Deep learning based noise reduction method for automatic 3D segmentation of the anterior of lamina cribrosa in optical coherence tomography volumetric scans.

A deep-learning (DL) based noise reduction algorithm, in combination with a vessel shadow compensation method and a three-dimensional (3D) segmentation technique, has been developed to achieve, to the authors best knowledge, the first automatic segmentation of the anterior surface of the lamina cribrosa (LC) in volumetric ophthalmic optical coherence tomography (OCT) scans. The present DL-based OCT noise reduction algorithm was trained without the need of noise-free ground truth images by utilizing the latest development in deep learning of de-noising from single noisy images, and was demonstrated to be able to cover more locations in the retina and disease cases of different types to achieve high robustness. Compared with the original single OCT images, a 6.6 dB improvement in peak signal-to-noise ratio and a 0.65 improvement in the structural similarity index were achieved. The vessel shadow compensation method analyzes the energy profile in each A-line and automatically compensates the pixel intensity of locations underneath the detected blood vessel. Combining the noise reduction algorithm and the shadow compensation and contrast enhancement technique, medical experts were able to identify the anterior surface of the LC in 98.3% of the OCT images. The 3D segmentation algorithm employs a two-round procedure based on gradients information and information from neighboring images. An accuracy of 90.6% was achieved in a validation study involving 180 individual B-scans from 36 subjects, compared to 64.4% in raw images. This imaging and analysis strategy enables the first automatic complete view of the anterior LC surface, to the authors best knowledge, which may have the potentials in new LC parameters development for glaucoma diagnosis and management.


Introduction
Glaucoma, the second leading cause of blindness worldwide [1], is a group of optic neuropathies characterized by progressive degeneration of retinal ganglion cells and their axons, resulting in a distinct appearance of the optic nerve head (ONH) and corresponding visual field loss [2]. The lamina cribrosa (LC), a series of perforated collagenous plate in the ONH through which retinal ganglion cell axons exit the eye, has been implicated as the primary site of axonal damage in glaucoma [3][4][5]. Indeed, previous histologic and experimental studies have reported several morphological changes of the LC in glaucoma eyes such as thinning, thickening, and posterior deformation [5][6][7][8]. The recent advance of imaging technologies such as spectral-domain optical coherence tomography (SD-OCT), enhanced depth imaging (EDI), and swept-source OCT (SS-OCT) enabled in vivo visualization of the LC and other deep ONH structures. Using these technologies, previous studies have shown LC changes in glaucoma eyes such as thinning [9], focal defects [10,11], and posterior displacement [12,13]. In addition, other studies have shown the significant influence of LC morphologic changes on the progression of glaucoma [14][15][16]. These reports have clearly shown the clinical relevance of the LC imaging for glaucoma practice. However, most of these previous studies rely on time-consuming and error-prone manual identification and measurements of the LC, precluding the widespread clinical application of the LC measurements in a clinical setting [17]. Existing automated segmentation method is limited to radial scans to achieve sufficient signal-to-noise ratio [18], and thus may not be applied to volumetric scans.
Quantitative analysis of the LC OCT images encounters multiple technical challenges. Speckle noise is inherent in OCT imaging in scattering media such as biological tissues [19] and decreases the visibility of the LC, especially in the area under the large blood vessels. One common practice to reduce speckle noise is to average multiple OCT scans acquired at the same location, which, while effective, is sensitive to eye movement and is practically limited to the use in 2D scans. Post-processing techniques utilizing wavelet filters [20,21] have also been explored with manually designed filters. In this paper, a data-driven deep-learning (DL) based noise reduction method has been developed utilizing the latest developments in machine learning [22]. Conventional DL-based noise reduction methods require noise-reduced images acting as ground truth teachers. These noise-reduced images are, by nature, difficult to acquire and subject to motion blur. In this study, a novel training method, as described by J. Lehtinen et al. [22], was used to train the DL algorithm to learn the statistical distribution of noise without the needs of noise-reduced images. This approach of deep learning from noisy single images is by nature less sensitive to motion blur and registration errors as experienced in the acquisition of ground truth teachers by OCT image averaging.
