Abstract

Optical coherence tomography (OCT) is a commonly used ophthalmic imaging modality. While OCT has traditionally been viewed cross-sectionally (i.e., as a sequence of B-scans), higher A-scan rates have increased interest in en face OCT visualization and analysis. The recent clinical introduction of OCT angiography (OCTA) has further spurred this interest, with chorioretinal OCTA being predominantly displayed via en face projections. Although en face visualization and quantitation are natural for many retinal features (e.g., drusen and vasculature), it requires segmentation. Because manual segmentation of volumetric OCT data is prohibitively laborious in many settings, there has been significant research and commercial interest in developing automatic segmentation algorithms. While these algorithms have achieved impressive results, the variability of image qualities and the variety of ocular pathologies cause even the most robust automatic segmentation algorithms to err. In this study, we develop a user-assisted segmentation approach, complementary to fully-automatic methods, wherein correction propagation is used to reduce the burden of manually correcting automatic segmentations. The approach is evaluated for Bruch’s membrane segmentation in eyes with advanced age-related macular degeneration.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (1)

2019 (1)

M. Pekala, N. Joshi, T. A. Liu, N. M. Bressler, D. C. DeBuc, and P. Burlina, “Deep learning based retinal OCT segmentation,” Comput. Biol. Med. 114, 103445 (2019).
[Crossref]

2018 (3)

A. Shah, L. Zhou, M. D. Abrámoff, and X. Wu, “Multiple surface segmentation using convolution neural nets: application to retinal layer segmentation in OCT images,” Biomed. Opt. Express 9(9), 4509–4526 (2018).
[Crossref]

R. F. Spaide, J. G. Fujimoto, N. K. Waheed, S. R. Sadda, and G. Staurenghi, “Optical coherence tomography angiography,” Prog. Retinal Eye Res. 64, 1–55 (2018).
[Crossref]

J. R. de Oliveira Dias, Q. Zhang, J. M. Garcia, F. Zheng, E. H. Motulsky, L. Roisman, A. Miller, C.-L. Chen, S. Kubach, L. de Sisternes, M. K. Durbin, W. Feuer, R. K. Wang, G. Gregori, and P. J. Rosenfeld, “Natural history of subclinical neovascularization in nonexudative age-related macular degeneration using swept-source OCT angiography,” Ophthalmology 125(2), 255–266 (2018).
[Crossref]

2017 (6)

A. H. Kashani, C.-L. Chen, J. K. Gahm, F. Zheng, G. M. Richter, P. J. Rosenfeld, Y. Shi, and R. K. Wang, “Optical coherence tomography angiography: A comprehensive review of current methods and clinical applications,” Prog. Retinal Eye Res. 60, 66–100 (2017).
[Crossref]

L. de Sisternes, G. Jonna, J. Moss, M. F. Marmor, T. Leng, and D. L. Rubin, “Automated intraretinal segmentation of SD-OCT images in normal and age-related macular degeneration eyes,” Biomed. Opt. Express 8(3), 1926–1949 (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]

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,” Neurocomputing 237, 332–341 (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. Opt. Express 8(7), 3292–3316 (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]

2016 (3)

S. Niu, L. de Sisternes, Q. Chen, T. Leng, and D. L. Rubin, “Automated geographic atrophy segmentation for SD-OCT images using region-based cv model via local similarity factor,” Biomed. Opt. Express 7(2), 581–600 (2016).
[Crossref]

L. Roisman, Q. Zhang, R. K. Wang, G. Gregori, A. Zhang, C.-L. Chen, M. K. Durbin, L. An, P. F. Stetson, G. Robbins, A. Miller, F. Zheng, and P. J. Rosenfeld, “Optical coherence tomography angiography of asymptomatic neovascularization in intermediate age-related macular degeneration,” Ophthalmology 123(6), 1309–1319 (2016).
[Crossref]

Z. Sun, H. Chen, F. Shi, L. Wang, W. Zhu, D. Xiang, C. Yan, L. Li, and X. Chen, “An automated framework for 3D serous pigment epithelium detachment segmentation in SD-OCT images,” Sci. Rep. 6(1), 21739 (2016).
[Crossref]

2015 (2)

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[Crossref]

