Volumetric Quantification of Choroid and Haller’s Sublayer Using OCT Scans: An Accurate and Unified Approach Based on Stratified Smoothing

Abstract

Background and Objective:

The choroid, a dense vascular structure in. the posterior segment of the eye, maintains the health of the retina by supplying oxygen and nutrients, and assumes clinical significance in screening ocular diseases including age-related macular degeneration (AMD) and central serous chorioretinopathy (CSCR). As a technological assist, algorithmic estimation of choroidal biomarkers has been suggested based on sectional (B-scan) optical coherence tomography (OCT) images. However, most such 2D estimation techniques are compute-intensive, yet enjoy limited accuracy and have only been validated on OCT image datasets of healthy eyes. Not surprisingly, fine-scale analyses, including those involving Haller’s sublayer, remain relatively rare and unsophisticated. Against this backdrop, we propose an efficient algorithm to quantify desired biomarkers with improved accuracy based on volume OCT scans. Specifically, we attempted an accurate, computationally fight volumetric segmentation method involving stratified smoothing to detect choroid and Haller’s sublayer.

Methods:

For detecting the various boundaries of the choroid and the Haller’s sublayer, we propose a common volumetric method that performs suitable exponential enhancement and maintains smooth spatial continuity across 2D B-scans. Further, we achieve suitable volumetric smoothing by primarily deploying light-duty linear regression, and sparingly using compute-intensive tensor voting, and hence significantly reduce overall complexity. The proposed methodology is tested on five health and five diseased OCT volumes considering various metrics including volumetric Dice coefficient and corresponding quotient measures to facilitate comparison vis-à-vis intra-observer repeatability.

Results:

On five healthy and five diseased OCT volumes, respectively, the proposed method for choroid segmentation recorded volumetric Dice coefficients of 93.53% and 93.30%, which closely approximate the respective reference observer repeatability values of 95.60% and 95.49%. In terms of related quotient measures, our method achieved more than 50% improvement over a recently reported method. In detecting Haller’s sublayer as well, our algorithm records statistical performance closely matching that of reference manual method.

Conclusion:

Advancing the state-of-the-art, the proposed volumetric segmentation, tested on both healthy and diseased datasets, demonstrated close match with the manual reference. Our method assumes significance in accurate screening of chorioretinal diseases including AMD, CSCR and pachychoroid. Further, it enables generating accurate training data for developing deep learning models for improved detection of choroid and Haller’s sublayer.

Graphical Abstract

1. Introduction

The choroid is a highly vascular plexus located in the posterior segment of the eye and interspersed between the retina and the sclera (refer Fig. 1(a)). It consists predominantly of luminal regions having blood vessels with diameters varying with depth. As one starts at sclera and gradually approaches the retinal pigment epithelium (RPE), one first encounters large vessel diameters at the Haller’s sublayer, then medium diameters at the Sattler’s sublayer and finally small diameters among choriocapillaris [1, 2]. As structural anomalies in the complex choroidal structure could indicate ocular disorders, their detection became imperative for clinicians. Visual detection of anomalies became possible with the advent of optical coherence tomography (OCT) imaging. However, an early OCT imaging system would only produce cross-sectional images, termed B-scans, in low resolution [3, 4, 5, 6]. With tremendous technological advances, a state-of-the-art system now provides high-resolution volume scans (refer to right panel of Fig. 1(a) for a representative OCT volume scan of the macular region) [3, 7, 6]. Accordingly, there has been a strong interest in not only detecting structural changes in the choroid, but also precisely connecting various diseases with specific nature of changes. In this regard, researchers have studied gross indicators such as choroidal thickness (CT) and choroidal volume (CV) [8, 9, 10], as well as choroid vascularity index (CVI) [11, 12, 13, 14]. The said indicators have been found to deviate from the normal in various chorioretinal pathologies, including central serous chorioretinopathy (CSCR) [13, 15, 16], age-related macular degeneration (AMD) [17, 18, 19, 20], polypoidal choroidal vasculopathy (PCV) [21, 10], pathological myopia (PM) [22], and diabetic retinopathy (DR) [23], Recent studies have delved deeper and attempted at understanding similar connections at finer scales. For instance, certain eye disorders, including various stages of AMD and pachychoroid, have been found to particularly affect large choroidal vessels. Accordingly, study of their relationship with analogous indicators based on Haller’s sublayer has assumed importance [2, 24, 25, 26]. Aiming further, clinicians have set the general goal of early disease detection using potential techniques that would localize minute changes to specific vessel segments [2, 27, 28, 29]. Against this backdrop, whether seeking to calculate gross indicators, or to precisely localize changes, one first needs a method to delineate the choroid and its Haller’s sublayer in volumetric OCT scans. In this paper, we propose such an algorithmic method, and demonstrate its accuracy and efficacy.

Figure 1:

(a) Sagittal cross section of the eye indicating posterior pole of the eye and optical coherence tomography (OCT) volume scan of the macular region depicting fovea, retina, choroid and sclera; (b) Classification of choroid vessels based on diameter and Steps/Milestones of this work: Detection of choroid inner boundary (CIB), choroid outer boundary (COB), and Haller’s Sattler’s interface (HSI).

Segmentation of the choroid and its Haller’s sublayer involves detection of the choroid inner boundary (CIB), the choroid outer boundary (COB) and the Haller’s-Sattler’s Interface (HSI) (see Fig. 1(b)). For these detection subtasks, researchers have employed both semi-automated and fully automated tools, taking graph-theoretic [15, 30, 31, 32], statistical [33, 34], deep learning [35, 36, 37, 38, 39, 40, 41, 42, 43, 44], and other approaches [16, 18, 45, 32]. Incidentally, most previous works confined to 2D B-scans and did not leverage inter-scan dependency. Further, those tended to approach detection of each desired boundary separately, leading to significant complexity. Specific works, while promising attractive benefits, had additional limitations. In particular, a recent method based on attenuation correction and graph search reported high numerical accuracy for choroidal segmentation; however, the algorithm was evaluated on healthy datasets only, leaving its utility for diseased datasets unclear [30]. Another method based on graph search desirably provided an open-source tool for retinal and choroidal segmentation; however, the high error rate might not meet clinical requirements [31]. Accuracy comparable to that attained by trained experts was reported in another work, employing structural similarity (SSIM) index and tensor voting to achieve smooth 2D segmentation; however, validation was not performed on diseased eyes, and spatial consistency between adjacent B-scans was not considered [8]. Subsequently, a deep learning based study involving 2D choroidal thickness measurement reported low mean error for both healthy and diseased datasets; however, as limited number of B-scans were used per eye, it remains unclear whether the underlying algorithm would retain high efficacy upon extension to volumetric segmentation [38]. Elsewhere in a different ophthalmological context not involving choroid, a deep learning method exploiting inter-scan dependency to a limited extent has been suggested [46]. Yet, towards realizing the desired 3D segmentation based on deep learning, there still remain significant challenges, including the requirement of large amount of accurately annotated volume OCT scans [47, 48]. Clearly, manual annotation at the required scale would involve infeasible amount of time, effort and other resources. As an alternative, we propose a volumetric segmentation technique for the choroid and the Haller’s sublayer that not only advances the state of the art, but can also be used for generating automated annotations at large scales to potentially facilitate training of future deep learning algorithms. In particular, we develop a 3D segmentation method that maintains inter-scan spatial consistency, caters to both healthy and diseased datasets, takes a common approach to each of the three boundary detection subtasks at hand, and proves to be efficient.

