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Lu S, Zhao H, Liu H, Li H, Wang N. PKRT-Net: Prior Knowledge-based Relation Transformer Network for Optic Cup and Disc Segmentation. Neurocomputing 2023. [DOI: 10.1016/j.neucom.2023.03.044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
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2
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Heikka T, Jansonius NM. Influence of signal‐to‐noise ratio, glaucoma stage and segmentation algorithm on
OCT
usability for quantifying layer thicknesses in the peripapillary retina. Acta Ophthalmol 2022; 101:251-260. [PMID: 36331147 DOI: 10.1111/aos.15279] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2022] [Revised: 10/10/2022] [Accepted: 10/18/2022] [Indexed: 11/06/2022]
Abstract
PURPOSE OCT can be used for glaucoma assessment, but its usefulness may depend on image quality, disease stage and segmentation algorithm. We aimed to determine how layer thicknesses as assessed with different algorithms depend on image quality and disease stage, how reproducible the algorithms are, and if the algorithms (dis)agree. METHODS Optic disc OCT data (Canon OCT-HS100) from 20 healthy subjects and 28 early, 29 moderate, and 23 severe glaucoma patients were assessed with four different algorithms (CANON, IOWA, FWHM, DOCTRAP). We measured retinal nerve fibre layer thickness (RNFLT) and total retinal thickness (TRT) along the 1.7-mm-radius OCT measurement circle centred at the optic disc. In healthy subjects, image quality was degraded with neutral density filters (0.3-0.9 optical density [OD]); three scans were made to assess repeatability. Results were analysed with ANOVA with Bonferroni corrected t-tests for post hoc analysis and with intraclass correlation coefficient (ICC) analysis. RESULTS For all algorithms, RNFLT was more sensitive to image quality than TRT. Both RNFLT and TRT showed differences between healthy and glaucoma (all algorithms p < 0.001 for both RNFLT and TRT) and between early and moderate glaucoma (RNFLT: p = 0.001 to p = 0.09; TRT: p < 0.001 to p = 0.03); neither was able to discriminate between moderate and severe glaucoma (p = 0.08 to p = 1.0). Generally, repeatability was excellent (ICC >0.75); agreement between algorithms varied from moderate to excellent. CONCLUSIONS OCT becomes less informative with glaucoma progression, irrespective of the algorithm. For good-quality scans, RNFLT and TRT perform similarly; TRT may be advantageous with poor image quality.
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Affiliation(s)
- Tuomas Heikka
- Department of Ophthalmology, University of Groningen University Medical Center Groningen Groningen The Netherlands
| | - Nomdo M. Jansonius
- Department of Ophthalmology, University of Groningen University Medical Center Groningen Groningen The Netherlands
- Graduate School of Medical Sciences (Research School of Behavioural and Cognitive Neurosciences) University of Groningen Groningen The Netherlands
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3
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Marques R, Andrade De Jesus D, Barbosa-Breda J, Van Eijgen J, Stalmans I, van Walsum T, Klein S, G Vaz P, Sánchez Brea L. Automatic Segmentation of the Optic Nerve Head Region in Optical Coherence Tomography: A Methodological Review. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2022; 220:106801. [PMID: 35429812 DOI: 10.1016/j.cmpb.2022.106801] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2021] [Revised: 03/07/2022] [Accepted: 04/01/2022] [Indexed: 06/14/2023]
Abstract
The optic nerve head (ONH) represents the intraocular section of the optic nerve, which is prone to damage by intraocular pressure (IOP). The advent of optical coherence tomography (OCT) has enabled the evaluation of novel ONH parameters, namely the depth and curvature of the lamina cribrosa (LC). Together with the Bruch's membrane minimum-rim-width (BMO-MRW), these seem to be promising ONH parameters for diagnosis and monitoring of retinal diseases such as glaucoma. Nonetheless, these OCT derived biomarkers are mostly extracted through manual segmentation, which is time-consuming and prone to bias, thus limiting their usability in clinical practice. The automatic segmentation of ONH in OCT scans could further improve the current clinical management of glaucoma and other diseases. This review summarizes the current state-of-the-art in automatic segmentation of the ONH in OCT. PubMed and Scopus were used to perform a systematic review. Additional works from other databases (IEEE, Google Scholar and ARVO IOVS) were also included, resulting in a total of 29 reviewed studies. For each algorithm, the methods, the size and type of dataset used for validation, and the respective results were carefully analysed. The results show a lack of consensus regarding the definition of segmented regions, extracted parameters and validation approaches, highlighting the importance and need of standardized methodologies for ONH segmentation. Only with a concrete set of guidelines, these automatic segmentation algorithms will build trust in data-driven segmentation models and be able to enter clinical practice.
