A Novel Algorithm for Extraction of the Layers of the Cornea

J.A. Eichel, A.K. Mishra, D.A. Clausi, P.W. Fieguth, K.K. Bizhevajaeichel, akmishra, dclausi, pfieguth, kbizheva@uwaterloo.ca

Vision and Image Processing Group, University of Waterloo, Canada

Abstract

Accurate corneal layer boundary extraction from opticalcoherence tomography can provide precise layer thicknessmeasurements required in the analysis of corneal disease.This paper establishes a novel approach to precisely obtainthe five primary corneal layer boundaries. The proposedmethod determines correspondence relationships betweenthe layer boundaries to facilitate robust boundary extrac-tion in the presence of noise and artifacts. The first phaseof the method applies morphological operators to enhancethe prominent structural features of the cornea. The secondphase uses a semi-automated segmentation algorithm to ex-tract the upper and lower boundaries of the cornea; theseboundaries are used to register the corneal image. The finalphase extracts all five boundaries using a global optimiza-tion method exploiting the medial correspondence relation-ship between each layers.

The proposed method is tested and verified using a rep-resentative set of optical coherence tomography images andcompared against several state of the art methods. The pro-posed method is demonstrated to be more robust to noise, toprovide more accurate segmentation results, and to requirefewer user interactions than the other published methods.

1. Introduction

The adult cornea is only about 1/2 millimeter thick and iscomprised of five layers: epithelium, Bowman’s membrane,stroma, Descemet’s membrane and the endothelium [1, 8].The precise measurement of the thickness of all cornea lay-ers is essential for the analysis of corneal swelling, acido-sis, and altered corneal oxygen consumption [9]. To obtaincorneal images, optical coherence tomography (OCT) tech-nology is used to capture the internal structure of the cornea.The images produced using OCT are characterized by lowsignal to noise ratio and image non-homogeneities. Robustand accurate boundary extraction poses a great challenge.

Kostadinka et al. [14] first captured the cornea layersusing a high speed, ultra high refractive optical coherence

tomography (UHROCT) imaging technology and then ap-plied image processing algorithms, such as Fuzzy Type IIwavelet despeckling. Although the images have been cap-tured and denoised, there is no computer vision literaturerelated to corneal layer boundary extraction to obtain theprecise measurement of layer thickness.

However, existing methods such as active contour [2,4, 7, 10], intelligent scissors [5], enhanced intelligent scis-sor [12], and edge relaxation and linking techniques couldbe adapted for segmentation of the layers of the cornea.Active contours or deformable models, fully-automatic seg-mentation approaches, are typically used to extract the layerboundaries. Unfortunately, none of these approaches aresuitable for corneal layer extraction because the layers ofthe cornea are characterized by low signal to ratio. Con-sequently, these fully-automated segmentation methods arenot capable of extracting layer boundaries. Rather, rigidmodel based approaches are preferred.

Mortenson et al. [5] first introduced intelligent scissors(IS), a semi-automatic segmentation algorithm, which as-sists the user during the interactive segmentation process.The user interaction allows the process to take advantageof user knowledge when defining the boundaries. For thismethod, the user selects seed points on the boundary and, asthe mouse moves along the boundary, the optimal bound-ary path between the starting point and the current pointis obtained. There are two main advantages to this ap-proach to segmentation. First, the segmentation is accom-plished in real-time; this allows for rapid image segmen-tation. Second, the boundary accuracy resulting from thistype of method is generally higher than automatic methodssince user knowledge is utilized throughout the process [5].

However, there are several drawbacks to existing IS-based methods for precise measurement of cornea thick-ness. First, like current automatic segmentation methods,the boundary definition for existing IS methods rely on im-age gradients; this dependence makes the algorithm sensi-tive to contrast non-uniformities found in low signal to noiseratios associated with OCT cornea images. Second, exist-ing IS methods require the clinician to perform relativelyaccurate manual tracing along the region boundary, which

can be time-consuming and laborious, particularly for com-plex regions of interest. To overcome some of the problemsassociated with IS, Wong et al. [12] proposed enhanced in-telligent scissors (EIS) that uses phase-based representationof the image as the external local cost, instead of the imagegradient. However, EIS approach alone is not suitable forthe extraction of the layers of the cornea.

To precisely locate the layers of the cornea, this pa-per proposes a semi-automatic model based segmentationmethod designed to minimize user input. First, the algo-rithm identifies the epithelium (upper) and the endothelium(lower) layer of the cornea using enhanced intelligent scis-sor (EIS), a user-interactive semi-supervised segmentationmethod. Second, a correspondence model is established be-tween the upper and lower layer of the cornea using me-dial axis transform (MAT). Finally, the boundaries are de-termined from discrete optimization followed by parameterestimation using prior information, the correspondence be-tween layers extracted using medial axis transform relation-ship.