In designing the proposed algorithm, we employ as preprocessing a two-step exponential enhancement method to counter the depth-dependent attenuation inherent in the OCT image acquisition process [11]. Further, while segmenting in 3D the three boundaries under consideration, namely, CIB, COB and HSI, we seek to maintain spatial smoothness in the planes of B-scan as well as in the orthogonal direction. For this purpose, we adopted a stratified smoothing approach where we make use of the heavy-duty tensor voting method sparingly [49], and a light linear regression method in remaining circumstances [50, 51], so that the proposed end-to-end algorithm is precise yet fast. A version of the proposed algorithm has proven useful in certain clinical studies [52]. Presently, we record algorithmic performance on OCT datasets corresponding to both healthy and diseased eyes. The proposed method appears robust to dataset-specific variabilities, while being accurate. In particular, in detecting the choroid based on five healthy and five diseased OCT volumes, the proposed method achieved high volumeteric Dice coefficient (DC) values of 93.53%±0.71% and 93.30%±1.61%, respectively, which are close to the corresponding observer repeatability values of 95.60%± 0.63% and 95.49%±1.36%. Importantly, in certain comparable cases, our method demonstrated significant (more than 50% in terms of suitable quotient measures based on DC) improvement over a recently reported method [8]. In detecting the Haller’s sublayer, the algorithmic and manual volumetric DC values are observed to also be in close agreement.

The rest of the paper is organized as follows. In Section 2, we provide details of the OCT datasets as well as reference manual segmentations. Subsequently, in Section 3, we describe the proposed methodology to segment the choroid layer and the Haller’s sublayer. The results are presented in Section 4. Finally, Section 6 concludes the paper with a discussion.

2. Datasets and Reference Delineations

As stated earlier, we seek to develop a volumetric segmentation algorithm to delineate the choroid and the Haller’s sublayer, and validate that on OCT volume datasets of healthy and diseased eyes against reference manual delineations. In preparation, we first describe the datasets and the process of generating reference delineations manually.

2.1. Datasets

This study was performed on retrospective data, collected with informed consent of patients. Such consent was in turn taken adhering to the tenets of declaration of Helsinki. In particular, the OCT scans of all healthy and diseased eyes were acquired using Heidelberg Retina Angiograph (HRA Spectralis, Heidelberg Engineering, Dossenheim, Germany) by a single retina specialist. The Spectralis OCT device provides up to 40,000 amplitude scans (A-scans) per second with a depth resolution of 7 μm in tissue and a transverse resolution of 14 μm using a super-luminescence diode with a mean wavelength of 870 nm. Raster imaging consisting of 97 high-resolution B-scans was performed on each eye, centering the scanning area at the fovea using an internal fixation light. Each B-scan was obtained for analysis after 25 frames, and averaged using built-in software (TruTrack; Heidelberg Engineering, Heidelberg, Germany) so as to ensure high quality. Altogether, we considered ten OCT volume datasets: H1-H5 consisting of scans of five healthy eyes, and D1-D5 consisting of scans of five diseased eyes, diagnosed with diabetic macular edema (DI), dry AMD (D2 and D3), macular hole (D4) and cystoid macular edema (D5). The datasets at hand were acquired with varying scanning area and axial length as detailed in Table 1.

Table 1:

OCT volume (around the fovea) for healthy and diseased datasets at hand. Where x and y indicates the scanning area dimensions and z represents the axial length.

Dataset number	Volume x × y × z in mm × mm × mm (pixel × pixel × pixel)
H1, H2, H4, H5 H3 D1, D2, D3, D4, D5	3 × 4.5 × 2 (97 × 768 × 472) 6 × 9 × 2 (97 × 1536 × 496) 6 × 6 × 2 (97 × 512 × 512)

Note: Acquisition is not continuous in the x direction, 97 scans uniformly separated were acquired.

2.2. Manual Segmentation

As alluded earlier, we take as reference manual delineations that were performed twice (on different days) by a retinal expert. At each attempt, the expert marked CIB, COB and HSI on each B-scan using the ubiquitous Image J software [53]. Specifically, while delineating any boundary, the expert initially marked an piece-wise linear curve by choosing sparse points using the ‘segmented line’ tool, and subsequently smoothened it by the ‘spline fit’ operation. Finally, fine adjustments were made to ensure that the drawn curve follows the perceived boundary accurately. Fig. 2 illustrates the steps involved in manually marking the COB. Similar steps were followed while marking CIB and HSI as well.

Figure 2:

Demonstration of manual marking using ImageJ: (a) piece-wise linear marking, (b) smoothened manual boundary after applying spline fit on (a), and (c) smoothened manual boundary obtained second attempt by the same observer but on a different day.

3. Proposed Algorithmic Segmentation Method

Our objective is to automatically delineate the choroid as well as the Haller’s sublayer in volumetric OCT scans. To this end, as pictorially depicted in Fig. 1, we proposed a method for detecting CIB (also known as choroidal-RPE interface), COB (also known as choroidal-scleral interface) and Haller’s and Sattler’s interface (HSI). For each such detection, we make use the same essential principles informed by the process of OCT image acquisition, which we outline first.

3.1. OCT image acquisition

An OCT imaging device takes an optical beam and splits it into two coherent beams, one of which is directed at the target region of a tissue, and the other is used as reference. Modern frequency domain equipment records as an A-scan the phase difference between the back scatter from the sub-surface features and the reference beam. In the process, speckle noise is known to arise [54]. In the axial direction, the intensity of the said back scatter reduces exponentially with the depth of corresponding features [55, 11]. Similar exponential attenuation is also observed due to the shadow cast by the retinal vessels present in the inner limiting membrane (ILM). Consequently, in an OCT B-scan (a horizontal stack of A-scans), the inner (shallower) retinal layer appears in higher contrast compared to outer (deeper) layers such as the choroid and the sclera (Fig. 1). Taking the above process into account, we propose for our delineation tasks a methodology, which is schematically depicted in Fig. 3. In particular, we describe preprocessing, the common enhancement technique, smoothing methods, and specific steps for detection of CIB, COB and HSI, in that order. In detecting each boundary, initial steps involve sequential processing of B-scans in a volume, followed by 3D smoothing.

Figure 3:

Schematic of the proposed methodology

3.2. Preprocessing

As alluded earlier, OCT imaging is affected by speckle noise and exponential decay in intensity with depth. In response, we performed the following preprocessing steps (Fig. 3). For mitigation of speckle noise, we empirically chose median filtering over other reported methods [11], such as statistical filtering [56] (e.g., Wiener filtering [57]) and deep learning [58], in view of the simplicity and the high efficacy of the former. In particular, we employed a 6×6 median filter. Given a representative B-scan (Fig. 7b), the median filtered outcome is shown in Fig. 7c. Subsequently, we performed contrast limited adaptive histogram equalization (CLAHE) to enhance contrast in the face of significant variability in different parts of the image [59]. Specifically, we divided each image into 8×8 blocks for this purpose, and depicted in Fig. 7c the equalized outcome demonstrating enhanced contrast between the stromal and the luminal intensities in the choroid.