J. Tian, B. Varga, G. M. Somfai, W.-H. Lee, W. E. Smiddy, and D. C. DeBuc, “Real-time automatic segmentation of optical coherence tomography volume data of the macular region,” PLoS One 10(8), e0133908 (2015).
[Crossref]

2014 (1)

2013 (4)

2012 (3)

2010 (1)

2008 (1)

M. K. Garvin, M. D. Abràmoff, 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. Imaging 27(10), 1495–1505 (2008).
[Crossref]

2006 (1)

K. Li, X. Wu, D. Z. Chen, and M. Sonka, “Optimal surface segmentation in volumetric images-a graph-theoretic approach,” IEEE Trans. Pattern Anal. Mach. Intell. 28(1), 119–134 (2006).
[Crossref]

1994 (1)

R. S. Ramrattan, T. L. van der Schaft, C. M. Mooy, W. De Bruijn, P. Mulder, and P. De Jong, “Morphometric analysis of Bruch’s membrane, the choriocapillaris, and the choroid in aging,” Investigative ophthalmology & visual science 35, 2857–2864 (1994).

1981 (1)

M. A. Fischler and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM 24(6), 381–395 (1981).
[Crossref]

Abdillahi, H.

P. A. Dufour, L. Ceklic, H. Abdillahi, S. Schroder, S. De Dzanet, U. Wolf-Schnurrbusch, and J. Kowal, “Graph-based multi-surface segmentation of OCT data using trained hard and soft constraints,” IEEE Trans. Med. Imaging 32(3), 531–543 (2013).
[Crossref]

Abrámoff, M. D.

Abràmoff, M. D.

B. J. Antony, M. D. Abràmoff, M. M. Harper, W. Jeong, E. H. Sohn, Y. H. Kwon, R. Kardon, and M. K. Garvin, “A combined machine-learning and graph-based framework for the segmentation of retinal surfaces in SD-OCT volumes,” Biomed. Opt. Express 4(12), 2712–2728 (2013).
[Crossref]

M. K. Garvin, M. D. Abràmoff, 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. Imaging 27(10), 1495–1505 (2008).
[Crossref]

An, L.

L. Roisman, Q. Zhang, R. K. Wang, G. Gregori, A. Zhang, C.-L. Chen, M. K. Durbin, L. An, P. F. Stetson, G. Robbins, A. Miller, F. Zheng, and P. J. Rosenfeld, “Optical coherence tomography angiography of asymptomatic neovascularization in intermediate age-related macular degeneration,” Ophthalmology 123(6), 1309–1319 (2016).
[Crossref]

Antony, B. J.

Baumann, B.

Bengio, Y.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521(7553), 436–444 (2015).
[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,” Neurocomputing 237, 332–341 (2017).
[Crossref]

Bock, R.

Bolles, R. C.

M. A. Fischler and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM 24(6), 381–395 (1981).
[Crossref]

Branchini, L.

Bressler, N. M.

M. Pekala, N. Joshi, T. A. Liu, N. M. Bressler, D. C. DeBuc, and P. Burlina, “Deep learning based retinal OCT segmentation,” Comput. Biol. Med. 114, 103445 (2019).
[Crossref]

Budai, A.

Burlina, P.

M. Pekala, N. Joshi, T. A. Liu, N. M. Bressler, D. C. DeBuc, and P. Burlina, “Deep learning based retinal OCT segmentation,” Comput. Biol. Med. 114, 103445 (2019).
[Crossref]

Cable, A. E.

Calabresi, P. A.

Carass, A.

Ceklic, L.

P. A. Dufour, L. Ceklic, H. Abdillahi, S. Schroder, S. De Dzanet, U. Wolf-Schnurrbusch, and J. Kowal, “Graph-based multi-surface segmentation of OCT data using trained hard and soft constraints,” IEEE Trans. Med. Imaging 32(3), 531–543 (2013).
[Crossref]

Chen, C.-L.

