A combined machine-learning and graph-based framework for the segmentation of retinal surfaces in SD-OCT volumes.

A combined machine-learning and graph-based framework for the segmentation of retinal surfaces in SD-OCT volumes Bhavna J. Antony,1 Michael D. Abràmoff,1,2,3,5,6 Matthew M. Harper,2,3 Woojin Jeong,2,4 Elliott H. Sohn,2,6 Young H. Kwon,2 Randy Kardon,2,3 and Mona K. Garvin1,3,∗ 1 Dept.

of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA, USA of Ophthalmology and Visual Sciences, The University of Iowa, Iowa City, IA, USA 3 Iowa City VA Healthcare System, Iowa City, IA, USA Department of Ophthalmology, Dong-A University, College of Medicine and Medical Research Center, Busan, Korea 5 Dept. of Biomedical Engineering, The University of Iowa, Iowa City, IA, USA 6 The Stephen A. Wynn Institute for Vision Research, Iowa City, IA, USA

2 Dept. 4

∗ [email protected]

Abstract: Optical coherence tomography is routinely used clinically for the detection and management of ocular diseases as well as in research where the studies may involve animals. This routine use requires that the developed automated segmentation methods not only be accurate and reliable, but also be adaptable to meet new requirements. We have previously proposed the use of a graph-theoretic approach for the automated 3-D segmentation of multiple retinal surfaces in volumetric human SD-OCT scans. The method ensures the global optimality of the set of surfaces with respect to a cost function. Cost functions have thus far been typically designed by hand by domain experts. This difficult and time-consuming task significantly impacts the adaptability of these methods to new models. Here, we describe a framework for the automated machine-learning based design of the cost function utilized by this graph-theoretic method. The impact of the learned components on the final segmentation accuracy are statistically assessed in order to tailor the method to specific applications. This adaptability is demonstrated by utilizing the method to segment seven, ten and five retinal surfaces from SD-OCT scans obtained from humans, mice and canines, respectively. The overall unsigned border position errors observed when using the recommended configuration of the graph-theoretic method was 6.45 ± 1.87 µm, 3.35 ± 0.62 µm and 9.75 ± 3.18 µm for the human, mouse and canine set of images, respectively. © 2013 Optical Society of America OCIS codes: (100.0100) Image processing; (100.2000) Digital image processing; (100.4994) Pattern recognition, image transforms; (100.6890) Three-dimensional image processing; (110.4500) Optical coherence tomography.

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Received 16 Aug 2013; revised 24 Oct 2013; accepted 27 Oct 2013; published 1 Nov 2013

(C) 2013 OSA 1 December 2013 | Vol. 4, No. 12 | DOI:10.1364/BOE.4.002712 | BIOMEDICAL OPTICS EXPRESS 2712

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Kowal, “Graphbased multi-surface segmentation of OCT data using trained hard and soft constraints,” IEEE Trans. Med. Imag. 32, 531–543 (2013). 21. M. K. Garvin, M. D. Abràmoff, X. Wu, S. R. Russell, T. L. Burns, and M. Sonka, “Automated 3-D intraretinal layer segmentation of macular spectral-domain optical coherence tomography images,” IEEE Trans. Med. Imag. 28, 1436–1447 (2009). 22. A. Lang, A. Carass, E. Sotirchos, P. Calabresi, and J. L. Prince, “Segmentation of retinal OCT images using a random forest classifier,” in Proc. SPIE Medical Imaging 8669, 86690R (2013). 23. B. J. Antony, M. D. Abràmoff, M. Sonka, Y. H. Kwon, and M. K. Garvin, “Incorporation of texture-based features in optimal graph-theoretic approach with application to the 3-D Segmentation of intraretinal surfaces in SD-OCT volumes,” in Proc. SPIE Medical Imaging 8314, 83141G (2012).

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24. K. Li, X. Wu, D. Z. Chen, and M. Sonka, “Optimal surface segmentation in volumetric images–a graph-theoretic approach,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 119–134 (2006). 25. M. Niemeijer, J. J. Staal, B. van Ginneken, M. Loog, and M. D. Abràmoff, “Comparative study of retinal vessel segmentation methods on a new publicly available database,” in Proc. of SPIE Medical Imaging 5370, 648–656 (2004). 26. M. D. Abràmoff, W. L. M. Alward, E. C. Greenlee, L. Shuba, C. Y. Kim, J. H. Fingert, and Y. H. Kwon, “Automated segmentation of the optic disc from stereo color photographs using physiologically plausible features,” Invest Ophthalmol Vis Sci 48, 1665–1673 (2007). 27. P. Viola, O. M. Way, and M. J. Jones, “Robust real-time face detection,” Int. J. Computer Vision 57, 137–154 (2004). 28. S. E. Grigorescu, N. Petkov, and P. Kruizinga, “Comparison of texture features based on Gabor filters,” IEEE Trans. Image Proc. 11, 1160–1167 (2002). 29. G. Quellec, S. R. Russell, and M. D. Abràmoff, “Optimal filter framework for automated, instantaneous detection of lesions in retinal images,” IEEE Trans. Med. Imag. 30, 523–533 (2011). 30. W. Freeman and E. Adelson, “The design and use of steerable filters,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 891–906 (1991). 31. L. Breiman, “Random forests,” Machine learning 45, 5–32 (2001). 32. B. J. Antony, M. D. Abràmoff, K. Lee, P. Sonkova, P. Gupta, Y. Kwon, M. Niemeijer, Z. Hu, and M. K. Garvin, “Automated 3D segmentation of intraretinal layers from optic nerve head optical coherence tomography images,” Proc. of SPIE Medical Imaging 7626, 76260U (2010). 33. B. J. Antony, M. D. Abràmoff, W. Jeong, E. H. Sohn, and M. K. Garvin, “Segmentation of multiple intra-retinal surfaces in volumetric SD-OCT images of mouse eyes using an improved Iowa reference algorithm,” Invest. Ophthalmol. Vis. Sci. E-Abstract 4892 (May 2013). 34. N. Nakano, H. O. Ikeda, M. Hangai, Y. Muraoka, Y. Toda, A. Kakizuka, and N. Yoshimura, “Longitudinal and simultaneous imaging of retinal ganglion cells and inner retinal layers in a mouse model of glaucoma induced by N-methyl-D-aspartate,” Invest. Ophthalmol. Vis. Sci. 52, 8754–62 (2011).