Figure 7:

Graphical depiction of the proposed algorithm: (a) input OCT volume scan; (b) representative B-scan; (c) median filtering; (d) adaptive histogram equalization; (e) vertical flip; (f) binarization (CIB); (g) morphological operations followed by vertical flip; (h) initial CIB estimate; (i) intermediate CIB estimate (green); (j) final CIB estimate (yellow); (k) binarization (COB); (1) morphological operations; (m) initial COB estimate; (n) intermediate COB estimate; (o) final COB estimate (yellow); (p) binarization (HSI); (q) choroidal large vessels (yellow); (r) initial HSI estimate; (s) intermediate HSI estimate (green); (y) final HSI estimate (yellow); and (u) outcome of volumetric boundary delineation task.

3.3. Common enhancement technique

As each of CIB, COB and HSI represents a boundary located at significant depth, we countered the aforesaid exponential attenuation using further image enhancement specific to detection of each boundary. However, the underlying technique (ignoring parametric variation) would still remain common (Fig. 3), and is described below. For each pixel $(i,j)$ in an OCT B-scan, the raw image intensity

$$I_{\text{raw}}(i,j)={\left(\frac{I(i,j)}{255}\right)}^4$$ (1)

is estimated from the 8-bit grayscale intensity $I(i,j)$. Subsequently, assuming the A-scan length to be $p$, i.e., $p$ rows in a B-scan, we obtained the compensated intensity at pixel $(i,j)$

$$I_{\text{comp}}(i,j)=\frac{I_{\text{raw}}(i,j)}{2{\sum }_{k=i}^p\left(I_{\text{raw}}(k,j)\right)},$$ (2)

which is known to minimize certain energy criterion. Further, we performed exponential contrast enhancement

$$I_{\exp }(i,j)={\left(I_{\mathrm{comp}}(i,j)\right)}^n$$ (3)

for suitable exponent $n$. Adding to previously reported operations (1), (2) and (3) [55, 11], we propose a final depth compensation step

$$I_{\text{depth}}\left(i,j\right)=i^2{I}_{\exp }\left(i,j\right)$$

that attempts to directly mitigate exponential attenuation. Finally, the enhanced grayscale intensity was obtained as

$$I_{\text{enh}}\left(i,j\right)=255{\left(I_{\text{depth}}\left(i,j\right)\right)}^{1/4},$$

using the inverse operation of (1). We shall apply the proposed enhancement slightly differently in the contexts of CIB detection and COB (and HSI) detection.

3.4. Morphological operations

In each case of boundary detection, the enhanced grayscale images, as described above, were binarized using the mid-scale threshold of 128. Subsequently, our objective was to find the largest connected component and take its edge as the initial estimate of the desired boundary. In practice, some discontinuities and hence multiple disjoint regions arise instead of single connected component. As a remedy, we applied morphological close (dilation followed by erosion) and open (erosion followed by dilation) operations to connect nearby objects [60]. In particular, the morphological close operation tends to connect large objects together, while the morphological open operation disconnects small noisy components. Next, we applied the connected components algorithm to obtain large connected components (instead of one largest component to ensure robustness), whose superior/inferior envelops were taken as the desired initial boundary estimate.

3.5. Stratified smoothing

As alluded earlier, our main focus remained on obtaining smooth seamless boundaries mimicking manual delineations in 3D. In other words, such boundaries should be smooth in both y-z planes (of individual B-scans, column index representing $y$ coordinate, and row index representing z coordinate) and x-z planes (B-scan index representing $x$ coordinate). Refer Fig. 7a for a depiction of the above coordinate system. More precisely, the row index z should be a smooth function of both $(x,y)$. In practice, an initial boundary estimate could be either discontinuous or jagged or both in parts. As a remedy, we smoothed such initial estimates. Specifically, we employed stratified smoothing based on two smoothing techniques, namely, tensor voting (TV) and robust locally estimated scatterplot smoothing (RLOESS). Tensor voting is more powerful and capable of removing discontinuity along with mitigating noise, but compute-intensive. In comparison, RLOESS is lighter, but only mitigates noise.

3.5.1. Achieving 3D smoothing via successive 2D smoothing

In a B-scan indexed $x$, the row index $z$ of an initial boundary estimate at column $y$ is given by a function $z=\varphi (x,y)$. We sought a smoothed version $\widehat{\varphi }(x,y)$ of $\varphi (x,y)$, where a suitable error between $\widehat{\varphi }$ and $\varphi$ should ideally be minimized subject to appropriate smoothness criterion. In practice, we obtained $\widehat{\varphi }(x,y)$ by smoothing $\varphi (x,y)$ alternatingly in x-z planes (keeping $y$ fixed) and in y-z planes (keeping $x$ fixed) to keep the compute-budget low (see Fig. 4). As alluded earlier, each round of 2D smoothing was performed using either TV or RLOESS, as appropriate.

Figure 4:

(a) Visualization of jagged surface z (possible discontinuities not shown) as a function of (x, y) requiring smoothing in 3D; (b) Illustration of 2D smoothing (in either x-z or y-z planes), which was alternatingly used to achieve 3D smoothing.

3.5.2. Smoothing using tensor voting

TV attempts at detecting and giving prominence to underlying salient structures in noisy binary images [49]. In the process, TV performs smoothing/interpolation based on a certain voting field, by propagating information using tokens, which convey various objects’ orientation preferences (i.e., votes) to their neighbors. In 2D TV, all the objects (points of interest) are first initialized with ball tensors which are isotropic and have unit strength. After the votes are cast and summed, proximate ball tensors transform to stick tensors (see Fig. 5), which has the stick component (saliency magnitude) in the direction parallel to the largest eigenvalue. Further, objects belonging to the same structure get grouped together based on their stickiness. This procedure had earlier been adopted in smoothing initial COB estimates [8]. Presently, we extended the use of TV to the detection of both CIB and COB at different stages. Specifically, in the process of CIB detection, TV was applied as the final smoothing step to mitigate minute local variations that still remained after a lighter 3D smoothing. On the other hand, while detecting COB, TV was applied to smooth discontinuous intermediate COB estimate as earlier.

Figure 5:

Illustration of tensor voting.

We took the saliency decay function (DF), specifying how the influence of a vote decays away from the object, as Gaussian

$$\mathrm{DF}(s,k,\sigma )=e^{(\frac{s^2+c{k}^2}{{\sigma }^2})},$$ (4)

where $s$ indicates the arc length, $k$ the curvature, $\sigma$ the scale of voting, determining the effective neighborhood size, and $c$ the degree of decay with curvature [8, 49]. As customary, we chose $s=2\theta /k$, k = 2sin(θ)/d, and $c=\left(16\log 10/{\pi }^2\right)(\sigma -1)$, where $d$ indicates the distance between the voter and the receiver, the two tokens at hand, and $\theta$ the angle between the line going through the voter and the receiver and the tangent of the osculating circle at the voter.

In theory, one could deploy TV for every 2D smoothing task (or even in 3D directly, albeit with suitable extension). However, TV being compute-intensive, we restricted its use to certain daunting 2D smoothing tasks involving discontinuity removal, and deployed a lighter smoothing algorithm RLOESS in less demanding circumstances [50, 51].