J. R. de Oliveira Dias, Q. Zhang, J. M. Garcia, F. Zheng, E. H. Motulsky, L. Roisman, A. Miller, C.-L. Chen, S. Kubach, L. de Sisternes, M. K. Durbin, W. Feuer, R. K. Wang, G. Gregori, and P. J. Rosenfeld, “Natural history of subclinical neovascularization in nonexudative age-related macular degeneration using swept-source OCT angiography,” Ophthalmology 125(2), 255–266 (2018).
[Crossref]

A. H. Kashani, C.-L. Chen, J. K. Gahm, F. Zheng, G. M. Richter, P. J. Rosenfeld, Y. Shi, and R. K. Wang, “Optical coherence tomography angiography: A comprehensive review of current methods and clinical applications,” Prog. Retinal Eye Res. 60, 66–100 (2017).
[Crossref]

L. Roisman, Q. Zhang, R. K. Wang, G. Gregori, A. Zhang, C.-L. Chen, M. K. Durbin, L. An, P. F. Stetson, G. Robbins, A. Miller, F. Zheng, and P. J. Rosenfeld, “Optical coherence tomography angiography of asymptomatic neovascularization in intermediate age-related macular degeneration,” Ophthalmology 123(6), 1309–1319 (2016).
[Crossref]

M. F. Kraus, J. J. Liu, J. Schottenhamml, C.-L. Chen, A. Budai, L. Branchini, T. Ko, H. Ishikawa, G. Wollstein, J. Schuman, J. S. Duker, J. G. Fujimoto, and J. Hornegger, “Quantitative 3D-OCT motion correction with tilt and illumination correction, robust similarity measure and regularization,” Biomed. Opt. Express 5(8), 2591–2613 (2014).
[Crossref]

Chen, D. Z.

K. Li, X. Wu, D. Z. Chen, and M. Sonka, “Optimal surface segmentation in volumetric images-a graph-theoretic approach,” IEEE Trans. Pattern Anal. Mach. Intell. 28(1), 119–134 (2006).
[Crossref]

Chen, H.

Z. Sun, H. Chen, F. Shi, L. Wang, W. Zhu, D. Xiang, C. Yan, L. Li, and X. Chen, “An automated framework for 3D serous pigment epithelium detachment segmentation in SD-OCT images,” Sci. Rep. 6(1), 21739 (2016).
[Crossref]

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, (Springer, 2017), pp. 177–184.

Chen, Q.

Chen, X.

Z. Sun, H. Chen, F. Shi, L. Wang, W. Zhu, D. Xiang, C. Yan, L. Li, and X. Chen, “An automated framework for 3D serous pigment epithelium detachment segmentation in SD-OCT images,” Sci. Rep. 6(1), 21739 (2016).
[Crossref]

Chiu, S. J.

S. J. Chiu, J. A. Izatt, R. V. O’Connell, K. P. Winter, C. A. Toth, and S. Farsiu, “Validated automatic segmentation of AMD pathology including drusen and geographic atrophy in SD-OCT images,” Invest. Ophthalmol. Visual Sci. 53(1), 53–61 (2012).
[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 SDOCT images congruent with expert manual segmentation,” Opt. Express 18(18), 19413–19428 (2010).
[Crossref]

Choi, W.

Conjeti, S.

Cunefare, D.

Dai, Y.

De Bruijn, W.

R. S. Ramrattan, T. L. van der Schaft, C. M. Mooy, W. De Bruijn, P. Mulder, and P. De Jong, “Morphometric analysis of Bruch’s membrane, the choriocapillaris, and the choroid in aging,” Investigative ophthalmology & visual science 35, 2857–2864 (1994).

De Dzanet, S.

P. A. Dufour, L. Ceklic, H. Abdillahi, S. Schroder, S. De Dzanet, U. Wolf-Schnurrbusch, and J. Kowal, “Graph-based multi-surface segmentation of OCT data using trained hard and soft constraints,” IEEE Trans. Med. Imaging 32(3), 531–543 (2013).
[Crossref]

De Jong, P.

R. S. Ramrattan, T. L. van der Schaft, C. M. Mooy, W. De Bruijn, P. Mulder, and P. De Jong, “Morphometric analysis of Bruch’s membrane, the choriocapillaris, and the choroid in aging,” Investigative ophthalmology & visual science 35, 2857–2864 (1994).

de Oliveira Dias, J. R.