1.

Introduction

Spectral-domain optical coherence tomography (SD-OCT) imaging allows for the quantitative study of retinal structures, and thus, finds widespread use in the detection and management of ocular diseases. For instance, in glaucoma, in addition to visual field tests and planimetry assessments, the thicknesses of the retinal nerve fiber layer (RNFL) and the ganglion cell layer (GCL) are used for diagnosis as well as to track its progression in patients [1]. The presence of disease may also introduce changes to the intensity distribution of the image in addition to structural changes. Thus, the automated segmentation of these structures in the presence of disease can be quite a challenging problem. Apart from its clinical use, SD-OCT imaging is also used in research studies that include animal models (such as mice, canines or primates) [2–6] rather than humans. The extension of current techniques to include animal anatomy is not trivial as the retina in animals can show significant differences. For instance, the retinal nerve fiber layer (RNFL) and the ganglion cell layer (GCL) are not visually differentiable in mouse or canine SD-OCT images (see Fig. 1), unlike in human scans where the RNFL is quite distinct. This combined nerve fiber-ganglion cell (NF+GC) layer is also significantly thinner in these animals than in humans. Another distinct difference is the absence of the foveal depression in rodent and canine eyes. Prominent anatomical differences such as these make the direct application of methods developed for humans scans on animal scans prone to error. These challenges are further compounded by the fact that a variety of scanners are often used, with the images being acquired using different imaging protocols. Thus, automated methods developed need to be adaptable to new models while remaining robust to varying image resolutions as well as disease-induced disruptions that may be encountered. Mishra et al. [7] and Yazdanpanah et al. [8] have previously described automated methods for the segmentation of retinal layers in SD-OCT images of rat retinas. However, the evaluation of these methods was limited to normal rats and the methods did not incorporate the threedimensional contextual information (see Fig. 1(a)) available in volumetric scans. This is of particular importance given the increasing ability to obtain isotropic images from animal retinae #195835 - $15.00 USD



that are rich in contextual information. The reproducibility of measurements from mice scans has been described briefly [9], however this experiment was limited to the reproducibility of total retinal thickness. Numerous techniques have, however, been proposed for the segmentation of retinal layers in human SD-OCT images [10–20]. Graph-based approaches [16, 21] transform the segmentation problem into an optimization one, where the aim is to find surfaces with the minimum cost. The graph-theoretic approach proposed by Garvin et al. [21] in particular, segments multiple surfaces in 3-D while ensuring the global optimality of the set of surfaces with respect to a cost function. This however, requires the careful design of the cost function, which when done by hand, can be a difficult and time-consuming task. For instance, common edge detectors such as the Sobel filter coupled with an image de-noising method or Gaussian derivatives could be used to design the cost function when edges are obvious. Selecting the filter that best suits each of the surfaces can itself be a difficult task, but this process is even more complicated in diseased scans where the images often show low contrast. Furthermore, the parameters of the chosen filters may need to be altered if the scans were acquired using a different imaging protocol or a different scanner. For instance, a 3-D edge detector that shows good performance on a volumetric scan containing 200 slices would likely not perform as well on a scan that contains a smaller number of slices. Proposed machine-learning based approaches [10, 18, 22], on the other hand, learn features associated with retinal layers of interest and the final segmentation is obtained through a pixel classification process. While these methods did not incorporate 3-D contextual information available in volumetric SD-OCT scans, they are however, easily adapted to new models as the only requirement is a new training set. The incorporation of the pixel classification result obtained through a machine-learning based approach into the cost function utilized by a graphbased approach would provide all the advantages of the graph-based approach, while retaining the easy adaptability of the machine-learning based methods. In particular, as the cost function utilized by the graph can be comprised of on a on-surface term (that is cost associated with a voxel lying on a particular surface) and an in-region term (that is the cost associated with a voxel belonging to a particular region), machine-learning based approaches can be used to learn surface and region properties of the image to generate probability maps that can be incorporated into the cost function. Such an approach is detailed in our preliminary work [23] where the inregion cost term was automatically designed using a machine-learning based approach. Lang et al. [19] also proposed a similar method where the on-surface cost term incorporated learned features. Both of these methods however, were only evaluated on images obtained from human patients. Here, we present a combined machine-learning and graph-theoretic method for the automated segmentation of retinal surfaces in SD-OCT images. A machine-learning based approach is used to design the entire cost function utilized by the graph-theoretic method approach [24]. In addition to designing the cost terms, it also important to gauge the impact of these learned features on the final segmentation accuracy to prevent the inclusion of terms that do not significantly improve the accuracy or in some cases, hurt the segmentation accuracy. This allows for the graph-theoretic method to be adapted and tailored to new models by retraining the system on a new dataset and finding the best set of learned components that provide the best segmentation accuracy. The adaptability of the method is demonstrated using three sets of images obtained from: 1) human patients that presented with glaucoma, 2) mice and 3) canines employed in a glaucoma study. Furthermore, these images were acquired using three different SD-OCT scanners with varying imaging protocols. The overall segmentation error compared to tracings obtained from human experts when using the recommended framework of the graph-theoretic method on these three sets was found to be 6.45 ± 1.87 µm, 3.35 ± 0.62 µm and 9.75 ± 3.18