3.5.3. Robust locally estimated scatterplot smoothing (RLOESS)

The intermediate boundary estimates (see Fig. 7i for CIB, Fig. 7n for COB and Fig. 7s for HSI) exhibit lack of smoothness across slices due to imaging and other artefacts, although those should ideally reflect the structural smoothness in the choroidal layer. We would use RLOESS to ensure the desired smoothness. Functionally, RLOESS performs a locally weighted least-squares regression, while removing outliers. Specifically, a second degree polynomial is fit to a subset of the data points at hand under the weighted least-squares criterion, giving higher weightage to nearby points. The choice of subset is defined by smoothing parameter $q$ which is a fraction of complete data. Further, the weight function $w\left(x_s\right)$ for a subset of data $x_s$ is given by

$$w\left(x_s\right)=\left\{\begin{array}{ll}(1-{\left|x_s\right|}^3),\hfill & \text{if}{x}_s<1\hfill \\ 0,\hfill & \text{otherwise}.\hfill \end{array}\right.$$ (5)

The functioning of RLOESS is illustrated in Fig. 6.

Figure 6:

Smoothing using RLOESS. Notation: q- data subset parameter (fraction of the original data) used at each data point for regression.

3.6. Volumetric Boundary Delineation

We performed volumetric delineation of the desired boundaries CIB, COB and HSI. While the basic philosophy remained similar in each case, we next describe boundary-specific steps following preprocessing (refer Fig. 3 and Sec. 3.2).

3.6.1. Choroid inner boundary (CIB) detection

As depicted in the left prong of Fig. 3, each preprocessed B-scan (Fig. 7d) was vertically flipped, i.e, z axis was inverted (Fig. 7e). The vertical flip allowed the retina to be artificially positioned at greater depth, hence get enhanced by the exponential and nonlinear process described in Sec. 3.3, and binarized (Fig. 7f). The binarized image was flipped back vertically to the original orientation, the morphological close, open and connected components operation were performed (Fig. 7g), and the initial CIB estimate was obtained by locating bottom pixels (Fig. 7h). On this, we performed RLOESS regression in y-z plane to obtain intermediate CIB estimate (Fig. 7i). After stacking such intermediate CIBs along x axis, we performed RLOESS regression in x-z planes. Noting the introduction of occasional discontinuity in the process, TV was next performed in y-z planes, and the output was taken as our final volumetric estimate of CIB (Fig. 7j).

3.6.2. Choroid outer boundary (COB) detection

Next, following the middle prong of Fig. 3, each preprocessed B-scan was enhanced as earlier, and binarized (Fig. 7k). The said enhancement was designed to counter aforementioned intensity attenuation with depth as a result of the imaging process. Subsequently, a region of interest of constant depth below the CIB was extracted as a rectangular (flattened) image (Fig. 7l). On the result, the aforesaid morphological operations were performed, and the initial COB estimate was obtained (Fig. 7m). Unlike in case of CIB (Fig. 7h), which is specified by the generally well-defined RPE, the initial estimate of COB, which is specified by the bottom-most large vessels and less well defined, is discontinuous. Next, we applied TV to ensure desired continuity, and obtained the intermediate COB estimate (Fig. 7n) [8]. After stacking such intermediate COBs along x axis, we performed RLOESS regression alternatingly in x-z planes and y-z planes, and the output was taken as our final volumetric estimate of COB (Fig. 7o).

3.6.3. Haller’s Sattler’s interface (HSI) detection

Next, as shown in the right prong of Fig. 3, we began with the binarized image (Fig. 7k) in the COB detection work flow, and detected large vessels in the volume demarcated by the final estimates of CIB and COB (Fig. 7p) following the method of Uppugunduri et al. [24]. Specifically, blood vessels (barring very small ones) were identified using the connected components algorithm, their cross-sectional areas were computed, and only those with areas greater than the mean value were retained. Note that this process was unlikely to identify all large vessels separately, but would produce blobs, each possibly representing a number of large vessels, which sufficed our purpose. Further, we obtained the initial HSI estimate as the linear interpolation between the topmost pixels of individual blobs, which ensures continuity (Fig. 7q). Next, we applied RLOESS regression on such intial estimate, and obtained the intermediate HSI estimate (Fig. 7r) [8]. After stacking such intermediate HSIs along x axis, we again performed RLOESS regression alternatingly in x-z planes and y-z planes, and the output was taken as our final volumetric estimate of HSI (Fig. 7s). In the end, final estimates of CIB (Fig. 7j), COB (Fig. 7o) and HSI (Fig. 7s) are combined to produce the result of the desired volumetric boundary delineation task (Fig. 7t).

3.7. Performance Measures

We evaluated the accuracy of the proposed volumetric delineation of CIB, COB and HSI as follows. First, denoting the row index z_CIB of CIB as a function of column index y at B-scan index x, we evaluated the overall closeness of the algorithmic estimate of z_CIB with its manual estimates. Next, we denoted the row index of COB as z_COB, and compared algorithmic and manual estimates of $\left(z_{\text{COB}}-z_{\text{CIB}}\right)$, which manifests as spatial distribution of choroidal thickness in 2D, and choroidal volume in 3D upon integration over the $(x,y)$ plane. Finally, we performed similar analysis for the Haller’s sublayer by replacing z_CIB by z_HSJ, the row index of HSI, in the preceding.

3.7.1. Dice coefficient measures

In each case, we used Dice coefficient ($\text{DC}$) as a measure of similarity between two delineations [61]. In general, the $\text{DC}$ between two Euclidean sets $A$ and $B$ is defined by

$$\text{DC}(A,B)=\frac{2\lambda (A\cap B)}{\lambda (A)+\lambda (B)},$$ (6)

where $\lambda (A)$ indicates the appropriate measure of set $A$. In particular, A(−) measures the length of a ID set, the area of a 2D set, and the volume of a 3D set. As $0\le \lambda (A\cap B)\le \min (\lambda (A),\lambda (B))$, DC is always a non-negative fraction, $0\le \text{DC}(A,B)\le 1$. At the extreme, $\text{DC}(A,B)=0$ if $A$ and $B$ are disjoint, and $\text{DC}(A,B)=1$ if $A$ and $B$ are identical. Further, the mean and the standard deviation of a set of $M$ numbers ${\left\{{\alpha }_m\right\}}_{m=1}^M$. were computed as $\overline{\alpha }=\mu \left(\left\{{\alpha }_m\right\}\right)=\frac{1}{M}{\sum }_{m=1}^M{\alpha }_m$ and $\sigma \left(\left\{{\alpha }_m\right\}\right)=\sqrt{\frac{1}{M}{\sum }_{m=1}^M{\left({\alpha }_m-\overline{\alpha }\right)}^2}$, respectively.