Other challenges for LC visualization and quantification are the significantly low OCT signal intensity and shadow artifacts. LC locates deep in the retina where the OCT signal is highly attenuated [23], and the large blood vessels merge at the optic nerve head (ONH) region leads to a shadow that can be severe [24]. In the present study, we also developed a shadow-compensation technique that aims to reduce the signal attenuation from blood vessels. By combining the advantages of the DL-based noise reduction and shadow compensation methods, we demonstrate that the visibility of the anterior LC border underneath blood vessels can be significantly enhanced. To improve the accuracy of the automatic 3D LC segmentation, an adaptive contrast enhancement method [25,26] is applied to enhance the visualization of the anterior LC border.
To our best knowledge, this is the first segmentation and analysis of OCT images using a DL-based noise reduction technique. Initial clinical study results give some evidence that the accuracy of 3D segmentation within slices is improved and good connectivity among volumes is observed. The combination of techniques presented in the paper has led to, for the first time to our best knowledge, the automatic complete view of the anterior LC surface.
In this study, three datasets are used separately for different purposes. The first dataset, which consists of 3D OCT images of 16 subjects acquired at different locations of the retina, are used for the training of the noise reduction algorithm. The second dataset, which consists of three pairs of single and 128x averaged scans acquired at ONH from distinct subjects, is used for the evaluation of the noise reduction algorithm. And the third dataset, which consists of 3D OCT scans of 36 subjects acquired at the ONH, is used for the evaluation of the segmentation algorithm. For manual evaluation of the segmentation, one eye per subject is randomly selected.

Enhanced OCT image visualization through deep learning based noise reduction
DL based algorithms have recently surpassed the performance of conventional methods in noise reduction tasks [27][28][29][30][31][32][33][34], and the applications of DL based algorithm to retinal layer segmentation have been reported [35][36][37][38][39]. Recent studies utilizing DL models for OCT image noise reduction have shown promising results [40,41]. However, to train the deep learning models, they all rely on paired images where one image is noisy and the other one is noise-reduced. Then the DL models are trained to reduce the noise of the noisy image that best matches the noise-reduced image. Mathematically, values of the parameters θ in the DL model are optimized by minimizing the total loss, defined as where i iterates among the training images, L is the loss function, f θ is the DL model,x i is the i-th noisy image, and y i is the corresponding i-th noise-reduced image. Noise-reduced OCT images are typically generated by averaging multiple scans taken at the same location. This is not a trivial task due to the motion of the eye, and thus faces a dilemma where averaging a large number of repeated scans reduces the noise level but may result in blurry images and the processing is highly labor-intensive. Though averaging a fewer number of repeated scans is less subject to motion artifacts, the resulting image may still contain a high level of noise. To overcome these limitations, we look at a different approach.
Recent studies show that deep-learning-based noise reduction does not necessarily need noise-reduced images for training [22,42]. Replacing Eq. (1) with the following: whereŷ i is instead the i-th noisy image, then the only requirement becomes thatŷ i is from the same location asx i but contains different noise content drawn from the same noise distribution. In other words, where x i is the true noise-reduced image, and δ and δ are the different noise manifestations from the same underlying distribution. As demonstrated in [22], the solution of minimizing Eq. 2 will result in f (x i ) = x i , which means that the DL model will generate the noise-reduced version ofx i without ever seeing noise-reduced images. Paired images ofx i andŷ i can be selected as the two repeated scans at the same location, where their difference may be caused by the noise fluctuation from the same distribution. This DL model significantly reduces the number of repeated scans needed for training. Thus, it may reduce the blurry effects caused by eye movement, as well as the error in the registration algorithm for multi-repeats averaging.