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Y

ILM

Optic Nerve Head

RNFL INL ONL

GCL+IPL OPL Z

Bruch's Membrane

IS/OS X

(a) Bright

(b) ILM

Medium

ELM

Bruch's Membrane

Dark

IS/OS Junction

ILM

NF-GCL IPL INL OPL ONL IS OS

NF+GCL IPL INL+OPL ONL

IS/OS

RPE

(c)

(d)

Fig. 1. (a) Illustration of a 3-D volumetric SD-OCT scan of a human eye centered on the optic nerve head. A central slice from a volumetric scan obtained from (b) a human subject showing 7 retinal surfaces, (c) a mouse showing 10 retinal surfaces and (d) a canine showing 5 retinal surfaces.

µm, respectively. 2. 2.1.

Methods Overview of graph-theoretic approach

The graph-theoretic method employed here is modeled on a previously described approach [21, 24], where the multiple surface segmentation problem is represented as a minimum-cost closure problem in a vertex-weighted graph. The graph structure is determined by the feasibility constraints, namely the topological and inter-surface constraints, that describe the set of surfaces. The weights of the vertices are derived from the cost function that can be expressed as a combination of on-surface and in-region terms. The on-surface cost reflects the unlikelihood that the voxel lies on a particular surface while the in-region cost term reflects the unlikelihood that the voxel belongs in a particular region. Given n non-intersecting surfaces, Si , i = {1, 2, ..., n}, and consequently n + 1 regions, R j , j = {0, 1, 2, ..., n}, the overall total cost cost CT can be expressed as a weighted combination of the on-surface costs, CSi , i ∈ {1, ..., n}, and in-region costs CR j , j ∈ {0, 1, ..., n}. n

n

CT = α ∑ CSi +(1 − α) ∑ CR j , where i=1

CSi =

∑ (x,y,z)|z=Si (x,y)

(1)

j=0

csur fi (x, y, z) and CR j =

∑

creg j (x, y, z) ,

(2)

(x,y,z)∈R j

and csur fi (x, y, z) and creg j (x, y, z) represent the on-surface cost associated with surface i and the in-region cost associated with region j, respectively. A minimum closure on this vertexweighted graph (computed by finding a minimum s-t cut on a closely related edge-weighted graph) now gives us the globally optimal set of n feasible surfaces.

High-intensity Region

Mediumintensity Regions Low-intensity Regions

(a)

(b)

Fig. 2. (a) A slice from a mouse SD-OCT image showing the (b) five inner layers, namely the NF+GCL, the IPL, the INL, the OPL and the ONL and their categorization into high-, medium- and low-intensity regions.

2.2.

Automated machine-learning based design of the cost function

In standard classification-based segmentation approaches [10, 18], the goal is to find the best classification possible for each region of interest. However, the classification of regions in the presence of multiple interacting surfaces where similarities could exist between one or more regions, often causes misclassifications to occur between the similar regions. In OCT images of the retina, (see Fig. 2), the retinal nerve fiber layer (RNFL) is distinctively bright, while the inner plexiform and outer plexiform layers are of medium intensity and the inner and outer nuclear layers have low intensity. We previously observed [23] that the independent identification of either of the two plexiform layers or the two nuclear layers can be quite difficult given their similar appearance. The inclusion of a location based feature, such as the distance relative to an identifiable structure [22], could help classify the structures independently. However, this increased dependence on a structural feature could hurt the method as disease-induced structural changes are not uncommon. However, when considering the use of classificationbased approaches for use as a cost function (rather than the final result) in a multi-surface graph-theoretic approach, the fact that the surfaces are found simultaneously only requires that neighboring regions/surfaces be differentiable from their immediate neighbors. This allows for for the regions/surfaces to be grouped on the basis of similar properties, which in turn can help reduce misclassifications between similar structures [23]. Thus, in this work, we grouped the regions on the basis of intensity into high-, medium- and low-intensity regions. The RNFL was considered a high-intensity region, while the plexiform layers and the nuclear layers were categorized as medium- and low-intensity regions, respectively. Similarly, as surfaces lie either below a high-intensity region with a lower intensity region below it, or vice versa, a classifier was trained to recognize dark-to-bright interfaces from the background, and bright-to-dark interfaces from the background. For example, in the mice scans (see Fig. 1(c)), the ILM and the bottom surface of the INL were considered darkto-bright interfaces, while the bottom surfaces of the NF-GCL, the IPL and the OPL were considered bright-to-dark interfaces. The classifier was also provided samples from “smooth” regions, to ensure that only true layer interfaces are identified. The machine-learning based cost function design process, as shown in Fig. 3, begins with the generation of on-surface and in-region descriptors using frequently utilized filters banks [25, 26], such as Haar features [27], Gabor features [28], Gaussian-steerable features and intensitybased features such as mean intensity, variance, entropy, skewness and kurtosis. For the Haar features, kernel sizes w = {1, 2, 4, 6} were used to create 2-rectangle and 4-rectangle features

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Train Classifier Random Forest Training Set

Generate Features Using Filter Banks: Haar, Gabor, Gaussian Steerable, Intensity Features

Bright-to-Dark

Dark-to-Bright

High-Intensity

Medium-Intensity

On-Surface Classifiers

In-Region Classifiers

Train Classifier Random Forest Low-Intensity

Fig. 3. Overview of the machine-learning-based cost function design.