Consider an OCT volume scan with $N_x$ 2D B-scans, each B-scan with $N_y$ 1D A-scans (columns), and each A-scan with $N_z$ pixels (rows). Under two delineations 1 and 2, let the respective delineated volumetric sets be $V^1$ and $V^2$ Then the corresponding volumetric (3D) DC measure was taken as $\text{DC}3=\text{DC}\left(V^1,V^2\right)$. We further considered average 2D DC measures, viewing the OCT volume scan as a collection of B-scans. Specifically, denote by $A_x^1$ and $A_x^2$ the 2D cross-sections at $x$ of respective volumetric sets $V^1$ and $V^2$, i.e., the competing 2D delineated sets corresponding to the B-scan $x\left(x=1,2,\dots ,N_x\right)$ under respective delineations 1 and 2. The corresponding area (2D) DC measure was taken as $\text{DC}{2}_x=\text{DC}\left(A_x^{\text{i}},A_x^{\text{ii}}\right)$. As performance measures, we computed the mean $\text{MDC}2=\mu \left(\left\{\text{DC}{2}_x\right\}\right)$ and the standard deviation $\text{SDC2}=\sigma \left(\left\{\text{DC}{2}_x\right\}\right)$ over $x=1,2,\dots ,N_x$. In the same vein, we performed DC analysis in ID as well. Specifically, denote by $L_{xy}^1$ and $L_{xy}^2$ the y-th (y =1,2 ,…, N_y) columns of $A_x^1$ and $A_x^2$, respectively. The corresponding linear (1D) DC measure was taken as $\text{DC}{1}_{xy}=\text{DC}\left(L_{xy}^1,L_{xy}^2\right)$. Finally, we computed the mean $\text{MDC}1=\mu \left(\left\{\text{DC}{1}_{xy}\right\}\right)$ and the standard deviation $\text{SDC}1=\sigma \left(\left\{\text{DC}{1}_{xy}\right\}\right)$ over $x=1,2,\dots ,N_x$ and $y=1,2,\dots ,N_y$ in a nested manner.

As alluded earlier, we considered a collection of $N$ volume OCT scans indexed $i=1,2,\dots ,N$. Further, we denoted by DC3_i the 3D DC measure for the i-th volume, and computed the mean and the standard deviation $\text{MDC}3=\mu \left(\left\{\text{DC}{3}_i\right\}\right)$ and $\text{SDC}3=\sigma \left(\left\{\text{DC}{3}_i\right\}\right)$, respectively, over $i=1,2,\dots ,N$. Turning to 2D measures, we indexed the mean and the standard deviation values for the i-th volume as MDC2_i; and SDC2ⁱ, respectively, and computed the corresponding overall figures as $\mu ({\left\{\text{MDC}{2}_i\right\}}_{i=1}^N)$ and $\sqrt{\mu ({\left\{\text{SDC}{2}_i^2\right\}}_{i=1}^N)}$. Analogously, in the above we substituted $\text{MDC}{2}_i$, by ${\text{MDC1}}_i$ and $\text{SDC}{2}_i$ by $\text{SDC}{1}_i$, in case of ID measures.

In certain previous studies, metrics other than DC such as absolute difference (AD) and correlation coefficient (CC) were employed to evaluate the segmentation performance. However, such metrics do not measure overlap, and may not suit the present context (see [62] for an argument made in relation to a different ophthalmological problem). In particular, notice that in Fig. 8(a) the area measured based on automated delineations (yellow lines) is equal to that of measured based on manual delineations (red lines). However, there is significant mismatch in the location of the boundaries that have minimal overlap. On the contrary, in the Fig. 8(b), although areas are not similar, the algorithmic and manual boundaries have large overlap, which could be desirable.

Figure 8:

Illustration of advantage of DC measure over other measures used for measuring the performance of proposed method based on computing choroid thickness: (a) case 1: area measure remains same for both manual (red) and automated (yellow) thickness measurement, while DC value quantify the match among them; (b) case 2:

3.7.2. Quotient measures

If the manual delineation were ideal, one would aim at reproducing it algorithmically. In that scenario, the DC between the ideal and algorithmic delineations would act as a performance measure. In reality, we observed that two expert graders, oblivious of each other, produced (slightly) different manual markings, and hence none should not be taken as the ground truth. In this setting, researchers had previously suggested comparison of the inter-grader similarity with the similarity between the algorithmic and the mean manual delineations [8]. Further, the aim was to bring the latter type of similarity close to the level of the former, and possibly surpass it. Formally, let us consider some generic similarity measure X, and denote its value with respect to two manual delineations M1 and M2 by ${\text{X}}^{ref}$ (“ref” in superscript stands for reference). By ${\text{X}}^{algo}$ (“algo” in superscript stands for algorithmic), let us denote the analogous quantity when one delineation M was obtained by averaging the outcomes of M1 and M2, and the other delineation was obtained algorithmically. In this setting, the generic quotient measure is defined as

$$\text{QX}=\frac{{\text{X}}^{algo}-{\text{X}}^{ideal}}{{\text{X}}^{ref}-{\text{X}}^{ideal}},$$ (7)

where ${\text{X}}^{ideal}$ denotes the ideal value of X. Clearly, when ${\text{X}}^{algo}$ is further away from ${\text{X}}^{ideal}$ than ${\text{DC}}^{ref}$ is, i.e., algorithmic similarity is worse than the manual one, then we have QX > 1. One desires QX to be close to unity, and even less than unity, if possible.

Now, considering an OCT volume, and choosing × as the volumetric DC, one defines the quotient $\text{QDC}3=\left(\text{DC}{3}^{algo}-1\right)/\left(\text{DC}{3}^{ref}-1\right)$ as the ideal value of DC equals one. Similarly, by choosing X as MDC1, MDC2 or MDC3 (equivalently, k as 1, 2 or 3), one defines the quotient measure $\text{QMDCk}=({\text{MDCk}}^{algo}-1)/({\text{MDCk}}^{ref}-1)$ for mean DC for any dimension. Similarly, one defines the quotient measure $\text{QSDCk}={\text{SDCk}}^{algo}/{\text{SDCk}}^{ref}$ for standard deviation of DC for dimension $k=1,2,3$ (i.e., choosing X as SDC1, SDC2 or SDC3, respectively, in (7)). Here, note that the standard deviation should ideally be zero, i.e., ${\text{SDCk}}^{ideal}=0$. Note that variants of MDC and SDC quotients apply to either single OCT volume or a collection of those.

4. Results and Discussion

As alluded earlier, we followed the methodology schematically depicted in Figs. 3 and 7. The associated parameters were chosen empirically based on repeated trial and error. Specifically, for detection of CIB, COB and HSI, we respectively set $n=10$, $n=10$ and $n=6$ for exponential contrast enhancement. We used a smoothing parameter of 0.2 in each instance of RLOESS regression (regardless of the plane at hand). While deploying tensor voting, we took $\sigma =10$ and $\sigma =80$ in the respective cases of CIB and COB detection. In Fig. 9, our algorithmic delineations of CIB, COB and HSI are shown in 2D against corresponding twofold blind manual delineations in five representative instances of each boundary. In particular, it can be noticed that these are some of the instances where initial spurious estimates (solid lines marked in green) got corrected by the proposed volumetric smoothing and the final smooth estimates (solid lines marked in yellow) matches closely with the corresponding manual references (dotted lines marked in red and magenta). Further, on representative healthy and diseased datasets, Fig. 10 depicts the volumetric segmentation achieved by proposed method vis-à-vis manual reference. Qualitatively, choroid and Haller’s sublayer volumes detected by the proposed method closely matches with the corresponding reference volumes. Next, we turn to quantitative evaluation of the efficacy of the proposed algorithm in relation to each segmentation subtask.

Figure 9:

Proposed vs manual segmentations: Columns 1, 2 and 3 represent five instances of CIB, COB and HSI demarcations, respectively. Color coding: Green - Initial algorithmic segmentation; Yellow - Final algorithmic segmentation; and Magenta and red - Manual segmentations.

Figure 10:

Volumetric segmentation of the choroid and the Haller’s sublayer: Column-1 - representative healthy and diseased datasets; column-2 - Proposed (yellow) and reference (red) volumetric delineations of CIB, COB and HSI; Column-3 - Extracted choroid layer in 3D; and Column-4 - Extracted Haller’s sublayer in 3D.