J. R. de Oliveira Dias, Q. Zhang, J. M. Garcia, F. Zheng, E. H. Motulsky, L. Roisman, A. Miller, C.-L. Chen, S. Kubach, L. de Sisternes, M. K. Durbin, W. Feuer, R. K. Wang, G. Gregori, and P. J. Rosenfeld, “Natural history of subclinical neovascularization in nonexudative age-related macular degeneration using swept-source OCT angiography,” Ophthalmology 125(2), 255–266 (2018).
[Crossref]

de Sisternes, L.

J. R. de Oliveira Dias, Q. Zhang, J. M. Garcia, F. Zheng, E. H. Motulsky, L. Roisman, A. Miller, C.-L. Chen, S. Kubach, L. de Sisternes, M. K. Durbin, W. Feuer, R. K. Wang, G. Gregori, and P. J. Rosenfeld, “Natural history of subclinical neovascularization in nonexudative age-related macular degeneration using swept-source OCT angiography,” Ophthalmology 125(2), 255–266 (2018).
[Crossref]

L. de Sisternes, G. Jonna, J. Moss, M. F. Marmor, T. Leng, and D. L. Rubin, “Automated intraretinal segmentation of SD-OCT images in normal and age-related macular degeneration eyes,” Biomed. Opt. Express 8(3), 1926–1949 (2017).
[Crossref]

S. Niu, L. de Sisternes, Q. Chen, T. Leng, and D. L. Rubin, “Automated geographic atrophy segmentation for SD-OCT images using region-based cv model via local similarity factor,” Biomed. Opt. Express 7(2), 581–600 (2016).
[Crossref]

DeBuc, D. C.

M. Pekala, N. Joshi, T. A. Liu, N. M. Bressler, D. C. DeBuc, and P. Burlina, “Deep learning based retinal OCT segmentation,” Comput. Biol. Med. 114, 103445 (2019).
[Crossref]

J. Tian, B. Varga, G. M. Somfai, W.-H. Lee, W. E. Smiddy, and D. C. DeBuc, “Real-time automatic segmentation of optical coherence tomography volume data of the macular region,” PLoS One 10(8), e0133908 (2015).
[Crossref]

Dufour, P. A.

P. A. Dufour, L. Ceklic, H. Abdillahi, S. Schroder, S. De Dzanet, U. Wolf-Schnurrbusch, and J. Kowal, “Graph-based multi-surface segmentation of OCT data using trained hard and soft constraints,” IEEE Trans. Med. Imaging 32(3), 531–543 (2013).
[Crossref]

Duker, J. S.

Duncan, J. L.

Durbin, M. K.

J. R. de Oliveira Dias, Q. Zhang, J. M. Garcia, F. Zheng, E. H. Motulsky, L. Roisman, A. Miller, C.-L. Chen, S. Kubach, L. de Sisternes, M. K. Durbin, W. Feuer, R. K. Wang, G. Gregori, and P. J. Rosenfeld, “Natural history of subclinical neovascularization in nonexudative age-related macular degeneration using swept-source OCT angiography,” Ophthalmology 125(2), 255–266 (2018).
[Crossref]

L. Roisman, Q. Zhang, R. K. Wang, G. Gregori, A. Zhang, C.-L. Chen, M. K. Durbin, L. An, P. F. Stetson, G. Robbins, A. Miller, F. Zheng, and P. J. Rosenfeld, “Optical coherence tomography angiography of asymptomatic neovascularization in intermediate age-related macular degeneration,” Ophthalmology 123(6), 1309–1319 (2016).
[Crossref]

Fang, L.

Farsiu, S.

Fauser, S.

Feuer, W.

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Figures (8)