In our study, a U-net [43] based DL model is trained to denoise B-scan images of 992 × 512 pixels. 3D OCT scans (DRI-OCT Triton; Topcon, Tokyo, Japan) at both the macular and ONH are included for training to improve the versatility of the model. In total, images from 16 subjects, resulting in 3,895 pairs of B-scans at different locations of the retina, are included for training.
The performance of the noise reduction algorithm is evaluated quantitatively using two metrics of peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). Both of these metrics are used to measure the similarities between a reference image R which is considered as noise-reduced, and a noisy image I. Assume all images consist of m × n pixels, the mean squared error (MSE) between images R and I is defined as And the PSNR (in dB) is defined as PSNR = 20 · log 10 (MAX I ) − 10 · log 10 (MSE), where MAX I is the maximum possible pixel intensity in the images. In our study, 8-bit images are used and thus MAX I = 255. Overall, a larger PSNR indicates a higher similarity between the two images.
In contrast to the absolute errors estimated by MSE and PSNR, SSIM is designed by modeling any image distortion as a combination of three factors, namely the loss of correlation s(R, I), the luminance distortion l(R, I), and the contrast distortion c(R, I) [44]. The SSIM is defined as where 2 and c 3 = c 2 /2, as defined in [45], are the small constants to stabilize the division with weak denominators. µ and σ are the average and variance of images I and R, respectively. σ RI is the correlation of images I and R. By definition, SSIM ranges from 0 to 1, and only reaches to 1 when the two images are exactly the same. The reference image R is generated by registering and averaging n repeated scans at the same location. A larger number of repeated scans n typically result in a lower noise level. Both the evaluation metrics PSNR and SSIM are sensitive to the noise-level of R. For example, if n is small, one may achieve high PSNR and SSIM scores, but the resulting image will still be noisy if R itself is noisy. It is a much technically difficult task for one to achieve high scores in both PSNR and SSIM if n is large.
In previous studies, n ranges from 6 to 60 [40,41]. With the current commercially available high-speed swept-source OCT devices such as the Triton OCT device that is operated at 100 kHz/sec, it is able to capture and average 128 repeated scans at a single location. To compare with the cleanest image possible, our reference images R are the line scan results (with n=128 repeats) acquired with a Triton OCT device. Image definitions are illustrated in Fig. 1, where the input noisy image I raw is one single B-scan out of the said 128 repeats, the noise reduced image I noise-reduced is the result of noise reduction in I raw using our DL model.
To validate the DL noise reduction algorithm, a data acquisition protocol that requires both the 128x averaged image and the single scan images at the same location of the eye is employed. This protocol sets a limitation on the validation dataset size and excludes the subjects that have been used for training the DL algorithm from the validation. Validation data is acquired at three different locations of the ONH.
The results of quantitative evaluations of DL-based noise reduction are summarized in Table 1. An increase of 6.6 ± 0.3 dB in PSNR and an improvement of 0.65 ± 0.01 in SSIM have been achieved. For comparison, results of conventional noise-reduction method with a 5 × 5 sized median filter, is shown in Table 1 as well. Qualitative evaluation examples are shown in Fig. 2, where (A), (B), (C), and (D) depicts the original single B-scan, the median filtered image with a 5 × 5 sized filter, the DL noise-reduced B-scan, and the 128x B-scan scans, respectively. For further detailed inspections, shown in (E),  Fig. 2 it can be observed that the OCT image information is well preserved in the DL noise-reduced images while noise has been significantly reduced to that comparable of the averaged 128x scans.
Noise reduced 3D OCT volumes can be generated from the individual noise reduced B-scans to create the en-face images for observation. An example is shown in Fig. 3, where a 3D raster scans of 6 × 6 mm 2 were acquired at the macular. To better visualize the choroidal structures, the 3D volume is flattened with respect to the Bruch's membrane. En-face images (B) and (C) are then extracted from the choroiocapillaris layer as highlighted by the yellow line in (A). En-face image (B) is reconstructed from the original scan volume while (C) is reconstructed from the noise-reduced volume. (D) and (E) are the zoom-ins (highlighted by the green boxes) of (B) and (C), respectively. It can be seen that the details of choriocapillaris can be identified with more confidence after noise reduction, and that the present DL-based noise reduction method does not rely on the DL of averaged images, which are generally subject to motion artifacts and registration errors, may provide the practical advantages in the visualization and identification of fine structures. Figure 4 shows another example that reveals the LC's pores structure. 3D raster scans of 6 × 6 mm 2 were performed at the ONH.   green boxes. With less noise, it can be observed that the LC's pores can be identified with more confidence in the noise reduced en-face image.