[29]. The Gabor filter is essentially a band pass filter represented as: g(x, y)(σ ,θ ,ψ) = e

02 2 02 x0 − x +γ 2 y 2σ ei(2π λ +ψ) ,

0

where

(3)

0

x = x cos θ + y sin θ , y = −x sin θ + y cos θ . The parameters σ , γ, λ , θ and ψ are the standard deviation, spatial aspect ratio, wavelength, orientation and the phase offset, respectively. A Gabor filter bank [23] was created using the symmetric (ψ = 0o ) and anti-symmetric (ψ = 90o ) filter responses of the Gabor filter with standard deviation σ = {1, 2, 4, 6}, and angle θ = {−90o , −60o , −30o , 0o , 30o , 60o , 90o }. The wavelength (λ ) was set to σ /0.56 as this corresponds to a half-response spatial frequency bandwidth of one octave and the spatial aspect ratio (γ) was set to 1. The energy features [28] were also computed by summing the squared symmetric and anti-symmetric filter responses for particular values of σ and θ , as shown below: q (4) Eσ ,θ (x, y) = G(x, y)2(σ ,θ ,0o ) + G(x, y)2(σ ,θ ,90o ) where, N

G(x, y)(σ ,θ ,ψ) =

M

∑ ∑ I(η, ν)g(σ ,θ ,ψ) (x − η, y − ν).

(5)

η=0 ν=0

The Gaussian filter bank [30] consisted of oriented filter derivatives up to order 1 at scales σ = {1, 2, 3, 4, 5} and orientations θ = {0o , 30o , 60o , 90o , −60o , −30o , −90o }, where 0 Gθ1 = cos(θ )G01 + sin(θ )G90 1 , where G1 =

∂ −(x2 +z2 ) ∂ −(x2 +z2 ) (e ) and G90 (e ). 1 = ∂x ∂z

(6)

These features were computed in 2-D within each B-scan using Eq. (6) and also in 3-D where G01 =

∂ −(x2 +y2 +z2 ) ∂ −(x2 +y2 +z2 ) (e ) and G90 (e ). 1 = ∂x ∂z

(7)

These features were then used to train a classifier, a random forest, in order to obtain probability maps for the regions and surfaces of interest. Random forests [31] are ensemble classifiers composed of a number of decision trees, where the classification of an input feature vector is determined by the majority vote cast by the individual trees. This classifier is robust and its performance is largely tied to two main parameters, the number of trees in the forest N and the number of features selected at random at each decision split m. Here, we used N = 350 trees (larger numbers increased the training period but did not improve accuracy) and m = 10. Regression was performed by computing the ratio of the majority votes to the total number of trees in the forest. We utilized the OpenCV implementation of random trees. The random forests were trained to provide a probability estimate that indicated the likelihood of an input #195835 - $15.00 USD



feature vector belonging to a particular region or surface. For instance, the high-intensity region random forest classifier provided the likelihood of each input feature vector belonging to a high-intensity region. Thus, separate classifiers were created to identify the three categories of regions and two categories of surfaces. The classifiers were initially trained using all the texture features computed. The individual feature significances were used to limit the feature set to those that contributed at least 2% to the overall feature significance. This final set of features were then used to retrain the random forest and create probability maps for the high-, medium- and low-intensity regions. A similar process was used to create probability maps for the dark-to-bright and bright-to-dark interfaces. Figure 4 show the probability maps obtained for a scan acquired from a human, a mouse and a canine. 2.3.