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Affiliation(s)
- Rita Marques
- Laboratory for Instrumentation, Biomedical Engineering and Radiation Physics (LIBPhys-UC), Department of Physics, University of Coimbra, Coimbra, Portugal; Biomedical Imaging Group Rotterdam, Department of Radiology & Nuclear Medicine, Erasmus MC, Rotterdam, Netherlands
| | - Danilo Andrade De Jesus
- Biomedical Imaging Group Rotterdam, Department of Radiology & Nuclear Medicine, Erasmus MC, Rotterdam, Netherlands.
| | - João Barbosa-Breda
- Research Group Ophthalmology, Department of Neurosciences, KU Leuven, Leuven, Belgium; Cardiovascular R&D Center, Faculty of Medicine of the University of Porto, Porto, Portugal; Ophthalmology Department, São João Universitary Hospital Center, Porto, Portugal
| | - Jan Van Eijgen
- Research Group Ophthalmology, Department of Neurosciences, KU Leuven, Leuven, Belgium; Department of Ophthalmology, University Hospitals UZ Leuven, Leuven, Belgium
| | - Ingeborg Stalmans
- Research Group Ophthalmology, Department of Neurosciences, KU Leuven, Leuven, Belgium; Department of Ophthalmology, University Hospitals UZ Leuven, Leuven, Belgium
| | - Theo van Walsum
- Biomedical Imaging Group Rotterdam, Department of Radiology & Nuclear Medicine, Erasmus MC, Rotterdam, Netherlands
| | - Stefan Klein
- Biomedical Imaging Group Rotterdam, Department of Radiology & Nuclear Medicine, Erasmus MC, Rotterdam, Netherlands
| | - Pedro G Vaz
- Laboratory for Instrumentation, Biomedical Engineering and Radiation Physics (LIBPhys-UC), Department of Physics, University of Coimbra, Coimbra, Portugal
| | - Luisa Sánchez Brea
- Biomedical Imaging Group Rotterdam, Department of Radiology & Nuclear Medicine, Erasmus MC, Rotterdam, Netherlands
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4
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Peng B, Lei J, Fu H, Jia Y, Zhang Z, Li Y. Deep video action clustering via spatio-temporal feature learning. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.05.123] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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5
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Towards multi-center glaucoma OCT image screening with semi-supervised joint structure and function multi-task learning. Med Image Anal 2020; 63:101695. [DOI: 10.1016/j.media.2020.101695] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2019] [Revised: 02/02/2020] [Accepted: 03/30/2020] [Indexed: 01/12/2023]
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6
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Channel and Spatial Attention Regression Network for Cup-to-Disc Ratio Estimation. ELECTRONICS 2020. [DOI: 10.3390/electronics9060909] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Cup-to-disc ratio (CDR) is of great importance during assessing structural changes at the optic nerve head (ONH) and diagnosis of glaucoma. While most efforts have been put on acquiring the CDR number through CNN-based segmentation algorithms followed by the calculation of CDR, these methods usually only focus on the features in the convolution kernel, which is, after all, the operation of the local region, ignoring the contribution of rich global features (such as distant pixels) to the current features. In this paper, a new end-to-end channel and spatial attention regression deep learning network is proposed to deduces CDR number from the regression perspective and combine the self-attention mechanism with the regression network. Our network consists of four modules: the feature extraction module to extract deep features expressing the complicated pattern of optic disc (OD) and optic cup (OC), the attention module including the channel attention block (CAB) and the spatial attention block (SAB) to improve feature representation by aggregating long-range contextual information, the regression module to deduce CDR number directly, and the segmentation-auxiliary module to focus the model’s attention on the relevant features instead of the background region. Especially, the CAB selects relatively important feature maps in channel dimension, shifting the emphasis on the OD and OC region; meanwhile, the SAB learns the discriminative ability of feature representation at pixel level by capturing the relationship of intra-feature map. The experimental results of ORIGA dataset show that our method obtains absolute CDR error of 0.067 and the Pearson’s correlation coefficient of 0.694 in estimating CDR and our method has a great potential in predicting the CDR number.