Fig. 1.
Fig. 1. Our user-assisted segmentation framework is comprised of three modules: (1) initial automatic segmentation; (2) manual correction of segmentation errors over a subset of the volume; and (3) propagation of the segmentation corrections to other regions of the volume. The framework is designed so that each module is relatively independent of the particular implementations of the other modules.
Fig. 2.
Fig. 2. Example of fully-automatic segmentation of the RPE and Bruch’s membrane in an OCT B-scan that intersects a CNV lesion. Note that, for clarity, the segmentation lines and B-scan are shown in their natural (unflattened) coordinate frames. In B-scans such as this one, where the RPE becomes separated from Bruch’s membrane, the automatic Bruch’s membrane segmentation can be anteriorly shifted from the true Bruch’s membrane position (turquoise arrows).
Fig. 3.
Fig. 3. Example of user-assisted segmentation correction within a restricted domain, for the same case as in Fig. 2. (Left panel) En face OCT plane, cropped from a larger field-of-view, that intersects a region of CNV. (Right panel) OCT B-scan, extracted from the en face OCT plane, also intersecting the region of CNV. Note that, for clarity, the segmentation lines and B-scan are shown in their natural (unflattened) coordinate frames. The teal contour corresponds to the automatically segmented internal limiting membrane; the orange contour corresponds to the automatically segmented RPE; the red contour corresponds to the automatically segmented Bruch’s membrane; and the dashed, light-green contour corresponds to the corrected Bruch’s membrane segmentation. The domain of correction, $\mathcal {D}^{\tilde {R}}$, is indicated by the dark-green dashed box in the left panel, the sides of which correspond to the vertical dark-green dashed lines in the OCT B-scan of the right panel. In this example, three OCT B-scans are corrected. Note that the B-scans are only corrected within $\mathcal {D}^{\tilde {R}}$.
Fig. 4.
Fig. 4. Illustration of Bruch’s membrane restriction. The manually segmented points ($k_1$ and $k_2$) and the border points ($n_b$ and $n_t$) act as ‘gates’ through which the shortest path must pass. Between these points, the graph is restricted to the band $\mathcal {B}_j$ with thickness $\Delta _{\mathcal {B}}$ (here: $\Delta _{\mathcal {B}}=2$). $\mathcal {B}_j$ is constructed via linear interpolation between the manual inputs and sub-domain borders. White cells denote unconnected vertices.
Fig. 5.
Fig. 5. Bar chart showing the user-assisted segmentation results for the GA and CNV datasets evaluated over $\mathcal {D}^{\tilde {R}}$; the dashed horizontal line indicates the axial digital (pixel) resolution, which is half of the axial optical resolution. MAD and $\sigma _{\textrm {MAD}}$ exhibit a monotonic decrease with an increasing number of corrected B-scans. The first bar of each dataset illustrates the MAD for the fully-automatic segmentation.
Fig. 6.
Fig. 6. Illustration of user-assisted Bruch’s membrane segmentation in an eye with GA (top row) and an eye with CNV (bottom row). For all panels, propagation correction was performed with a correction density corresponding to $\Delta k = 180$ µm. Note that, for clarity, the segmentation lines and B-scans are shown in their natural (unflattened) coordinate frames. (a) OCT B-scans extracted from the locations of the dashed lines in column-b and column-c. For each panel, the teal contour corresponds to the automatically segmented internal limiting membrane; the orange contour corresponds to the automatically segmented RPE; and the green lines correspond to the manually segmented (ground truth) Bruch’s membrane. In the panels labelled “Fully-Automatic,” the red contours correspond to the fully-automatic Bruch’s membrane segmentation. In panels labelled “User-Assisted,” the red contours correspond to the user-assisted segmentation achieved via correction propagation. (b) Signed-difference maps between the fully-automatic segmentations and fully-manual segmentations. (c) Signed-difference maps between the user-assisted segmentations and the fully-manual segmentations. The dark-green contours in the panels of column-b and column-c correspond to lesion boundaries. The black rectangles in the panels of column-b and column-c correspond to the domains of correction, $\mathcal {D}^{\tilde {R}}$.
Fig. 7.
Fig. 7. Effect of user-assisted segmentation on choriocapillaris OCTA slabs. The panels of the top row correspond to the full 6 mm $\times$ 6 mm fields-of-view, and the panels of the bottom row correspond to enlargements of those of the top row. All en face OCTA slabs were formed via median projection of the OCTA volume from Bruch’s membrane to ∼25 µm immediately posterior to Bruch’s membrane. Lesion boundaries are outlined in teal. User-assisted segmentation was performed as described in Fig. 6. (a) Choriocapillaris OCTA slab of an eye with GA (same as in Fig. 6) generated by using a fully-automatic segmentation. (b) Choriocapillaris OCTA slab of the same GA eye generated by using the user-assisted segmentation. (c) Choriocapillaris OCTA slab of an eye with CNV (same as in Fig. 6) generated by using a fully-automatic segmentation. (d) Choriocapillaris OCTA slab of the same CNV eye generated by using the user-assisted segmentation. Comparing panel-a and panel-b, the dominant effect of the user-assisted segmentation is a reduced appearance of larger choroidal vasculature within the region of atrophy (e.g., yellow arrow within teal outline). This reduction is a consequence of the fully-automatic segmentation being posteriorly shifted relative to the fully-manual (and user-asssisted) segmentation, as illustrated in Fig. 6. Even beyond the GA margin, the choriocapillaris OCTA signal appears lower with the user-assisted segmentation than with the fully-automatic segmentation (e.g., yellow arrow beyond teal outline). Comparing panel-c and panel-d, the user-assisted segmentation results in a finer CC/CNV patterning, which, again, is particularly noticeable within the lesion margins. In some regions, the user-assisted segmentation results in higher choriocapillaris OCTA signals (e.g., red arrows); in others, the user-assisted segmentation results in lower choriocapillaris OCTA signals (e.g., yellow arrow).
Fig. 8.
Fig. 8. Effect of user-assisted segmentation on visualization of CNV lesion. User-assisted segmentation was performed as described in Fig. 6). All en face OCTA slabs were formed via mean projection of the OCTA volume from the automatically segmented RPE to the Bruch’s membrane, and therefore correspond to the type-I lesion component. (a) CNV OCTA slab generated by using a fully-automatic segmentation. (b) CNV OCTA slab of the same CNV eye generated by using the user-assisted correction. (c, d) Enlargements of panel-a and panel-b, respectively. When comparing panel-c and panel-d, several regions that appear vessel-free with the fully-automatic segmentation show vessels with the user-assisted segmentation (e.g., red arrows).