Segmentation process

The retinal surfaces segmented in the human, mice and canine scans are depicted and labeled in Fig. 1(b), (c) and (d), respectively. Although the number of target surfaces differs for the different datasets, the overall segmentation process used a two-stage approach [21,32], which begins by segmenting the outer surfaces, namely the internal limiting membrane (ILM), the junction of the inner and outer segments (IS/OS junction) and the bounding surfaces of the retinal pigment epithelium (RPE). The four inner layers were subsequently segmented simultaneously in the second step. These layers included the upper high-intensity layer, which in humans is the retinal nerve fiber layer (RNFL), but in mice and canines consists of the nerve fiber and ganglion cell layer (NF-GCL); the second layer, which in humans consists of the ganglion cell layer (GCL) and the inner plexiform layer (IPL) but in mice and canines is the inner plexiform layer; the inner nuclear layer (INL) and the outer plexiform layer (OPL). The estimates of the feasibility constraints [24] utilized by the graph-theoretic method, namely the smoothness and surface-interaction constraints, were derived from the available manual tracings. In particular, the maximum change in the surface topology for each surface and the minimum and maximum distances between pairs of surfaces was estimated from the available tracings. These values (relaxed to accommodate unseen surface variations) were then used to define the smoothness and surface-interactions constraints. As the outer surfaces, the bounding surfaces for outer segments for instance, are extremely close to each other, which made the learning of regional features difficult. While such a term could have been included for the segmentation of the RPE in the mice scans, these surfaces were segmented simultaneously with the ELM, the bounding surfaces of the outer segments and Bruch’s membrane, where the incorporation of a learned in-region term was extremely challenging. Thus, we excluded this term for all the outer surfaces. The inner layers however, are ideal for learning in-region as well as on-surface cost terms and the segmentation of these surfaces included either a learned in-region or an on-surface cost term or a combination of both. The automated feature selection based on the individual feature significance (see Section 2.2) yielded a total of 20 and 19 features for the in-region and on-surface cost terms, respectively, in the human dataset. Similarly, for the mice data, 21 features were used to learn the in-region and on-surface terms, while in the canine datasets, 17 features were used to learn these cost terms. In addition to finding a good set of features that describe the regions and surfaces, it is also important to find the weight α in Eq. (2), that defines the combination of the in-region and onsurface cost terms [21]. As each of the surfaces may prefer a different on-surface to in-region cost term ratio, it may be preferable to find the optimal set of weights βi for each of the surfaces. The cost function can now be expressed as: αi n n (1−αi ) , if 1 − αi > 0 (8) CT = ∑ βiCSi + ∑ CR j , and βi = Clarge , if 1 − αi ≈ 0. j=0 i=1

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Mouse

Canine

Low Intensity

Medium Intensity

High Intensity

Bright-to-Dark Dark-to-Bright

Original

Human

Fig. 4. The top row shows slices from SD-OCT volumes obtained from (left) a human, (middle) a mouse and (right) a canine. The probability maps obtained for the dark-to-bright surfaces and bright-to-dark are shown in the second and third rows, respectively. The probability maps obtained for the high-, medium and low-intensity regions are as shown in the fourth, fifth and sixth rows, respectively.

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where αi is the value that provides the lowest segmentation error for surface i, and Clarge = 100. The optimization used here follows the process outlined in [21]. We began by formulating the cost function using Eq. (2) and then tested a range of α in increments of 0.1. When an estimate of α was found, smaller steps were used to further refine the optimization. 3.

Experimental methods

3.1.

Data description

The proposed method was evaluated on three sets of images obtained from human patients, mice and canines. All procedures involving human subjects conformed to the principles outlined in the Declaration of Helsinki and were conducted after obtaining informed consent from the patients. All animal procedures were approved by the Animal Care and Use Committee at the University of Iowa (mice data) or the Department of Veterans Affairs Institutional Animal Care and Use Committee (canine data), and complied with the ARVO statement for the Use of Animals in Ophthalmic and Vision Research. The datasets are described in further detail below: The first set contained 10 optic nerve head (ONH) OCT volumes acquired from 10 human glaucoma patients on a spectral-domain Cirrus (Carl Zeiss Meditec, Inc., Dublin CA) scanner [32]. Each volumetric scan was obtained from a region 6mm × 6mm × 2mm and contained 200 × 200 × 1024 voxels. Manual tracings were obtained from two independent observers (experienced in retinal anatomy) on a total of 100 slices. In particular, each dataset was divided into sections of 20 slices and a single slice was chosen at random from within each section, thereby preventing any selection bias. Seven retinal surfaces (depicted in Fig. 1(b)) were traced, namely the bounding surfaces of RNFL, the GCL+IPL, the INL, the OPL, the outer nuclear layer (ONL), and the lower bound of the retinal pigment epithelium (RPE). As the surfaces become indistinct within the ONH-region, this area was excluded during evaluation. The ONH was approximated using a circle 1.05mm in diameter.

d2

d1

(a)

(b)

(c)

(d)

Fig. 5. (a) Illustration of a volumetric SD-OCT scan obtained from a mouse, showing the circular “valid” region of the projection image. The circular nature of the scan results in large noisy regions in slices near the (b) the periphery. The optic nerve head causes shadows in the (c) central slices of the scan. (d) The evaluation of the segmentation accuracy was therefore, limited to an annular region defined by d1=0.2mm and d2=1.2mm in order to avoid the ONH and the noisy peripheral regions.

The second set contained 10 SD-OCT images obtained from 10 normal mice on a spectraldomain Bioptigen scanner (Bioptigen, Inc. Durham, NC). These volumetric scans were centered on the ONH and were obtained from an area 1.4mm × 1.4mm × 2mm and contained 400 × 400 × 1024 voxels. Ten retinal surfaces, as depicted in Fig. 1(c), were segmented on these scans, five within the inner retina, namely the bounding surfaces of the nerve fiber-ganglion cell complex (NF+GCL), the inner plexiform layer (IPL), the INL, and the OPL; and five in the outer retina, namely, the external limiting membrane (ELM), the IS/OS junction, the bottom of the outer segments and the upper and lower boundaries of the RPE. Due to the curvature of

the retina, only a circular region within the 1.4mm x 1.4mm scanned area contains valid information. Figure 5(a) depicts a volumetric scan and the circular projection image usually seen in these images. Figures 5(b) and (c) show examples of a peripheral slice and a central slice, respectively. Thus, the evaluation of the segmentation accuracy was also limited to an annular region (see Fig. 5(d)) defined by two circles 0.2mm and 1.2mm in diameter in order to exclude the ONH and the noisy peripheral regions. Manual tracings were obtained from a retinal specialist on a total of 100 slices, where 10 slices where chosen from each of the 10 datasets. The slices were chosen at random from sections 30 slices deep while avoiding the first and last 50 slices as the section of the retina imaged in the first and last 50 slices comprise less than 50% of the B-scan.