The proposed method is described in Section 3. Sec-tion 4 demonstrates the use of proposed method to extractthe layers of the cornea. Finally, the conclusion and futureresearch are discussed in Section 5.

2 Theory of the Proposed Method

The OCT corneal image contains five distinct layerboundaries and is illustrated in figure 2. The epithelium andendothelium outer boundaries have the highest contrast andthe Descemet’s membrane has the lowest contrast.

Several corneal images are initially segmented using thefollowing methods: a edge linking and relaxation label-ing [6], parametric active contours [7, 4], geometric activecontours [10], optimal boundary detection [11] and edge-free active contours [3] to extract the five layers of thecornea. Unfortunately, none of these method give satisfac-tory segmentation results for the corneal image. The failureof these methods are due to following reasons:

• The OCT image has low signal to noise ratio and con-tains image non-homogeneities.

• The boundary detection methods are dependent uponthe image gradient obtained from the noisy OCT im-age.

• The inner boundaries of the OCT image are indistinct.

The poor performance of the geometric active contour, oneof the better segmentation algorithms, is illustrated in fig-ure 1.

Instead, a model of the cornea is used to guide activecontours to segment the noisy image. Let the layer bound-aries be represented using continuous parametric curves.

Figure 1. The level set based geometric ac-tive contour [10] fails to segment the layersin the cornea due to very low signal to noiseratio of the cornea image.

Let Ωα,θ(s), (s ∈ [0, 1], α ∈ [0− ε, 1 + ε], θ ∈ [0, 360]) bea parametric curve, represented using a spline, deformablemodel, or polynomial with s, the arclength as the parame-ter. The parameter ε is a small positive value allowing thealgorithm to search for boundaries in the neighborhood sur-rounding α = 0 and α = 1.

In literature [7, 4] the curve Ωα,θ(s) = Ω(s) is modeledas an energy minimizing spline with total energy as:

E =

1∫0

α(s)Ω2s(s)︸ ︷︷ ︸

Elastic

+β(s)Ω2ss(s)︸ ︷︷ ︸

Membrane

− γ(s)Eext(Ω(s))︸ ︷︷ ︸External

ds

(1)where Ωs(s) and Ωss(s) are the first and second derivativesof v(s) with respect to the arclength s, and the parametersα(s), β(s) and γ(s) are the penalties imposed on slope, cur-vature and the external force of the active contours, respec-tively. Typically, to allow convergence of the active contourto the image edges, the energy is defined to be a function ofthe image gradient (g),

Eext = g2(I) = (δGσ ∗ I)2 (2)

for some first derivative of Gaussian (δGσ) with bandwidthσ, where ∗ is the convolution operator and I ∈ [0, 1] is theintensity map of the cornea image.

The goal is to obtain the corneal boundaries by minimiz-ing equation (1). However, as one can see from Figure 2the layers of the cornea are not distinct. Therefore, the gra-dient map alone is not able to attract the snake towards thelayers of the cornea. Further, the layer boundaries of thecornea obey spatial statistics. Consequently, a model based

EpitheliumBowman’s membrane StromaDescemet’s membraneEndothelium

Figure 2. Cornea image with layers of interest. The epithelium and endothelium layers of the corneaare distinct while the other layers are obscured.

approach is suitable to segment the layers of the cornea. Un-like the active contour which uses a deformable model, theproposed method uses a prior model, Ωα,θ(s) defined usingparameters α and θ to represent the layer boundaries. Theproposed method assumes there is a correspondence rela-tionship between the layers and that each layer can be repre-sented using a piecewise continuous non-deformable linearspline Ωα,θ(s). The total cost associated with the spline is:

f(α, θ) =∮

Ω(α,θ)(s)

((1− I)2 + g2(I)

)ds (3)

The goal is to obtain optimal value of α and θ correspondingto the maxima of f(α, θ), Mathematically,[

α, θ]

= arg maxα,θ

(f(α, θ)) (4)

An efficient approach to solve (4) is provided in Section 3.

3 Proposed Approach

This section describes how the proposed approach ex-tracts the corneal layer boundaries. The proposed approachconsists of three steps: 1) preprocessing 3.1, 2) obtainingcorrespondence model 3.2 and 3) locating the layers of thecornea 3.3.

