A machine-learning graph-based approach for 3D segmentation of Bruch's membrane opening from glaucomatous SD-OCT volumes

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.

Keywords: Bruch’s membrane opening; Ophthalmology; Optic disc; Retina; SD-OCT; Segmentation.

Figure 1

Illustration of (a) retinal structures including ILM and BM surfaces, BMO points and BMO-MRW parameter on a single SD-OCT slice and (b) BMO points in 3D.

Figure 2

Flowchart of overall method.

Figure 3

(a) Illustration of lines and their corresponding B-scans in the original domain and (b) sampling the original volume for creating the radial volume. The shape of the opening is more consistent in (b) than in (a) as the BMO points (orange circles) in (a) become close to each other which causes identification of the points to be more difficult.

Figure 4

Radial surface segmentation and projection image creation. (a) Example radial scan with segmented surfaces where red, green, and yellow are the ILM, IS/OS, and BM surfaces, respectively. Note that the IS/OS and BM surfaces are interpolated inside the ONH. (b) The projection image obtained as described in Section 2.1. (c) The reformatted radial projection image in which the 2D BMO projection locations appear as a horizontal path.

Figure 5

Illustration of NIP feature locations for a query point p.

Figure 6

(a) Illustration of the donut of search region for training set. The negative class (cyan dots) are randomly sampled from the area between ellipses and the positive class (yellow crosses) are taken from the area inside the small purple ellipse. (b) Illustration of search region for testing set which is an ellipse with the same size as the outer ellipse (dark blue) of the donut around the estimated 3D BMO location (yellow cross). The green shaded areas in (a) and (b) are excluded from the search region due to the fact that BMO never locates above the ILM surface. (c) A slice (corresponding to the B-scan shown in (b)) of the 3D cost function utilized for identifying the BMO 3D path which is obtained by inverting the output of the RF classifier.

Figure 7

Graph construction. There are weighted edges between each node (green) and its neighboring nodes (red). The neighboring constraint in r-direction (Δ_r) and in z-direction (Δ_z) determine the amount of allowed variation from slice to slice.

Figure 8

Refinement Graph, 𝒢_Z, construction. The red box indicates one voxel on the BMO path in the downsampled volume which corresponds to 15 voxels in the original resolution. The edges are color coded with warmer colors corresponding to higher weights. For a particular node (green) in slice θ₁, all nodes in the subsequent slice, θ₁ + 1, with a distance less than Δ_d are considered as neighbors. The yellow nodes indicate those nodes with a distance larger than Δ_d.

Figure 9

Example results, left column is the original B-scan along with the ILM surface and the right column demonstrates the segmentation results. The blue, yellow, and green circles indicate the BMO_proposed, BMO_iterative, and BMO_manual, respectively. The lines connecting the BMO points to the ILM surface, indicate the corresponding BMO-MRW measures.

Figure 10

The Bland-Altman plots of (a) BMO_iterative-MRW and (b) BMO_proposed-MRW in comparison with BMO_manual-MRW. The proposed method has a tighter fit and lower error than the iterative approach.

Figure 11

An example of identifying the BMO point using the proposed method within the shadow of a large blood vessel.

Figure A.12

An example of edge-based cost function computation. (a) The 2^nd scale of SWT decomposition. Note that BMO boundary appears in the horizontal coefficients while the blood vessels mostly appear in vertical and diagonal coefficients. (b) The vessel-free radial projection image. (c) The edge-based cost function computed by applying the Gaussian derivative filter, ℱ_σrσθ (r, θ), to the vessel-free radial projection image.