4.1. CIB detection

We begin with quantitative performance comparison for the CIB detection subtask. To this end, we compared vertical (z) coordinates of the CIB detected by algorithmic and manual methods at each column (y). More precisely, in each case, we considered the portion of each column from the top to the detected z coordinate, computed suitable ID DC measures, and compared those statistically in Table 2. For the sake of brevity, we restrict to ID analysis in the context of CIB detection. We shall carry out 2D (area-based) and 3D (volumetric) analysis as well in the comprehensive contexts of choroid and Heller’s layer segmentation. Returning to the aforesaid table, we observed that the overall mean Dice coefficient (MDC1) between measurements obtained by the proposed method and the manual reference is observed to be 99.76% (SDC1: 0.10%) on the five healthy datasets, and 99.49% (SDC1: 0.15%) on the five diseased datasets. This indicates high accuracy and consistency of CIB detection in both healthy and diseased cases with slightly better performance in the former. We also considered intra-observer repeatability in terms of MDC1 between the two manual demarcations, which turned out to be 99.79 % (SDC1: 0.09%) and 99.71 % (SDCl:0.13%), respectively, in healthy and diseased cases, indicating marginally higher level of accuracy in the former. Further, QMDC1 and QSDC1, quotient measures for DC, were observed to be close to one overall with respective values 1.18 and 1.12 for the healthy and 1.74 and 1.21 for the diseased datasets. This indicated that the proposed algorithm performed near par with manual delineation on the average. In case of specific datasets, quotients less than one (i.e., algorithmic performance exceeding manual one) was observed. Examples include QMDC1 for heathy dataset H5, and QSDC1 for healthy datasets H1, H2 and H4 and diseased dataset D1.

Table 2:

Relative performance comparison of CIB detection methods based on linear Dice coefficient: Variation of proposed (algorithmic) method versus manual reference (M) against variation between two manual delineations (M1 versus M2).

Dataset type	Method	Parameter	Unit	Dataset					Overall
				H1	H2	H3	H4	H5
	Proposed	MDC1	%	99.76	99.84	99.65	99.76	99.78	99.76
	vs M	SDC1	%	0.08	0.04	0.14	0.06	0.16	0.10
Healthy	Manual	MDC1	%	99.78	99.85	99.78	99.79	99.75	99.79
	(M1 vs M2)	SDC1	%	0.08	0.05	0.11	0.09	0.10	0.09
	Quotients	QMDC1	Ratio	1.11	1.13	1.62	1.12	0.90	1.18
		QSDC1	Ratio	0.95	0.87	1.30	0.72	1.56	1.12
				D1	D2	D3	D4	D5
	Proposed	MDC1	%	99.70	99.05	99.52	99.52	99.66	99.49
	vs M	SDC1	%	0.11	0.34	0.11	0.10	0.11	0.15
Diseased	Manual	MDC1	%	99.76	99.44	99.76	99.78	99.79	99.71
	(M1 vs M2)	SDC1	%	0.11	0.33	0.07	0.05	0.07	0.13
	Quotients	QMDC1	Ratio	1.24	1.69	2.06	2.20	1.63	1.74
		QSDC1	Ratio	0.95	1.02	1.55	1.95	1.66	1.21

4.2. Choroid Segmentation

Next, we turn to the choroid, which is marked as the region between the detected CIB and COB. We evaluated the accuracy of algorithmic choroid segmentation in three ways—in terms of choroid volume estimated, choroid area obtained per B-scan in each volume, and thickness per A-scan (column) in each B-scan of a volume.

4.2.1. Volume measurement

In Table 3, algorithmically obtained choroid volume estimates were compared with those based on manual references in terms of 3D Dice coefficient (DC3) values, which were either close to or greater than 90% for individual healthy and diseased datasets. Further, overall MDC3 between volume estimates obtained algorithmically and manually were observed to be 93.53% (SDC3: 0.71%) on healthy datasets, and 93.30% (SDC3: 1.61%) on diseased datasets, indicating essentially similar levels of accuracy with expectedly less variability in healthy cases. Corresponding intra-observer repeatability in terms of MDC3 between two manual demarcations turned out to be 95.60% (SDC3: 0.63%) and 95.49% (SDC3: 1.36%), respectively, in healthy and diseased cases, indicating insignificant difference in the mean performance with less variability in healthy cases. Indeed, the corresponding QMDC3 (quotient measure for MDC3) values for healthy and diseased datasets were respectively 1.47 and 1.48, very close to each other, and reasonably close to one. The corresponding QSDC3 values, indicating relative variability, were respectively 1.12 and 1.18, which are quite similar and close to one. In short, relative to the manual method, the proposed algorithm performs almost identically for both healthy and diseased datasets.

Table 3:

Relative performance comparison of choroid detection methods based on volumetric Dice coefficient: Variation of proposed (algorithmic) method relative to manual reference (M) against that between two manual delineations (M1 versus M2).

				Dataset
Dataset type	Method	Parameter	Unit	Hl	H2	H3	H4	H5	MDC3	SDC3
	Proposed vs M	DC3	%	93.34	93.75	92.38	93.95	94.20	93.53	0.71
Healthy	Manual (M1 vs M2)	DC3	%	95.99	95.73	94.72	95.22	96.31	95.60	0.63
									QMDC3	QSDC3
	Quotients	QDC3	Ratio	1.66	1.46	1.44	1.27	1.57	1.47	1.12
				D1	D2	D3	D4	D5
	Proposed vs M	DC3	%	91.70	93.97	94.53	94.86	91.44	93.30	1.61
Diseased	Manual (M1 vs M2)	DC3	%	94.65	94.39	95.68	97.77	94.99	95.49	1.36
									QMDC3	QSDC3
	Quotients	QDC3	Ratio	1.55	1.07	1.27	2.31	1.71	1.48	1.18

4.2.2. Area measurement

Next, in Table 4, we compare algorithmically obtained area estimates for each dataset with those based on manual references in terms of mean 2D Dice coefficient (MDC2) values taken over constituent B-scans. For both healthy and diseased datasets, we observe MDC2 values close to corresponding DC3 values (seen in Table 3) with generally low SDC2 values (less than 3% except in dataset D1), indicating satisfactory consistency. Such consistency is observed at an even greater degree in case of manual references, where the performance difference between healthy and diseased datasets is not significant. In contrast, turning to quotient measures, we observe that the algorithmic performance relative to manual references is better in healthy datasets compared to that in diseased ones in terms of QMDC2. The aforesaid superiority is more pronounced when the quotient QSDC2 is considered.

Table 4:

Relative performance comparison of choroid detection methods based on area Dice Coefficient: Variation of proposed (algorithmic) method versus manual reference (M) against variation between two manual delineations (M1 versus M2).

