[Crossref]

Sanchez, C.

Schlegl, T.

T. Schlegl, S. M. Waldstein, and H. Bogunovic, “Fully Automated Detection and Quantification of Macular Fluid in OCT Using Deep Learning,” Ophthalmology 125(4), 549–558 (2018).
[Crossref]

Schmidt-Erfurth, U.

U. Schmidt-Erfurth, K. Kriechbaum, and A. Oldag, “Three-dimensional angiography of classic and occult lesion types in choroidal neovascularization,” Invest. Ophthalmol. Visual Sci. 48(4), 1751–1760 (2007).
[Crossref]

Schroff, F.

L. Chen, Y. Zhu, G. Papandreou, F. Schroff, and H. Adam, “Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2018).

L. Chen, G. Papandreou, F. Schroff, and H. Adam, “Rethinking Atrous Convolution for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

Shah, A.

A. Shah, , et al., “Multiple surface segmentation using convolution neural nets: application to retinal layer segmentation in OCT images,” Biomed. Opt. Express 9(9), 4509–4526 (2018).
[Crossref]

A. Shah, M. D. Abramoff, and X. Wu, “Simultaneous multiple surface segmentation using deep learning,” in Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support, 3–11, (2017).

Shah, S. M.

W. M. Abdelmoula, S. M. Shah, and A. S. Fahmy, “Segmentation of Choroidal Neovascularization in Fundus Fluorescein Angiograms,” IEEE Trans. Biomed. Eng. 60(5), 1439–1445 (2013).
[Crossref]

Sheet, D.

Shelhamer, E.

E. Shelhamer, J. Long, and T. Darrell, “Fully Convolutional Networks for Semantic Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2015).

Shi, F.

S. Zhu, F. Shi, D. Xiang, W. Zhu, H. Chen, and X. Chen, “Choroid Neovascularization Growth Prediction With Treatment Based on Reaction-Diffusion Model in 3-D OCT Images,” IEEE J. Biomed. Health Inform. 21(6), 1667–1674 (2017).
[Crossref]

S. Zhu, X. Chen, F. Shi, D. Xiang, and W. Zhu, “3D choroid neovascularization growth prediction based on reaction-diffusion model,” Proceedings of the SPIE, (2016).

Singh, S.

A. Dasgupta and S. Singh, “A fully convolutional neural network based structured prediction approach towards the retinal vessel segmentation,” IEEE International Symposium on Biomedical Imaging (ISBI), (2017).

Su, L.

Sui, X.

X. Sui, Y. Zheng, B. Wei, H. Bi, J. Wu, X. Pan, Y. Yin, and S. Zhang, “Choroid segmentation from optical coherence tomography with graph edge weights learned from deep convolutional neural networks,” J. Neurocomput. 237, 332–341 (2017).
[Crossref]

Sulaiman, R. S.

R. S. Sulaiman, J. Quigley, X. Qi, M. N. O’Hare, M. B. Grant, and M. E. Boulton, “A simple optical coherence tomography quantification method for choroidal neovascularization,” J. Ocul. Pharmacol. Ther. 31(8), 447–454 (2015).
[Crossref]

Sun, J.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep Residual Learning for Image Recognition,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2016).

Tai, Y.

Y. Tai, J. Yang, and X. Liu, “Image Super-Resolution via Deep Recursive Residual Network,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

Takahashi, K.

T. Fukuchi, K. Takahashi, M. Uyama, and M. Matsumura, “Comparative Study of Experimental Choroidal Neovascularization by Optical Coherence Tomography and Histopathology,” Jpn. J. Ophthalmol. 45(3), 252–258 (2001).
[Crossref]

Takerkart, S.

S. Takerkart, R. Fenouil, J. Piovano, A. Reynaud, L. Hoffart, F. Chavane, T. Papadopoulo, J. Conrath, and G. S. Masson, “A quantification framework for post-lesion neovascularization in retinal angiography,” In Proc. IEEE Int. Symp. Biomed. Imag, 1457–1460, (2008).

Tan, O.

Y. Jia, S. T. Bailey, D. J. Wilson, and O. Tan, “Quantitative Optical Coherence Tomography Angiography of Choroidal Neovascularization in Age-Related Macular Degeneration,” Ophthalmology 121(7), 1435–1444 (2014).
[Crossref]

Theelen, T.

Tsai, C. L.

C. L. Tsai, Y. L. Yang, S. J. Chen, K. S. Lin, C. H. Chan, and W. Y. Lin, “Automatic Characterization of Classic Choroidal Neovascularization using AdaBoost for Supervised Learning,” Invest. Ophthalmol. Visual Sci. 52(5), 2767–2774 (2011).
[Crossref]

Tyring, A. J.

Uyama, M.

T. Fukuchi, K. Takahashi, M. Uyama, and M. Matsumura, “Comparative Study of Experimental Choroidal Neovascularization by Optical Coherence Tomography and Histopathology,” Jpn. J. Ophthalmol. 45(3), 252–258 (2001).
[Crossref]

VanderBeek, B. L.