3.1 Preprocessing

Preprocessing of the corneal image is performed to im-prove the ability of EIS to snap to the outer and innermostlayer boundaries. This step improves the boundary con-trast while reducing the contrast of other regions. Contrast-limited adaptive histogram equalization (CLAHE) is ap-plied to obtain more consistent contrast throughout the en-tire image [17]. Morphological operators are then appliedin the preprocessing phase of this algorithm to enhance lowcontrast edges on the epithelium and endothelium bound-aries [15]. If these edges have higher contrast, IS will bebetter able to snap to the boundaries.

The boundaries are first enhanced using multiple struc-turing operators designed to enhance arch-like structures.The open operator is applied to a grey scale image for ahorizontal line. The slope of the line is then increased andthe open operator is applied again so that the previous hor-izontal response becomes connected to adjacent points onthe curved boundary. The slope of the line is increased andthe process is repeated, connecting all points on the curve.The slope is then decreased from the horizontal to connectpoints on the opposite side of the boundary layer, associatedwith negative slope. Finally, Gaussian blurring is applied toremove noisy edges and to create uniform regions that per-mit the enhanced intelligent scissors to more easily snap tothe higher contrast boundaries.

3.2 Correspondence model

The proposed approach uses EIS [12], an user interactivesegmentation method, on the preprocessed image to extracta rough outline of the epithelium and endothelium (Fig-ure 2). Then, the proposed approach creates a correspon-dence model based on the initial user defined boundaries ofthe epithelium and endothelium layers; the two boundariesare related using medial axis transform.

Let Ωα,θ(s), (s ∈ [0, 1]α ∈ [0−ε, 1+ε], θ ∈ [0, 360]) bea parametric curve which can be represented using spline,deformable model, or polynomial with s, the arclength asthe parameter.

The curve Ωα,θ(s) can be defined from correspondencesbetween the user segmented curves associated with the ep-ithelium and endothelium boundaries. When α = 0 andθ=0, Ωα,θ(s) corresponds exactly to the user segmented ep-ithelium boundary. Similarly, Ωα=1,θ=0(s) corresponds tothe user segmented endothelium boundary.

As α increases from 0 − ε to 1 + ε, Ωα,θ(s) transformsfrom the epithelium boundary to the endothelium bound-ary. This transformation relies on point to point correspon-dences between the two boundaries. For each point, pα=0,i,on the epithelium boundary, the corresponding point on theendothelium boundary, pα=1,i, is determined using medialaxis transform theorem. This association can be representedby a vector vi where pα,i = pα=0,i + αvi. When α = 1,pα=1,i corresponds to the curve Ωα=1,θ=0(s).

The parameter θ determines the rotation associated withthe curve. Points pα,i, are rotated about pα,i=0 for values ofθ. The points on the epithelium and endothelium boundariesare defined for θ = 0.

The function value Ωα,θ(s), and the axes α, theta, ands are illustrated in Figure 3.

3.3 Extracting corneal layers

With curves Ωα=0,θ=0(s) and Ωα=1,θ=0(s) defined fromthe user segmentation results, optimization techniques areapplied to search for feasible values of α and θ that pro-duce local maxima of equation (3). From the prior staticsobtained from segmenting several hundred cornea imagesusing the proposed algorithm, all five layers obey the samecorrespondence relationship as the correspondence relation-ship between epithelium and endothelium. Therefore, allfive layers have the same orientation; the orientation is fixedat θ = 0. So, (3) can be written as

f(α) =∮

Ω(α,θ)(s)

((1− I)2 + g2(I)

)ds (5)

The goal is to obtain optimal value of α and θ correspondingto the maxima of f(α, θ), Mathematically, from the prior

Figure 3. The function value Ωα,θ(s) is shownin blue, and the axes α, theta, and s are shownin black. The upper and lower boundaries, inred, define the shape of the function Ωα,θ(s).

knowledge, the five peaks corresponding to the five layersof the cornea are associated with the minima of f(α). How-ever, the direct extraction of these peaks is difficult due tothe non-linear and noisy nature of the function f(α). There-fore, the proposed algorithm incorporates prior knowledgeassociated with the spatial location of the layers of thecornea into f(α).

Based on a large sample set of 800 corneal images, aprobability density function in the form of a Gaussian mix-ture model is created for the five values of α as follows:

ψ(α) =5∑i=1

(ℵ(µi, σi)) (6)

Where µi and σi are the mean and standard deviation of thelayers. Proposed approach obtains a bilateral function Υ(α)by:

Υ(α) = f(α) ∗ ψ(α). (7)

The five values of α corresponding to five significant peaksof Υ(α) are obtained and assigned to the five correspondingcorneal layer boundaries.