				Dataset
Dataset type	Method	Parameter	Unit	Hl	H2	H3	H4	H5	Overall
	Proposed	MDC2	%	92.06	93.69	92.19	93.79	93.15	92.97
	vs M	SDC2	%	1.49	1.51	2.14	1.46	1.63	1.65
Healthy	Manual	MDC2	%	95.69	95.42	94.48	95.07	96.15	95.37
	(M1 vs M2)	SDC2	%	1.21	1.41	1.42	2.08	0.97	1.42
	Quotients	QMDC2	Ratio	1.84	1.38	1.41	1.26	1.78	1.51
		QSDC2	Ratio	1.23	1.07	1.50	0.70	1.67	1.16
				D1	D2	D3	D4	D5
	Proposed	MDC2	%	90.81	92.13	91.04	94.78	89.59	91.67
	vs M	SDC2	%	3.22	2.22	2.14	1.54	2.36	2.29
Diseased	Manual	MDC2	%	94.53	94.23	95.28	97.71	94.72	95.29
	(M1 vs M2)	SDC2	%	1.87	2.22	1.98	0.45	1.51	1.61
	Quotients	QMDC2	Ratio	1.67	1.36	1.89	2.27	1.97	1.76
		QSDC2	Ratio	1.72	0.99	1.08	3.36	1.56	1.43

4.2.3. Thickness Measurement

On the five healthy datasets, the overall MDC1 and SDC1 between column-wise thickness estimates obtained by the proposed algorithm and manual reference are observed to be 96.92% and 1.14%, while those values observed between two manual delineations are 97.21% and 1.11%, respectively (Table 5). Further, the respective quotient measures QMDC1 and QSDC1 are observed to be 1.12 and 1.02, both close to one, indicating that the proposed method performs almost at par with intra-oberserver repeatability. An earlier method¹, when tested on the same datasets, reported QMDC1 of 1.66 and QSDC1 of 1.63 [8]. With respect to either of those, the proposed algorithm exhibits a performance improvement of more than 50%. Similarly, on the five diseased datasets at hand (where the said spherical approximation may not hold, and hence the earlier technique does not apply), the overall MDC1 and SDC1 between the column-wise thickness estimates obtained by proposed and manual reference are observed to be 95.67% and 1.76% while those values observed between two manual segmentations are 96.94% and 1.33%, respectively. Further, the quotient measures QMDC2 and QSDC2 are observed to be 1.41 and 1.32, indicating good agreement between segmentation by proposed and manual methods even in the diseased cases. Thus, the proposed algorithm appears to improve upon the earlier method both in terms of accuracy and scope.

Table 5:

Relative performance comparison of choroid detection methods based on linear Dice Coefficient: Variation of proposed (algorithmic) method versus manual reference (M) against variation between two manual delineations (M1 versus M2).

				Dataset
Dataset type	Method	Parameter	Unit	H1	H2	H3	H4	H5	Overall	Reference [8]	Performance Improvement
	Proposed	MDC1	%	97.32	96.89	95.11	97.30	97.98	96.92	95.47	-
	vs M	SDC1	%	1.07	1.40	1.58	0.88	0.78	1.14	1.73	-
Healthy	Manual	MDC1	%	97.55	97.08	96.14	97.08	98.18	97.21	97.28	-
	(M1 vs M2)	SDC1	%	0.79	1.25	1.25	1.71	0.56	1.11	1.06	-
	Quotients	QMDC1	Ratio	1.09	1.06	1.27	0.93	1.11	1.12	1.66	51.04%
		QSDC1	Ratio	1.35	1.11	1.27	0.51	1.40	1.02	1.63	59.39%
				D1	D2	D3	D4	D5
	Proposed	MDC1	%	94.28	96.20	96.07	96.90	94.89	95.67
	vs M	SDC1	%	2.93	1.54	1.40	1.03	1.89	1.76
Diseased	Manual	MDC1	%	945.92	96.96	96.82	98.43	96.56	96.94
	(M1 vs M2)	SDC1	%	1.72	1.45	1.70	0.43	1.30	1.33
	Quotients	QMDC1	Ratio	1.49	1.25	1.23	1.97	1.48	1.41
		QSDC1	Ratio	1.65	1.07	0.83	2.40	1.45	1.32

Further, we presented A-scan-wise Dice scores (DC1) of thickness measurements as spatial heat maps. Specifically, we compared DC1 between measurements by the proposed algorithm and that by the manual reference vis-à-vis DC1 between the two manual delineations. Figs. 11 and 12, respectively, depict the thickness and DC1 heat maps for each of the healthy and the diseased datasets. Encouragingly, we observe generally close match in both respects in each of the healthy and the diseased cases. However, algorithmically obtained heatmaps appear smoother than those corresponding to manual ones, likely due to the volumetric smoothing adopted in the former.

Figure 11:

Thickness heat-map representation for five healthy eyes datasets (H1-H5): Columns represent their en-face, automated thickness, manual thickness map, column-wise calculated Dice coefficient (DC) map for automated and manual results respectively.

Figure 12:

Thickness heat-map representation for five diseased eyes datasets (D1-D5): Columns represent their en-face, automated thickness, manual thickness map, column-wise calculated DC for automated and manual results respectively.

4.3. Haller’s Sublayer Detection

As alluded earlier, Haller’s sublayer is specified by the HSI and the COB as inner and outer boundaries, respectively. Accordingly, to evaluate Haller’s sublayer detection performance, we compare the DC values obtained between algorithmic and manual estimates. However, manual demarcation of HSI presents significantly more challenge compared to that of either CIB or COB. In particular, observers must carefully judge whether individual blood vessels are of medium or large diameter, draw a notional boundary between vessels of competing sizes, and repeat the process for each B-scan. Indeed, our experts took significantly larger time and effort in delineating HSI than they did in delineating either CIB or COB. In view of the above, we considered only one healthy dataset (H4) and one diseased dataset (D2) for studying Haller’s sublayer segmentation. As alluded earlier, dataset D2 corresponds to dry AMD disease with signature degeneration in retinal layer and inner choroidal vessels. Consequently, vessels in the Haller’s sublayer are more clearly visible in D2, than in the competing healthy dataset H4. This phenomenon is observed in representative images of H4 and D2 (Fig. 13). Not surprisingly, manual delineations of the HSI are less ambiguous in D2 than in H4. Corresponding algorithmic delineations also exhibit similar behaviour.

Figure 13:

Manual and automated delineations of HSI for a B-scan taken from H4 and D2 datasets. Notice that the HSI delineations by both manual and automated methods of D2 is less ambiguous and closely matching as opposed to those of H4.

4.3.1. Volume Measurement

Next, we report statistical performance in Table 6. In terms of volumetric DC (DC3), performance for the algorithmic method is observed to be close to that for the manual method for the healthy dataset H4 as well as the diseased dataset D2. In fact, the quotient values QDC3, indicating the algorithmic performance in relation to the manual reference, appears essentially indistinguishable for those cases.

Table 6:

Algorithmic performance of HSI detection using Dice Coefficient calculated based on volume: comparison between proposed vs manual reference (M) and two manual delineations (M1 vs M2).

Evaluation criteria	Method	Parameter	Unit	Healthy Dataset	Diseased Dataset
Dice coefficient (DC) in 3D	Proposed vs M	DC3	%	86.23	86.85
	Manual (M1 vs M2)	DC3	%	89.02	89.55
	Quotients	QDC3	Ratio	1.25	1.26
Dice coefficient (DC) in 2D	Proposed vs M	MDC2 (SDC2)	% (%)	85.94 (3.72)	86.76 (3.12)
	Manual (M1 vs M2)	MDC2 (SDC2)	% (%)	88.70 (3.54)	89.14 (3.27)
	Quotients	QMDC2 QSDC2	Ratio Ratio	1.24 1.04	1.22 0.95
Dice coefficient (DC) in 1D	Proposed vs M	MDC1(SDC1)	% (%)	85.84 (3.25)	84.96 (5.31)
	Manual (M1 vs M2)	MDC1(SDC1)	% (%)	90.82 (2.46)	87.63 (3.78)
	Quotients	QMDC1 QSDC1	Ratio Ratio	1.54 1.32	1.21 1.40

4.3.2. Area Measurement

The overall MDC2 between area estimates obtained by proposed and manual reference are observed to be 85.94% (SDC2: 3.72%) for healthy (H4) and 86.76% (SDC2: 3.12%) for diseased (D2) dataset under consideration. These values are at par with the respective MDC2 values measured between two manual segmentations, which are 88.70% (SDC2: 3.54%) for the healthy and 89.14% (SDC2: 3.27%) for the diseased dataset. Further, the corresponding quotient QMDC2 takes similar values of 1.24 for the healthy and 1.22 for the diseased dataset which are close to one. The other quotient measure QSDC2 takes values that are even closer to one.