M. Chen, J. Wang, I. Oguz, B. L. VanderBeek, and J. C. Gee, “Automated segmentation of the choroid in edi-oct images with retinal pathology using convolution neural networks,” in Fetal, Infant and Ophthalmic Medical Image Analysis, 177–184, (2017).

Venhuizen, F.

Wachinger, C.

Waldstein, S. M.

T. Schlegl, S. M. Waldstein, and H. Bogunovic, “Fully Automated Detection and Quantification of Macular Fluid in OCT Using Deep Learning,” Ophthalmology 125(4), 549–558 (2018).
[Crossref]

Wang, C.

Wang, G.

P. Luo, G. Wang, L. Lin, and X. Wang, “Deep Dual Learning for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

G. Wang, P. Luo, L. Lin, and X. Wang, “Learning Object Interactions and Descriptions for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

Wang, H.

J. Fu, J. Liu, Y. Member, H. Wang, and Lu, “Stacked Deconvolutional Network for Semantic Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

Wang, J.

M. Chen, J. Wang, I. Oguz, B. L. VanderBeek, and J. C. Gee, “Automated segmentation of the choroid in edi-oct images with retinal pathology using convolution neural networks,” in Fetal, Infant and Ophthalmic Medical Image Analysis, 177–184, (2017).

Wang, X.

Y. Xu, K. Yan, J. Kim, X. Wang, C. Li, L. Su, S. Yu, X. Xu, and D. D. Feng, “Dual-stage deep learning framework for pigment epithelium detachment segmentation in polypoidal choroidal vasculopathy,” Biomed. Opt. Express 8(9), 4061–4076 (2017).
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G. Wang, P. Luo, L. Lin, and X. Wang, “Learning Object Interactions and Descriptions for Semantic Image Segmentation,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2017).

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Figures (8)

Fig. 1.
Fig. 1. CNV pathologic analysis results. The area surrounded by the red line is the CNV lesion, which is annotated by more than one ophthalmologist. Yellow arrows indicate CNV characteristics and blue arrows indicate other factors that influence CNV segmentation.
Fig. 2.
Fig. 2. The architecture of MPB-CNN network. All the three branches share the same network structure, but use convolutional kernels of different scales to capture multi-scale information.
Fig. 3.
Fig. 3. SD-OCT volumetric images. (a) is an SD-OCT cube, which contains $1024 \times 512 \times 128$ voxels with a corresponding trim size of $2\,{\rm{mm}} \times 6\,{\rm{mm}} \times 6\,{\rm{mm}}$ in (b). In (a), green, red and yellow lines represent the internal limiting membrane (ILM), the boundary of CNV, and the bruch’s membrane (BM), respectively. The four numbers in (a) respectively represent the four categories labels in the practical experiment.
Fig. 4.
Fig. 4. The architecture of each branch.
Fig. 5.
Fig. 5. Comparing between standard convolution and atrous convolution.
Fig. 6.
Fig. 6. Quantitative comparison about the overlap of FCN, DFCN, M-FCN, M-DFCN and MPB-CNN.
Fig. 7.
Fig. 7. The comparison of 2D and 3D segmentation results with visual effects among FCN, DFCN, M-FCN, M-DFCN and MPB-CNN. Red line is the boundary of the CNV lesion from ground truth, green line is the boundary of CNV lesion from the automated segmentation.
Fig. 8.
Fig. 8. The final visualization results of the proposed method. The last row shows a failure mode. The red line is the boundary of the CNV lesion from ground truth, the green line is the boundary of the CNV lesion from the automated segmentation, the yellow line is the ILM segmented automatically from deep learning, the blue line is the BM segmented automatically from deep learning.

Tables (4)

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Table 1. Parameter setting for our network

Tables Icon

Table 2. Performance comparison of different networks on CNV dataset

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Table 3. Effect validation of the branch supervision on CNV dataset

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Table 4. Effect validation of the gradient constraint on CNV dataset

Equations (10)

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

y [ i ] = k x [ i + r k ] w [ k ]
y = f ( x ) x
y i = f i ( x i 1 ) = f i ( f i 1 ( f 1 ( x 0 ) ) )
y ~ i = y i y 2 y 1 = f i ( f i 1 ( f 1 ( x 0 ) ) ) f 2 ( f 1 ( x 0 ) ) f 1 ( x 0 )
y ~ i = P i [ y i ] P 2 [ y 2 ] P 1 [ y 1 ] = P i [ f i ( f i 1 ( f 1 ( x 0 ) ) ) ] P 2 [ f 2 ( f 1 ( x 0 ) ) ] P 1 [ f 1 ( x 0 ) ]
E i = x Ω ω ( x ) log p l ( x )
L ( Θ ) = E + α E 1 + β E 2 + γ E 3
G = n g ( n ) = n g x n 2 + g y n 2
m i n Θ L ( Θ ) s . t . m a x   G
L o s s = L ( Θ ) + e μ G = E + α E 1 + β E 2 + γ E 3 + e μ G

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