Shadow compensation
In the present study, shadow compensation is performed to recover the lost energy in the shadowed regions. There have been efforts to reduce the shadow artifact by compensating the energy [25,26,46]. The method by Fabritius et al. [46] requires segmenting the retinal pigment epithelium (RPE) layer, where shadow compensation is performed by adding an offset intensity to all the A-lines affected by the retinal vessels below RPE. This method keeps the original contrast of the scan but is based on time-consuming segmentation and may be subject to the associated error. The method by Girard et al. [25,26] does not require segmenting any retinal layers or identifying A-lines affected by vessels. Every pixel in an OCT image is compensated through the same equation. However, this compensation method may alter the contrast of the original image as deeper pixels get more compensation through the equation. Improvement has been made by setting a stopping point of compensation when cumulative intensity below a pixel is smaller than some threshold. While this prevents the over-saturation of deep pixels and improves the contrast in the main images, it still may introduce a contrast difference between neighboring frames and lead to new artifacts in the en face images.
In the present study of automated 3D segmentation, a new requirement arises that the shadow artifact shall be removed or compensated, as viewed from all directions of the volume, namely, the fast-axis B-scan, the slow-axis B-scan, and the en face image. The energy in each pixel of the A-line can be represented with its intensity level as follows [25,26].
where i is the A-line number of a total of N A-lines and j is the depth index in each A-line with a total depth of D [26,46]. For image enhancement, n can be any number that is greater than 1. The total energy in each A-line can be expressed as  Another observation can be made from the energy profile. As retinal OCT images correlate with retina morphology [47], without the presence of random noise or shadow artifact, the energy profile is expected to be smooth as the tissues are continuous and any changes would be gradual. Under these circumstances, the energy profile would ideally contain only the slow variations. In contrast, both the random noises and shadows mostly yield to high-frequency fluctuations observed in the energy profile. As such, applying low-pass filtering to the energy profile may effectively reduce the influence by shadows in the OCT image. As an example, a red curve is shown in Fig. 5(B) depicts the low-pass-filtered energy profile.
The normal thickness of human macula in OCT scans is measured to be around 200 µm− 400 µm [48] while a typical A-line covers more than 2 mm. Therefore, a large part of the A-line carries mostly the background noise. Since only the structure region needs to be enhanced and the noise level should be kept as close to original as possible, segmenting the structure region is needed. A simple calculation of the noise intensity level in the image can be used as a reference to find the starting and ending point of structure in each A-line. This process is illustrated by a sample result shown in Fig. 6. The starting and ending points of the structural region along the A-line is determined by detecting the intersections of the cutoff intensity and the moving average energy profile. This fast segmentation allows shadow compensation within the structure region without enhancing the noise. To compensate the image, the pixel intensities within the structure region in each A-line are linearly scaled so that the final total energy matches the filtered energy level. Figure 7 shows the comparison between the original (A) and the compensated (B) images. The segmentation lines (yellow) for the structure region is also shown in the original image. It is worth noting that the compensation is more effective for the narrow vessels (red arrows in Fig. 7) than for the thick vessel (green arrow in Fig. 7), as there may be some low-frequency components left in the filtered energy profile. By the use of 3D volume data, this limitation can be mitigated by applying the compensation again along the slow axis. This will further improve the compensation, provided that the neighboring frames are aligned in the volume. Since the data in the study is already aligned, compensation is applied along both directions, enabling a 3D-compensation. Figure 8 shows the comparison between noise-reduced B-scans of LC structure before (A) and after (B) shadow compensation. It can be observed that the shadow-compensation combined with noise-reduction further improves the visibility of LC border (highlighted with red arrows). However, deep LC structures are yet to be further enhanced.