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7
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8
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Ishibashi T, Sakimoto S, Shiraki N, Nishida K, Sakaguchi H, Nishida K. Association between disorganization of retinal inner layers and visual acuity after proliferative diabetic retinopathy surgery. Sci Rep 2019; 9:12230. [PMID: 31439887 PMCID: PMC6706380 DOI: 10.1038/s41598-019-48679-z] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2019] [Accepted: 08/09/2019] [Indexed: 11/16/2022] Open
Abstract
We report to evaluate if disorganization of the retinal inner layers (DRIL) obtained by swept-source optical coherence tomography (SS-OCT) predicts the postoperative best-corrected visual acuity (BCVA) to treat proliferative diabetic retinopathy (PDR). Twenty-one eyes of 21 patients who underwent vitrectomy for PDR were studied retrospectively. BCVA and SS-OCT images were obtained until 6 months postoperatively. The associations between BCVA and SS-OCT parameters measured in a 1-mm central foveal area were evaluated. The DRIL length, external limiting membrane disruption, and ellipsoid zone (EZ) disruption 1 month postoperatively were associated positively with the postoperative logarithm of the minimum angle of resolution (logMAR) BCVA at 1, 3, and 6 months (1 month, p = 0.009, p = 0.013, p = 0.001; 3 months, p = 0.03, p = 0.021, p = 0.002; and 6 months, p = 0.021, p = 0.013, and p = 0.005, respectively). The eyes with a 500-µm or longer DRIL 1 month postoperatively (19%, 4/21 eyes) had significantly worse VA at 1, 3, and 6 months postoperatively (p = 0.007, p = 0.008, and p = 0.020, respectively). Multilinear regression analysis of all visits until 6 months postoperatively showed that the DRIL was correlated more significantly (p = 0.0004) with logMAR BCVA than the disrupted EZ length. The DRIL in the early postoperative period may predict the visual outcomes after treating PDR.
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Affiliation(s)
- Tomoyuki Ishibashi
- Department of Ophthalmology, Osaka University Graduate School of Medicine, Suita, Japan
| | - Susumu Sakimoto
- Department of Ophthalmology, Osaka University Graduate School of Medicine, Suita, Japan.
| | - Nobuhiko Shiraki
- Department of Ophthalmology, Osaka University Graduate School of Medicine, Suita, Japan
| | - Kentaro Nishida
- Department of Ophthalmology, Osaka University Graduate School of Medicine, Suita, Japan
| | - Hirokazu Sakaguchi
- Department of Ophthalmology, Osaka University Graduate School of Medicine, Suita, Japan
| | - Kohji Nishida
- Department of Ophthalmology, Osaka University Graduate School of Medicine, Suita, Japan
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9
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Chen Z, Peng P, Shen H, Wei H, Ouyang P, Duan X. Region-segmentation strategy for Bruch's membrane opening detection in spectral domain optical coherence tomography images. BIOMEDICAL OPTICS EXPRESS 2019; 10:526-538. [PMID: 30800497 PMCID: PMC6377878 DOI: 10.1364/boe.10.000526] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2018] [Revised: 12/12/2018] [Accepted: 12/17/2018] [Indexed: 06/09/2023]
Abstract
Bruch's membrane opening (BMO) is an important biomarker in the progression of glaucoma. Bruch's membrane opening minimum rim width (BMO-MRW), cup-to-disc ratio in spectral domain optical coherence tomography (SD-OCT) and lamina cribrosa depth based on BMO are important measurable parameters for glaucoma diagnosis. The accuracy of measuring these parameters is significantly affected by BMO detection. In this paper, we propose a method for automatically detecting BMO in SD-OCT volumes accurately to reduce the impact of the border tissue and vessel shadows. The method includes three stages: a coarse detection stage composed by retinal pigment epithelium layer segmentation, optic disc segmentation, and multi-modal registration; a fixed detection stage based on the U-net in which BMO detection is transformed into a region segmentation problem and an area bias component is proposed in the loss function; and a post-processing stage based on the consistency of results to remove outliers. Experimental results show that the proposed method outperforms previous methods and achieves a mean error of 42.38 μm.