(a)

(b)

Fig. 6. Regions of low signal strength and the optic nerve head region were excluded from the validation. (a) A slice from an SD-OCT scan obtained from a canine, showing the optic nerve head region within which surfaces are difficult to discern and the (b) corresponding mask. The region within the red lines was excluded.

The third data set consisted of SD-OCT retinal scans obtained from a colony of nineteen Basset Hounds. The colony consisted of three nonaffected canines, six canines with genetic susceptibility to glaucoma, but without the disease and 10 canines with genetic susceptibility that presented with glaucoma. Baseline scans of each animal were obtained at 6 months of age. Subsequent SD-OCT scans were obtained after provocative testing by acute elevation of intraocular pressure (AEIOP). The scans were centered on the macula and were obtained on a Heidelberg SD-OCT Spectralis scanner (Heidelberg Engineering, Germany). Varying protocols were used to acquire these scans, but the typical scan encompassed a region 4.2mm x 4.5mm x 1.9mm and contained 768x19x496 voxels. An independent observer (experience in retinal anatomy of canines) traced five surfaces (as shown in Fig. 1(d)), namely the bounding surfaces of the NF+GCL, the IPL and the ONL. The INL and the OPL are segmented but they are extremely thin and the observer was unable to trace these surfaces consistently. Thus, the accuracy evaluation was limited to five surfaces. Furthermore, certain sections of the images showed low signal strength as depicted in Fig. 6. These regions where the surfaces were not visible were excluded from the evaluation as well. 3.2.

Accuracy evaluation

A cross validation scheme was used to train the classifiers and evaluate the final segmentation accuracy. For the human and mice datasets that contain ten images each, eight scans were used to train the system and the remaining two were segmented after the incorporation of the learned cost terms. This was repeated four times until all the scans were segmented. In the case of the canine scans, 14 datasets of the 19 were used to train the classifiers and the remaining datasets were segmented. This was repeated three more times to provide segmentation results on all of the 19 datasets. The division of the scans into the four sets used in this cross-validation experiment was done randomly. The unsigned border position errors between the automated segmentations and the manual

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tracings were used as the measure of the segmentation accuracy. As the cost function can be represented as a weighted combination of on-surface and in-region cost terms, in addition to evaluating the overall segmentation accuracy, it is also important to gauge the individual impact of these learned features. This will not only help to tailor the graph-theoretic method to specific applications, it will also prevent the inclusion of features that may potentially hurt the segmentation results. This was done by comparing the segmentation results obtained when using the new cost function designs to those obtained when using a baseline approach. Note that the baseline approaches did not incorporate any learned cost terms but utilized either an on-surface cost term [33] or a weighted combination of an in-region and an on-surface cost term [32]. Three possible frameworks were, therefore tested, where the graph-theoretic method incorporated: 1. a combination of learned in-region cost terms and Gaussian-derivative based on-surface terms (Experiment I), 2. only learned on-surface cost terms (Experiment II), and 3. a combination of learned in-region and on-surface cost terms (Experiment III). Baseline approaches have been previously described for the human [32] and mice scans [33], however, designing one for the canine dataset proved to be extremely difficult. Thus, this dataset does not have a baseline approach. Paired t-tests that were corrected for multiple comparisons were used to compare the results obtained. 4. 4.1.

Results Data obtained from human subjects

Table 1 shows the overall border position errors for the 7 surfaces obtained using Experiments I, II and III as well as the results obtained when no learned component was incorporated into the segmentation method [32] (labeled ‘Baseline’). The overall border position error obtained for Experiments I, II and III was 6.45 ± 1.87 µm, 8.26 ± 2.72 µm and 8.67 ± 2.88 µm, respectively. The errors observed for the inner surfaces for all three experiments were also comparable with the inter-observer variability [32] that was 12.79 ± 3.36 µm, 13.74 ± 2.04 µm, 9.28 ± 3.00 µm and 7.67 ± 1.69 µm for surfaces 2, 3, 4 and 5, respectively. The segmentation errors observed in Experiment I showed significant improvement (p < 0.001) over the baseline results for all four inner surfaces. The incorporation of only the learned on-surface cost resulted in smaller errors than the baseline results, however, they were not significantly different from the baseline results. In Experiment III, surface 2 (bottom of the RNFL) and surface 5 (top of the ONL) significantly improved in comparison with baseline results. The best results for all surfaces, however, were obtained using the learned in-region cost term. Figures 7(a) shows a near-central slice from a scan obtained from a human glaucoma patient. Errors were commonly seen near the ONH-region when no learned cost terms were incorporated into the graph-theoretic method [32] as shown in Fig. 7(c) as the gradients that mark the layer boundaries are quite small and are in fact, comparable to the speckle noise seen in these images. The incorporation of the learned in-region cost term had the most significant impact on the results as shown in Fig. 7(d). The incorporation of the learned on-surface cost term and the combination of the in-region and on-surface cost term also improved the segmentation accuracy from the baseline results as depicted in Figs. 7(e) and (f), respectively. 4.2.

Data obtained from mice

The unsigned border position errors were computed on a total of 97 slices as not all of the 10 surfaces could be confidently traced on 3 slices. The overall border position errors for the

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Table 1. Unsigned border position error (mean ± SD) in µm computed on the human dataset.