Contrast enhancement of deep LC tissues
Adaptive contrast enhancement methods have been developed for the visualization of deep tissues underneath the anterior LC [25,26]. This method, however, may yield an artifact that appears as a bright band in the lower part of the OCT image below the compensation depth limit [25]. In the example shown in Fig. 9(A), where the structure is low in the image, the bright band cuts through the LC structure and obscure the anterior border (highlighted by the red box), adding difficulty for both human and the algorithm to detect the border. In this study, we utilize the advantages of our noise reduction method and set a linear contrast adjustment step to the noise-reduced image to minimize the appearance of noise floor at the deep layers before applying the adaptive contrast enhancement method. The resulting image is shown in Fig. 9(B), where it can be found that the bright-band-artifact has been significantly reduced while the contrast of the LC border is further improved.

3D automated segmentation of anterior lamina cribrosa
The current study included subjects with open-angle glaucoma and glaucoma suspect who underwent a swept-source OCT ONH 3D scan. A Triton OCT device was used to image the ONH and the parapapillary area. We retrospectively surveyed 36 consecutive patients who underwent swept-source OCT imaging at Osaka University Hospital. Baseline clinical data such as age, intraocular pressure, type of disease, and lens status were collected from medical charts. Glaucoma was defined as having both funduscopic glaucomatous appearance of the ONH (localized or diffuse neuroretinal rim thinning and/or retinal nerve fiber layer defect) and a corresponding visual field damage. Eyes with fundoscopic glaucomatous appearance of the ONH and retinal nerve fiber layer defect in OCT image without evidence of a corresponding visual field damage were defined as glaucoma suspects. Patients with secondary glaucoma and angle-closure glaucoma were excluded. All procedures of the study conformed to the Declaration of Helsinki and were approved by the institutional review board of Osaka University Hospital. 72 eyes of 36 subjects were enrolled, including 33 eyes with normal tension glaucoma, 26 eyes with primary open angle glaucoma, 6 eyes with exfolication glaucoma, and 5 eyes with glaucoma suspect. The average ± standard deviation age of the participants was 64.3 ± 11.8. 22 patients were female.
In this study, optic disc images from a 6 × 6 mm 2 area are acquired. Each volume scan consists of 256 B-scans each with 992 × 512 pixels. For each subject, images from one eye are selected for analysis.
Border of LC is detected by using a two-round segmentation method. In this new approach, we first define the region of interest (ROI) from the automatically detected scleral ring disc area. The choose of a small ROI offers the advantage of reducing the amount of calculation and thus enables a fast 3D segmentation of the LC border. Five neighboring slices are averaged for signal-to-noise ratio (SNR) improvement. The 3D volume within the disc area is interpolated to exhibit isotropic resolutions in the horizontal directions. 2D and 3D canny edge detectors are then applied to ensure the connectivity of edges throughout the 3D ROI volume and maintain edges for detecting the local changes. Different weights are applied to the horizontal and vertical gradients of the canny edge detectors. The weights are based on the prior knowledge of the LC anatomy, and are chosen to detect mainly the horizontal edges corresponding to the anterior LC border.
The first round of our segmentation process is to detect the raw LC border and acquire the confidence level of the detection. For each pixel in a slice, the cost is calculated by combining the edge map with the weighted gradients. The accumulated cost map is then calculated by summing up the cost along the minimum path to each location. The points with the minimum accumulated cost for each A-line are treated to be the candidates forming the LC border. Due to the presence of blood vessel, local weak OCT signal intensity and edges from ILM and border tissue, some of the candidate points are removed from further calculation. A second-order weighted polynomial fitting is applied to search the tentative LC edges, and the confidence of the detection accuracy is then calculated.