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Affiliation(s)
- Zailiang Chen
- School of Information Science and Engineering, Central South University, Changsha 410083,
China
| | - Peng Peng
- School of Information Science and Engineering, Central South University, Changsha 410083,
China
| | - Hailan Shen
- School of Information Science and Engineering, Central South University, Changsha 410083,
China
| | - Hao Wei
- School of Information Science and Engineering, Central South University, Changsha 410083,
China
| | - Pingbo Ouyang
- The Second Xiangya Hospital of Central South University, Changsha 410011,
China
| | - Xuanchu Duan
- Changsha Aier Eye Hospital, Changsha 410015,
China
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10
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Fu H, Cheng J, Xu Y, Wong DWK, Liu J, Cao X. Joint Optic Disc and Cup Segmentation Based on Multi-Label Deep Network and Polar Transformation. IEEE TRANSACTIONS ON MEDICAL IMAGING 2018; 37:1597-1605. [PMID: 29969410 DOI: 10.1109/tmi.2018.2791488] [Citation(s) in RCA: 331] [Impact Index Per Article: 47.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
Glaucoma is a chronic eye disease that leads to irreversible vision loss. The cup to disc ratio (CDR) plays an important role in the screening and diagnosis of glaucoma. Thus, the accurate and automatic segmentation of optic disc (OD) and optic cup (OC) from fundus images is a fundamental task. Most existing methods segment them separately, and rely on hand-crafted visual feature from fundus images. In this paper, we propose a deep learning architecture, named M-Net, which solves the OD and OC segmentation jointly in a one-stage multi-label system. The proposed M-Net mainly consists of multi-scale input layer, U-shape convolutional network, side-output layer, and multi-label loss function. The multi-scale input layer constructs an image pyramid to achieve multiple level receptive field sizes. The U-shape convolutional network is employed as the main body network structure to learn the rich hierarchical representation, while the side-output layer acts as an early classifier that produces a companion local prediction map for different scale layers. Finally, a multi-label loss function is proposed to generate the final segmentation map. For improving the segmentation performance further, we also introduce the polar transformation, which provides the representation of the original image in the polar coordinate system. The experiments show that our M-Net system achieves state-of-the-art OD and OC segmentation result on ORIGA data set. Simultaneously, the proposed method also obtains the satisfactory glaucoma screening performances with calculated CDR value on both ORIGA and SCES datasets.
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11
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Bates NM, Tian J, Smiddy WE, Lee WH, Somfai GM, Feuer WJ, Shiffman JC, Kuriyan AE, Gregori NZ, Kostic M, Pineda S, Cabrera DeBuc D. Relationship between the morphology of the foveal avascular zone, retinal structure, and macular circulation in patients with diabetes mellitus. Sci Rep 2018; 8:5355. [PMID: 29599467 PMCID: PMC5876400 DOI: 10.1038/s41598-018-23604-y] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2017] [Accepted: 03/15/2018] [Indexed: 01/06/2023] Open
Abstract
Diabetic Retinopathy (DR) is an extremely severe and common degenerative disease. The purpose of this study was to quantify the relationship between various parameters including the Foveal Avascular Zone (FAZ) morphology, retinal layer thickness, and retinal hemodynamic properties in healthy controls and patients with diabetes mellitus (DM) with and with no mild DR (MDR) using Spectral-Domain Optical Coherence Tomography (Spectralis SDOCT, Heidelberg Engineering GmbH, Germany) and the Retinal Function Imager (Optical Imaging, Ltd., Rehovot, Israel). Our results showed a higher FAZ area and diameter in MDR patients. Blood flow analysis also showed that there is a significantly smaller venous blood flow velocity in MDR patients. Also, a significant difference in roundness was observed between DM and MDR groups supporting the development of asymmetrical FAZ expansion with worsening DR. Our results suggest a potential anisotropy in the mechanical properties of the diabetic retina with no retinopathy that may trigger the FAZ elongation in a preferred direction resulting in either thinning or thickening of intraretinal layers in the inner and outer segments of the retina as a result of autoregulation. A detailed understanding of these relationships may facilitate earlier detection of DR, allowing for preservation of vision and better clinical outcomes.