Surface 1 2 3 4 5 6 7 Mean

Baseline 4.90 ± 1.54 14.43 ± 5.63 10.96 ± 4.06 10.46 ± 2.79 10.73 ± 2.78 3.87 ± 1.32 7.24 ± 1.74 8.94 ± 3.76

(a)

(d)

Experiment I 4.90 ± 1.54 9.82 ± 3.37 6.47 ± 1.99 6.42 ± 2.12 6.41 ± 2.11 3.87 ± 1.32 7.24 ± 1.74 6.45 ± 1.87

(b)

(e)

Experiment II 4.90 ± 1.54 13.28 ± 4.55 9.07 ± 2.94 9.13 ± 2.82 8.55 ± 2.58 5.66 ± 0.54 7.22 ± 1.32 8.26 ± 2.72

Experiment III 4.90 ± 1.54 12.68 ± 5.51 10.96 ± 4.59 10.44 ± 4.05 8.84 ± 3.44 5.66 ± 0.54 7.22 ± 1.32 8.67 ± 2.88

(c)

(f)

Fig. 7. (a) A near-central slice from an SD-OCT scan acquired from a human subject that presented with glaucoma alongside (b) the manual tracings obtained from an independent observer and the automated results obtained using (c) the previously described method [32] that did not incorporate any learned cost terms, (d) learned in-region cost function, (e) onsurface cost function and (f) a combination of both.

10 surfaces obtained using Experiments I, II and III were 3.45 ± 0.80 µm, 3.46 ± 0.76 µm and 3.35 ± 0.62 µm, respectively (see Table 2). The border position errors obtained when no learned components were incorporated into the graph-theoretic method [33] was 3.58 ± 1.33 µm. The incorporation of the learned cost terms (in Experiments I, II and III) significantly improved (p < 0.001) the results for surface 2 over the baseline results. The incorporation of the learned in-region cost term also significantly reduced (p < 0.001) the errors noted in surface 5 over the baseline results. Figures 8(a) and (b) show a slice from a mouse scan and the manual tracings obtained from a retinal specialist. Figures 8(d)-(f) show the results obtained using the learned in-region cost, on-surface cost and a combination of both, respectively. This slice showed higher errors than the average when no learned cost term was incorporated into the graph-theoretic method. The

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Table 2. Unsigned border position error (mean ± SD) in µm obtained on the mice data.

Surface 1 2 3 4 5 6 7 8 9 10 Mean

Baseline 2.48 ± 0.72 6.97 ± 2.20 2.86 ± 0.55 2.80 ± 0.73 3.16 ± 0.97 3.08 ± 1.08 2.72 ± 0.98 3.39 ± 1.20 4.50 ± 0.97 3.87 ± 1.36 3.58 ± 1.33

Experiment I 2.48 ± 0.72 4.80 ± 0.86 3.97 ± 0.50 2.95 ± 0.83 2.74 ± 0.64 3.08 ± 1.08 2.72 ± 0.98 3.39 ± 1.20 4.50 ± 0.97 3.87 ± 1.36 3.45 ± 0.80

Experiment II 2.48 ± 0.72 5.16 ± 1.34 3.30 ± 0.73 2.88 ± 0.75 4.05 ± 1.18 3.01 ± 0.86 2.89 ± 0.80 3.57 ± 0.98 3.58 ± 1.17 3.72 ± 1.15 3.46 ± 0.76

Experiment III 2.48 ± 0.72 4.45 ± 0.56 3.24 ± 0.83 2.59 ± 0.71 3.98 ± 1.33 3.01 ± 0.86 2.89 ± 0.80 3.57 ± 0.98 3.58 ± 1.17 3.72 ± 1.15 3.35 ± 0.62

slice is very close to the ONH region (0.13mm away from the center of the scan), and the large vessel shadows make the central area difficult to segment. However, the use of the learned in-region and on-surface cost terms corrected these segmentation errors.

(a)

(d)

(b)

(e)

(c)

(f)

Fig. 8. A near-central slice from an SD-OCT volume of a mouse retina alongside (b) the manual tracings obtained from a retinal specialist and the automated results obtained using (c) an approach that did not incorporate any learned cost terms and after the inclusion of learned (d) in-region cost function, (e) on-surface cost function and (f) a combination of both.

4.3.

Data obtained from canines

The overall border position errors for the 10 surfaces obtained using Experiments I, II and III were 9.75 ± 3.18, 11.39 ± 4.82 and 10.14 ± 4.26, respectively. The unsigned border position errors for the five surfaces are tabulated in Table 3. The segmentation errors noted in surface

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2 (bottom of NF+GCL) in Experiment I was significantly smaller (p < 0.01) than those noted in Experiments II and III. The errors noted in surface 3 (bottom of the IPL) was smallest when both learned cost terms were incorporated into the graph-theoretic method and was significantly better (p < 0.001) than when only learned on-surface costs were incorporated, but did not significantly differ from the errors noted when only the learned in-region cost term was used. The errors noted in surface 4 (upper surface of the ONL) in all three experiments did not significantly differ from each other. Table 3. Overall unsigned border position error (mean ± SD) in microns obtained on the 19 canine scans.