The second round of our segmentation process starts with detecting the LC at the slices of low confidence, which is carried out by utilizing the LC border of their neighboring slices. The accumulated cost map calculation is the same as that of the first round, whereas candidate points are removed if their distance to the neighboring LC borders is large. Again, the updated LC border is calculated using a weighted polynomial fitting.
After the above two rounds of segmentation process, a final step is to apply a 3D smoothing to achieve a better smoothness across the 3D volume. A flow chart illustrating the LC anterior segmentation process is depicted in Fig. 10. Details of the two-round segmentation process are given below.

Edge map generation
To detect the edges for segmenting the possible LC anterior border, both a 2D and a 3D canny edge detector are utilized. The 2D canny edge detector is customized from a commercially available software that is used in retina OCT boundary segmentation [49,50]. A threshold of 0.92, and a kernel size based on the pixel resolution are chosen to detect the edges from dark to bright.
Since large blood vessels exist in the optic disc area, OCT signals in part of the anterior LC can be severely attenuated, causing possible loss of connectivity in the anterior LC border. A volumetric OCT scan provides the 3D information that can be useful for recovering the connectivity of the anterior LC border. Using a centered difference on the Gaussian smoothed images and a non-maximum suppression method to find the directional local maxima in a gradient array, 3D canny edges are detected within the ROI [51]. A horizontal standard deviation σ H = 5 and a vertical standard deviation σ V = 8 are used for gaussian smoothing in this work and the images are interpolated to achieve isotropic resolutions in both the horizontal directions.
The 2D canny edge detector may vary between the consecutive B-scans, while the 3D canny edge detector may detect unnecessary edges from neighboring B-scans. To address these possible issues, a refinement and selection of edges are performed, where the connected edges are separated into multiple edges if the angle is found to be larger than 30 degree, and all the vertical edges are removed based on the LC border anatomy. With this process, only the overlapped edges between 2D canny edge detector and 3D canny edge detector are retained, as they are more likely to correspond to the LC border.

Cost map
In addition to the edges, locations with large values of intensity gradient may serve to detect the LC border as well. By taking the horizontal derivative of the Gaussian filtered intensity image with a large kernel size, an intensity gradient map is calculated. The large kernel smooths the local variations and fills in the lost information by utilizing the neighboring pixels. This gradient map offers the advantages that it may provide additional search guidance in the case where the canny edges are not connected due to weak local signals. Here a cost map is created by a linear combination of the edge map with the intensity gradient values, defined as follows.
where C(i, j, k) is the cost for each pixel, i, j, k are the indexes in the A-line, depth and slice direction, respectively. w 1 , w 2 and w 3 are weights. Edge represents the edge map, and Gradient H (i, j, k) and Gradient V (i, j, k) represents the intensity gradient values in horizontal and vertical directions, respectively. Since w 3 is only a fraction of w 2 , the vertical gradient, i.e. horizontal edges, generally have the larger weights. All the weights w 1 , w 2 and w 3 have negative values, and they are chosen to be −1, −0.1, −1, respectively in the present study. As such, the LC border is expected to exhibit a small cost, since the LC border generally has the large gradients and detected edges in edge map. For each location (i, j, k 0 ) in the slice k 0 , the accumulated cost is the sum of the costs of the pixels along the path from the left of the ROI to (i, j, k 0 ) [52].
where acc(i, j, k) is the accumulated cost to reach (i, j, k) with minimum cost along the path, n is the number of pixels in A-line direction, and m is the number of pixels in depth direction. And u is the search range of neighboring pixels which determines the connectivity of the path. A value of u = 2 is used in this work, so that 5 pixels in the neighboring A-line are searched to find the minimum cost to propagate the path within a slice.