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Affiliation(s)
- Nathan M Bates
- Bascom Palmer Eye Institute, Miller School of Medicine, University of Miami, Miami, FL, USA
| | - Jing Tian
- Bascom Palmer Eye Institute, Miller School of Medicine, University of Miami, Miami, FL, USA
| | - William E Smiddy
- Bascom Palmer Eye Institute, Miller School of Medicine, University of Miami, Miami, FL, USA
| | - Wen-Hsiang Lee
- Bascom Palmer Eye Institute, Miller School of Medicine, University of Miami, Miami, FL, USA
| | - Gabor Mark Somfai
- Retinology Unit, Pallas Kliniken, Olten, Switzerland.,Semmelweis University, Budapest, Hungary
| | - William J Feuer
- Bascom Palmer Eye Institute, Miller School of Medicine, University of Miami, Miami, FL, USA
| | - Joyce C Shiffman
- Bascom Palmer Eye Institute, Miller School of Medicine, University of Miami, Miami, FL, USA
| | - Ajay E Kuriyan
- Bascom Palmer Eye Institute, Miller School of Medicine, University of Miami, Miami, FL, USA
| | - Ninel Z Gregori
- Bascom Palmer Eye Institute, Miller School of Medicine, University of Miami, Miami, FL, USA
| | - Maja Kostic
- Bascom Palmer Eye Institute, Miller School of Medicine, University of Miami, Miami, FL, USA
| | - Sandra Pineda
- Bascom Palmer Eye Institute, Miller School of Medicine, University of Miami, Miami, FL, USA
| | - Delia Cabrera DeBuc
- Bascom Palmer Eye Institute, Miller School of Medicine, University of Miami, Miami, FL, USA.
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12
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Fu H, Xu Y, Lin S, Zhang X, Wong DWK, Liu J, Frangi AF, Baskaran M, Aung T. Segmentation and Quantification for Angle-Closure Glaucoma Assessment in Anterior Segment OCT. IEEE TRANSACTIONS ON MEDICAL IMAGING 2017; 36:1930-1938. [PMID: 28499992 DOI: 10.1109/tmi.2017.2703147] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Angle-closure glaucoma is a major cause of irreversible visual impairment and can be identified by measuring the anterior chamber angle (ACA) of the eye. The ACA can be viewed clearly through anterior segment optical coherence tomography (AS-OCT), but the imaging characteristics and the shapes and locations of major ocular structures can vary significantly among different AS-OCT modalities, thus complicating image analysis. To address this problem, we propose a data-driven approach for automatic AS-OCT structure segmentation, measurement, and screening. Our technique first estimates initial markers in the eye through label transfer from a hand-labeled exemplar data set, whose images are collected over different patients and AS-OCT modalities. These initial markers are then refined by using a graph-based smoothing method that is guided by AS-OCT structural information. These markers facilitate segmentation of major clinical structures, which are used to recover standard clinical parameters. These parameters can be used not only to support clinicians in making anatomical assessments, but also to serve as features for detecting anterior angle closure in automatic glaucoma screening algorithms. Experiments on Visante AS-OCT and Cirrus high-definition-OCT data sets demonstrate the effectiveness of our approach.