Surface 1 2 3 4 5 Mean

Experiment I 6.65 ± 1.88 14.50 ± 3.80 10.12 ± 4.98 10.49 ± 5.30 7.00 ± 2.03 9.75 ± 3.18

Experiment II 6.65 ± 1.88 18.05 ± 3.10 14.30 ± 5.90 10.74 ± 5.47 7.00 ± 2.03 11.39 ± 4.82

Experiment III 6.65 ± 1.88 17.31 ± 4.83 9.69 ± 5.05 9.88 ± 5.98 7.00 ± 2.03 10.14 ± 4.26

Figure 9 (a) shows a slice from an SD-OCT volumes obtained from a canine and the manual tracings obtained from an independent observer are as shown in Fig. 9(b). The segmentation results obtained after the incorporation of the learned in-region cost term, on-surface cost term and a combination of the two is as shown in Figs. 9(c)-(e), respectively.

(a)

(c)

(b)

(d)

(e)

Fig. 9. (a) A slice from an SD-OCT image obtained from a canine alongside (b) the manual tracings obtained from an independent observer and the automated results obtained using (c) the learned in-region cost term, (d) on-surface cost function, and (e) a combination of both.

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5.

Discussion and conclusion

Machine-learning based approaches and graph-theoretic approaches [19, 21, 32] proposed for the segmentation of retinal surfaces in SD-OCT images have their own distinct advantages. Machine-learning based approaches are easily adapted to new models while graph-theoretic approaches are able to segment multiple surfaces simultaneously in 3-D while ensuring the global optimality of the solution with respect to a cost function. Here, we described a framework that combines a machine-learning based technique and a graph-theoretic approach [24] for the automated segmentation of retinal surfaces in SD-OCT images. The machine-learning based automated design of the cost function allowed for the method to be quickly adapted to new models such as animal retinae as well as to the images obtained on a variety of scanners with varying imaging protocols. The impact of the incorporation of the learned components final segmentation accuracy was also assessed, thereby allowing for the method to be tailored to specific applications as its only requirement is a training set. As the cost function design relies on the training set, we observed that the difficulty of the manual tracings had an impact on the ability to learn the costs for the regions and surfaces of interest. This difficulty is apparent in the human dataset, where all the images were acquired from subjects that presented with glaucoma. The contrast in these images was quite low and the difficulty associated with confidently identifying the surfaces is indicated in the high interobserver variability. While the method was able to differentiate between the regions quite well, learning the surfaces proved to be quite difficult on this set. This is also reflected in the final recommendation of the framework, where the incorporation of the learned in-region cost (Experiment I) showed the best overall results. Similar results were noted in the canine dataset, where the scans were also largely obtained from disease-affected animals. These images were quite anisotropic, with few slices acquired along the y-axis, making the inclusion of 3-D features or contextual information in the method difficult. It is also important to note that these images were acquired on a Spectralis SD-OCT scanner where the voxel depth is 3.86 µm. Thus, the overall error is on the order of 2-4 voxels, which is comparable to the results obtained on the other two sets of images. These images also often showed low contrast making the development of a baseline method that would be provide adequate accuracy extremely difficult to design. The low contrast also affected the ability to accurately trace the inner surfaces, and subsequently confounded the learning of the surface properties. Here, again the framework recommended the incorporation of the learned in-region cost term. However, certain surfaces fared well with the combination of the two learned cost terms, indicating that perhaps the learned components could be included for certain surfaces and excluded for other surfaces that are difficult to learn. However, this is quite difficult to gauge, given the numerous interactions that exist when the surfaces are segmented simultaneously. These interactions are difficult to account for and likely had an impact on the optimization process used to find the βi for each surface. Thus, while the results obtained for Experiment III (that included the learned on-surface and in-region cost term) was expected to be the best, it was found to not be the case for the human and canine set, indicating that perhaps these weights should be optimized simultaneously and not independently. This will, however, be investigated in our future work. In the case of the mice scans, the framework recommended the use of a combination of the learned in-region and on-surface cost terms. Although, certain surfaces, such as the outer surfaces, seemed to not need the learned cost terms, the inclusion of the cost terms had a significant impact on the segmentation accuracy of the NF+GCL. This structure is segmented frequently and has been shown to correlate with disease [34]. As this structure thins and becomes difficult to discern, we expect the inclusion of the learned cost terms, especially the in-region cost term, to have a significant impact on the segmentation accuracy.

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The graph-theoretic method is a natural choice where numerous regions (with possible similarities) need to be segmented, and the automated machine-learning based cost function design allows for this method to be easily adapted to numerous applications. The machine-learning component however, is quite dependent on the examples included in the training set. Thus, the extension of this method to data that show significant disruptions to the retinal structure, such as the presence of a fluid-filled region, would require the inclusion of an adequate number of samples in the training set. However, despite this restriction, the automated machine-learning approach requires less domain (animal/model specific) knowledge on the part of the algorithm development team. Here, we demonstrated the successful employment of this method for the segmentation of retinal surfaces in SD-OCT images obtained from humans, mice and canines. As this imaging modality finds increasing use in research studies involving different animal models, we expect that this adaptable method could prove to be an extremely useful tool. Acknowledgements This work was supported, in part, by the Department of Veterans Affairs (Center for the Prevention and Treatment of Visual Loss, Career Development Award, MKG, 1IK2RX000728, and Career Development Award, MMH); the National Eye Institute of the National Institutes of Health R01 EY023279, R01 EY018853, and R01 EY019112. We would also like to thank Drs. Pavlina Sonkova, Helga Kecova and Elena Hernandez-Merino, and Austin Boekman and Alex Wiederin for their assistance in completing this work.

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