Lamina cribrosa segmentation
The segmentation of anterior LC does not directly utilize the shortest path method as performed in retinal layer segmentation [49,50]. This is because the low SNR in a large blood vessel region may result in path error and may even propagate to regions without blood vessels. The present LC segmentation method utilizes the minimum locations across the accumulated cost map. The minimum locations for each A-line, which correspond to the points with minimum cost accumulated from left of the ROI to that A-line location, are the possible LC border locations and thus they are chosen to be the candidates for further detection. Due to the complicated intensity change within the disc area [53], some minimum location points are not suited for the LC detection. In the present method, LC border detection is conducted in two rounds. In the first round, points where the vertical distance to ILM is less than 5 pixels are removed, as they may be affected by the large gradient of the ILM. The leftmost and rightmost points (1/4 of ROI) are also removed if they are found to have vertical distance larger than 30 pixels with respect to the mean of the remaining points, indicating those points may correspond to the edges of the border tissue. For the remaining minimum location points, a weighted second-order polynomial fitting is applied.
The utilization of 3D volume data offers a practical advantage that information from neighboring frames may help to segment a more difficult frame where the LC border is unclear. To quantify the reliability of the segmentation, we define the confidence of the detection as the reciprocal of the averaged vertical distance between the polynomial fitted curve to the candidate points.
where conf k 0 is the confidence of the slice k 0 , p is the candidate point, f is the polynomial fitting curve at the same horizontal location as p, and n is the number of candidate points after removal. The confidence lower than 0.05, namely average distance of larger than 20 pixels, is considered to be an unreliable detection and require a second round of detection.
In the second round of detection, the unreliable slices located closest to the reliable slices are the first ones to be re-detected and then marked as reliable detection. Then their neighboring unreliable slices are re-detected. This re-detection process iterates until all the unreliable slices are detected throughout the whole volume. The workflow of the second-round detection is similar to that of the first round, which includes generation of the cost map, calculation of the accumulated cost, and search of minimum location points to serve as the candidates of the LC border. Differently, the candidate points in the second-round detection are selected according to the distance to the neighboring LC border. Upon the completion of the two-round detection, a 3D smoothing with a median filter of the size 5 × 5 (A-line× slice) is applied to the whole volume to correct the discontinuity that may exist in the segmentation line.

3D lamina cribrosa segmentation results
OCT images with automatic LC segmentation were reviewed by glaucoma specialists. For each eye, 5 B-scans at the center of the ONH, 10 pixels superior and inferior with respect to the center of the ONH and 20 pixels superior and inferior with respect to the center of the ONH, were selected for review. The segmentation of each scan was scored as good, bad, or uncertain. Segmentation was scored as good if more than 2/3 of the anterior LC surface was accurately detected, bad if less than 2/3 of the anterior LC surface was correctly detected, and uncertain if the anterior LC surface was not able to identify even in a visual inspection by the expert.
Examples of LC segmentation results are shown in Fig. 11. In the image, the green dotted line is the manual segmentation results by medical experts and the red dash-dotted lines are the automated segmentation results from our algorithm.
In total, 180 individual B-scans from 36 subjects are reviewed for their segmentation accuracy. Detailed results are shown in Table 2. LC detect-ability is defined as the percentage of B-scans where medical experts can confidently identify the anterior LC border. An improvement of over 25% in segmentation accuracy is achieved, and 98.3% of the enhanced B-scans were found detectable. In the present study, the ground truth segmentation results are defined as the automatic segmentation boundaries that have been manually corrected by the medical experts. The average absolute differences between the automatic segmentation boundaries and ground truth segmentation boundaries measured after different enhancement stages are shown in Table 3. In total, 177 B-scans (3 excluded for uncertainty of the anterior of LC) are manually corrected. The average absolute vertical difference of each pixel between the automatic segmentation results and the ground truth results are calculated after each enhancement stage. Table 3 summarizes the applied enhancement method and the corresponding average absolute differences. The sign " " indicates which enhancement method is applied and "-" indicates what method is skipped. For example, the first row in Table 3 shows the results using the original B-scan images without any enhancement, and the final row shows the results that have employed all the enhancement methods.