Tables (2)

Tables Icon

Table 1. Description of the datasets used to evaluate our proposed user-assisted Bruch’s membrane segmentation algorithm. All cases are 6 mm × 6 mm volumes. Superscripts * and § indicate eyes of the same patient (i.e., OD/OS).

Tables Icon

Table 2. Mathematical notation sorted by occurrence in the manuscript.

Equations (20)

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P k RPE = { p i , j | ( i , j ) I × J }
E k RPE = ( i , j ) I × J N RPE ( p i , j )
N RPE ( p i , j ) ) = { ( p i , j , p i 1 , j + 1 ) } { ( p i , j , p i , j + 1 ) } { ( p i , j , p i + 1 , j + 1 ) }
w k RPE ( e i , j , m , n ) = e x p [ 2 ( V RPE ( i , j , k ) + V RPE ( m , n , k ) ) + ϵ ]
P j BM , R ~ = { p i , k | ( i , k ) I × K R }
E j BM , R ~ = ( i , k ) I × K R N BM , R ~ ( p i , k )
N BM , R ~ ( p i , k ) = { ( p i , k , p i 3 , k + 1 ) } { ( p i , k , p i 2 , k + 1 ) } { ( p i , k , p i 1 , k + 1 ) } { ( p i , k , p i , k + 1 ) } { ( p i , k , p i + 1 , k + 1 ) } { ( p i , k , p i + 2 , k + 1 ) { ( p i , k , p i + 3 , k + 1 ) } }
V BM | K = { k } = 1 2 ( sgn ( V | K = { k } Q ) + 1 ) ( V | K = { k } Q )
w j BM ( e i , k , m , o ) = 2 ( V BM ( i , j , k ) + V BM ( m , j , o ) ) + ϵ
P j BM , R = P j BM B j
B j = k K R T ( p L ( k ) , k )
L ( k ) = ( k k ( k ) ) g ( k + ( k ) ) g ( k ( k ) ) k + ( k ) k ( k ) + g ( k ( k ) ) ,
k ( k ) = arg min k K k M | k k |
k + ( k ) = arg min k K k M + | k k |
K k M = { k K R | k k } { n b }
K k M + = { k K R | k k } { n t }
T ( p i , k ) = { { p i , k } , k K M I k Δ B ( p i , k ) , else
I k Δ B ( p i , k ) = i I , | i i | Δ B { p i , k }
E j BM , R = E j BM , R ~ | P j BM , R
w j BM , R = w j BM , R ~ | E j BM , R

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