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13
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Miri MS, Abràmoff MD, Kwon YH, Sonka M, Garvin MK. A machine-learning graph-based approach for 3D segmentation of Bruch's membrane opening from glaucomatous SD-OCT volumes. Med Image Anal 2017; 39:206-217. [PMID: 28528295 DOI: 10.1016/j.media.2017.04.007] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2016] [Revised: 04/24/2017] [Accepted: 04/26/2017] [Indexed: 01/26/2023]
Abstract
Bruch's membrane opening-minimum rim width (BMO-MRW) is a recently proposed structural parameter which estimates the remaining nerve fiber bundles in the retina and is superior to other conventional structural parameters for diagnosing glaucoma. Measuring this structural parameter requires identification of BMO locations within spectral domain-optical coherence tomography (SD-OCT) volumes. While most automated approaches for segmentation of the BMO either segment the 2D projection of BMO points or identify BMO points in individual B-scans, in this work, we propose a machine-learning graph-based approach for true 3D segmentation of BMO from glaucomatous SD-OCT volumes. The problem is formulated as an optimization problem for finding a 3D path within the SD-OCT volume. In particular, the SD-OCT volumes are transferred to the radial domain where the closed loop BMO points in the original volume form a path within the radial volume. The estimated location of BMO points in 3D are identified by finding the projected location of BMO points using a graph-theoretic approach and mapping the projected locations onto the Bruch's membrane (BM) surface. Dynamic programming is employed in order to find the 3D BMO locations as the minimum-cost path within the volume. In order to compute the cost function needed for finding the minimum-cost path, a random forest classifier is utilized to learn a BMO model, obtained by extracting intensity features from the volumes in the training set, and computing the required 3D cost function. The proposed method is tested on 44 glaucoma patients and evaluated using manual delineations. Results show that the proposed method successfully identifies the 3D BMO locations and has significantly smaller errors compared to the existing 3D BMO identification approaches.
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Affiliation(s)
- Mohammad Saleh Miri
- Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA, 52242, United States
| | - Michael D Abràmoff
- Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA, 52242, United States; Department of Biomedical Engineering, The University of Iowa, Iowa City, IA, 52242, United States; Department of Ophthalmology and Visual Sciences, The University of Iowa, Iowa City, IA, 52242, United States; Iowa City VA Health Care System, Iowa City, IA, 52246, United States
| | - Young H Kwon
- Department of Ophthalmology and Visual Sciences, The University of Iowa, Iowa City, IA, 52242, United States
| | - Milan Sonka
- Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA, 52242, United States; Department of Ophthalmology and Visual Sciences, The University of Iowa, Iowa City, IA, 52242, United States
| | - Mona K Garvin
- Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA, 52242, United States; Iowa City VA Health Care System, Iowa City, IA, 52246, United States.
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Xiao S, Tan M, Xu D, Dong ZY. Robust Kernel Low-Rank Representation. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2016; 27:2268-2281. [PMID: 26441431 DOI: 10.1109/tnnls.2015.2472284] [Citation(s) in RCA: 58] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Recently, low-rank representation (LRR) has shown promising performance in many real-world applications such as face clustering. However, LRR may not achieve satisfactory results when dealing with the data from nonlinear subspaces, since it is originally designed to handle the data from linear subspaces in the input space. Meanwhile, the kernel-based methods deal with the nonlinear data by mapping it from the original input space to a new feature space through a kernel-induced mapping. To effectively cope with the nonlinear data, we first propose the kernelized version of LRR in the clean data case. We also present a closed-form solution for the resultant optimization problem. Moreover, to handle corrupted data, we propose the robust kernel LRR (RKLRR) approach, and develop an efficient optimization algorithm to solve it based on the alternating direction method. In particular, we show that both the subproblems in our optimization algorithm can be efficiently and exactly solved, and it is guaranteed to obtain a globally optimal solution. Besides, our proposed algorithm can also solve the original LRR problem, which is a special case of our RKLRR when using the linear kernel. In addition, based on our new optimization technique, the kernelization of some variants of LRR can be similarly achieved. Comprehensive experiments on synthetic data sets and real-world data sets clearly demonstrate the efficiency of our algorithm, as well as the effectiveness of RKLRR and the kernelization of two variants of LRR.
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