An example of the 3D segmentation of the anterior of LC is shown in Fig. 12, where (A) and (B) depict the LC anterior surface curvature. The pseudo color display indicates an inward bowing into the ONH. To the best knowledge of the authors, this is the first visualization of the whole LC anterior surface curvature. The LC tissue exhibits complex 3D structural changes during the development of glaucoma. Previous studies on the LC structure using OCT typically were limited on a few B-scans and quantified using a single number, which may be insufficient to describe the full complexity of the LC structural changes. A complete view of the anterior of LC as enabled by our newly developed technique may pave ways for the more comprehensive study.

Discussions and conclusion
In this study, a custom DL-based noise reduction algorithm in OCT images, a custom shadow compensation algorithm, and an edge-detection based segmentation algorithm were developed for the quantitative analysis of volumetric OCT scans. We presented the automatic 3D segmentation of the anterior of LC as an application example that benefits much from the combination of these algorithms. Though the results presented are of the 3D images acquired with a SS-OCT, our method can be applied to SD-OCT as well. Automatic 3D segmentation of the anterior surface of LC is technically challenging, as multiple factors that include the local weak signal intensity caused by the presence of large blood vessels, the complexity of the shape of LC, and LC defect may lead to segmentation error. In this study, a 3D canny edge detection and a two-round segmentation method that employs the neighboring information were deployed to take advantage of the morphological structure in a volumetric OCT scan. For the B-scans with clear LC border, the segmentation can match the local changes, whereas for the B-scans with uncertain LC border due to large blood vessels, an LC border closed to the neighboring LC border location is segmented with local adjustment. In this way, the present 3D segmentation algorithm improves the smoothness across the LC and segments out the fine structure of the anterior of LC. The significant improvements in SNR and image contrast by our DL-based noise reduction and shadow compensation methods have made the use of the spatial information of the volumetric scan more feasible and practical.
Our combined algorithm was validated using OCT images from 36 subjects and the results show that the detectability and segmentation accuracy of the anterior LC have been improved to 98.3% and 90.6%, respectively. Previous studies have shown that several morphological characteristics such as depth [12], curvature [13,16], thickness [9,15], focal defects [10,14,54], and global shape index [17,55] are strongly correlated with the presence, severity, or the progression of glaucoma. Their results clearly show the potential of LC morphological characteristics as biomarkers for diagnosing and monitoring glaucoma. However, identification of the LC in these studies depends on manual segmentation, which requires highly-trained experts and considerable time. Accurate, efficient, and reproducible detection of the LC is crucial for utilizing LC parameters in glaucoma diagnosis and management. It is our hope that our imaging/analysis approach may pave ways for the future development of new LC biomarkers.
Recent advancement in DL based algorithms and graph cut algorithms [56,57] may further improve the feasibility and accuracy of the automated 3D LC segmentation, and DL networks have been applied to segment multiple retinal layers [35][36][37][38][39]58,59]. The development of deep learning models generally requires a large amount of training data. On the other hand, it is challenging even for medical experts to confidently identify the anterior of LC in a whole 3D volume in raw OCT images. The OCT noise reduction and enhancement techniques presented in this paper have been shown to be a useful tool to help medical doctors confidently identify the LC border through the whole 3D volume that enabled the development of automated 3D segmentation of the LC. Further advanced automated LC segmentation methods such as DL based methods may be explored in future.
The present pilot study exhibits one example application of our newly developed imaging/analysis approach. It may also be useful for the segmentation and visualization tasks for other 3D structures such as the choroid structure, anterior structure, and OCT angiography. While the present study reported the segmentation results using SS-OCT, our automatic 3D segmentation method can be applied to the measurements using SD-OCT as well.

Funding
Council for Science, Technology and Innovation Cross-ministerial Strategic Innovation Promotion Program (SIP), "Innovative AI Hospital System" (Funding Agency: National Institute of Biomedical Innovation, Health and Nutrition (NIBIOHN)); Charitable trust fund for ophthalmic research in commemoration of Santen Pharmeceutical's Founder.