4.3.3. Thickness Measurement

In the same vein, the overall MDC1 between thickness estimates obtained by proposed and manual reference are observed to be 85.84% (SDC1: 3.25%) for the healthy dataset H4 and 84.96% (SDC2: 5.31%) for the diseased dataset D2. These values approximate respective MDC2 values measured between two manual segmentations, which are 90.82% (SDC1: 2.46%) for the healthy and 87.63% (SDC1: 3.78%) for the diseased dataset. Further, the quotient measure QMDC1 (QSDC1) is observed to be 1.54 (1.32) for the healthy and 1.21 (1.40) for the diseased dataset. This indicates that the proposed method performs reasonably close to manual segmentation.

Proceeding further, Fig. 14 depicts spatial heat maps of A-scan-based thickness measurements and Dice scores (DC1) obtained by the proposed as well as the manual methods for the healthy (H4) and the diseased (D2) datasets. Similar to choroidal thickness heat maps, we observe that the algorithmic heat maps are comparable to the manual ones. Further, as alluded earlier, the heat maps obtained by proposed volumetric smoothing approach appear smoother than those corresponding to manual ones.

Figure 14:

Haller’s sublayer thickness heat-map representation for a healthy (H4) and a diseased (D2) OCT retinal datasets: Columns [1–5] represent their en-face, automated and manual thickness maps, column-wise DC calculated for automated and manual results respectively.

5. Notes on implementation

Implementation of the proposed algorithm was performed using MATLAB R2019a scientific programming platform on a workstation having Intel Core i7 processor, 16 GB RAM and 64-bit Windows 7 Enterprise operating system. Various operations including tensor voting [49], RLOESS [50] and morphological operations were performed using MATLAB toolboxes. The average computational time for the datasets Hl, H2, H4 and H5 was approximately recorded as 25 sec per B-scan while that for dataset H3 it was recorded as 30 sec per B-scan. Further, for diseased datasets D1-D5, we observed an average computational time of approximately 28 seconds.

6. Discussion

In this paper, we proposed a robust volumetric segmentation algorithm to detect the vascular choroid layer and the Haller’s sublayer having large blood vessels. We not only improved upon existing choroid detection methods, but also applied the proposed technique to segmentation of the Haller’s sublayer, which has so far received considerably less attention compared to that of the choroid. Indeed, for both problems, we leveraged the idiosyncrasies of OCT volume acquisition, and proposed the same computationally efficient algorithm (with minor variations). Our algorithm also exploits structural continuity in 3D by employing volumetric smoothing. Performance of the proposed algorithm was validated against that of the manual method on both healthy and diseased datasets. For each type of datasets, we obtained ID, 2D and 3D Dice coefficients, each consistently exceeding 90%, and observed close agreement between the algorithmic and the manual performances, the latter being measured in terms of intrar-observer repeatability. Further, in case of healthy datasets, for which reported performance of an earlier algorithm was used as the baseline [8], we observed a significant improvement exceeding 50% in each quotient measure under consideration.

Earlier report on healthy datasets also included measures based on absolute volume different (AVD) and relative AVD (RAVD) [8], whose use we advocated against in Sec. 3.7 due to their unsuitability. With this caveat, we still provide numerical comparison based on such measures in Table 7 only to maintain historical continuity. On the same healthy datasets, the proposed algorithm provides significantly lower estimates of mean AVD (MAVD) and mean RAVD (MRAVD) than the earlier method did. Importantly, in the process, the corresponding quotient measure QAVD improves by 34%. However, as alluded earlier, this figure should be inferred only as a historical trend, and not as a bona fide indicator of enhanced performance.

Table 7:

Comparison of Choroidal volumes estimated using the proposed method and manual reference for healthy datasets; Notation: M1 - Manual segmentation-1, M2 - Manual segmentation-2, M - Average of both M1 and M2; PI - Performance improvement.

	Unit	Method	H1	H2	H3	H4	H5	Mean	Reference [8]
		Proposed (P)	3.39	2.84	7.13	3.14	3.44	3.99	3.97	-
Volume		M1	3.32	3.05	7.51	3.10	3.41	4.08	4.34
	mm3	M2	3.29	2.95	7.72	3.21	3.39	4.11	4.11	-
		M	3.31	3.01	7.61	3.16	3.41	4.09	4.27	-
								MAVD	MAVD	Change
								(MRAVD)	(MRAVD)
AVD	mm3	P and M	0.09 (2.57)	0.16 (5.39)	0.47(6.27)	0.02 (0.57)	0.04(1.18)	0.15 (3.20)	0.30 (7.12)	−122%
(RAVD)	(%)	M1 and M2	0.03 (0.90)	0.10 (3.46)	0.21 (2.82)	0.11 (3.45)	0.02 (0.55)	0.09 (2.23)	0.12 (2.90)	−30%
								QMAVD	QMAVD	PI
QAVD	ratio		2.85	1.56	2.22	0.16	2.16	1.79	2.40	34%

As mentioned before, current developments in deep leaning techniques indicate strong potential for achieving improved performance levels in image segmentation applications [37, 38, 39, 40, 44]. Accordingly, in the immediate future, we shall attempt volumetric choroidal segmentation using deep learning methods. However, such methods would require large volumes of labeled training data, usually generated by means of tedious manual annotations [41, 42, 43]. As an efficient alternative, we plan to use the present algorithm to facilitate label generation. In addition, we also envision building upon the proposed method (as well as its future avatars) and detecting/analyzing vessel-level biomarkers, including cross-sectional measurements, localized to Haller’s sublayer. In this direction, preliminary results on choroidal vessel tracing in 3D and detection of cross-section have recently been reported [63, 28].

The proposed algorithm assumes significance in current research in chorioretinal diseases, including AMD, pentosan polysulfate (PPS) maculopathy and CSCR, where accurate estimation of choroidal thickness, volume and vascularity index could be clinically crucial [64, 65, 66, 67], However, we anticipate the most significant impact on the investigation of the pachychoroid disease spectrum. Pachychoroid diseases show enlargement of the Haller’s sublayer along with attenuation of the inner choroid including choriocapillaris. However, to the best of the authors’ knowledge, there is no literature on associated physiological changes in the Haller’s sublayer in different age groups. More generally, similar analyses in relation to various diseases and comparison with age-matched healthy subjects could enhance our understanding of pathological mechanisms. The proposed automated method, which is fast, accurate as well as robust, can facilitate bridging gaps in knowledge by enabling large-scale clinical studies that compare suitable biomarkers in diseased subjects against those in age-matched healthy subjects.