4 Test Results and Discussions

This section demonstrates the performance of the pro-posed method compared to EIS and IS over a set of repre-sentative corneal images. Other segmentation methods werealso tested, but, since they were dependent on the imagegradient, failed completely for the corneal images.

4.1 Methods Compared

In this section, the performance of the proposed methodis compared to enhanced intelligent scissors (EIS) and to in-telligent scissors (IS); EIS and IS are both user interactivesegmentation methods. The proposed approach requiresuser input when extracting the upper and lower layers ofthe cornea. Using the user inputs to define the shape of thecornea, the method accurately extracts all five layer bound-aries. The performance of the level set (LS) [10] and gra-dient vector flow based snake (GVFS) [16] was tested on asubset of cornea images. Since, the images are noisy andlack significant gradient information, LS and GVFS did notproduce any meaningful results on test data sets. Therefore,LS and GVFS were excluded from further consideration.

4.2 Data Sets and Experimental Set up

The proposed algorithm was executed on corneal tomo-grams acquired by Department of Physics and Astronomyat the University of Waterloo. The images, containing 512by 512 pixels, were obtained from three test subjects us-ing a variety of OCT imaging techniques. One techniqueproduced a high contrast edge of the epithelium layer, lo-cated at cornea to air interface. The focus of the tomogramwas centered at this point, which produced a high contrastepithelium layer, but a low contrast endothelium layer. Asecond technique inverted the corneal image by focusingon the endothelium layer. Since the refraction index dif-fered for each layer boundary, the second method producedmedium contrast for both the endothelium and epitheliumlayers. The other, less preferable, imaging techniques pro-duced artifacts within the corneal image; they created darkartifacts through the apex of the cornea or vertical whitebands distributed over the entire cornea. These artifacts arethe result of imperfect hardware configurations and causethe visibility of the corneal image to become obstructed.The algorithms are evaluated for images representing eachtype of technique.

In this section, the proposed method, EIS, and IS areevaluated using five representative samples from the dataset that illustrate the various imaging techniques executedduring the data collection process. The segmentation resultswere obtained using a dual core 2.5 GHz computer with 2GB of RAM. The algorithms considered for evaluation areimplemented in Matlab R2008b.

4.3 Segmentation Results

The segmentation result of proposed method, EIS, andIS across five cornea images are shown in Figure 4. Eachcorneal image contains five layer boundaries that must be

segmented so that the thickness of each layer can be mea-sured. In all test images, the proposed approach success-fully extracts the layers of the cornea. The segmentationresults for EIS and IS primarily depend upon the interactioncapability of the user; better results are produced as the usermanually specifies more points. Both EIS and IS requireabout 10 to 15 minutes for the manual user input for eachimage to produce the level of accuracy shown in Figure 4.

To evaluate the accuracy of the algorithms, the groundtruth for each image is specified by manually selectingpoints on each layer boundary. This process requires about15 minutes of manual user input to specify over 100 pointsfor each image. The algorithms are evaluated by how closethe segmented boundaries are to the ground truth. For eachpoint along the ground truth boundary, the shortest distancebetween the ground truth and the segmentation result is cal-culated. The average distance and standard deviation iscomputed for each layer. The results are summarized inFigure 5.

On average, the proposed algorithm successfully locatesthe layer boundary within 1.5 pixels of the manually speci-fied ground truth. This algorithm typically requires the userto specify only 4 points. In addition, when acquiring statis-tics, about 800 images were segmented using less than 20seconds worth of manual user input per image. The amountof user interaction required to obtain the level of accuracypermits large numbers of corneal measurements to be ob-tained in sufficiently less time than is required for manualsegmentation.

The use of the EIS to outline the cornea and model of thevarious layers allows the proposed algorithm to be capableof greater accuracy than fully-automated algorithms by ac-commodating significant amounts of noise. For the testssets with the greatest number of artifacts, image #1 andimage #3, the maximum deviation of the generated bound-aries is within 4 pixels of the manually specified boundaries.In addition, the algorithm also performs well for low con-trast regions, such as image #5.

When compared to the other methods, the proposed algo-rithm produces boundaries that are closer to the ground truththan those produced by EIS or IS. The standard deviationfor the proposed algorithm is also less, indicating a moreconsistent boundary over the entire image. Although allmethods perform well for the higher contrast layer bound-aries (the epithelium and endothelium), the proposed algo-rithm performs significantly better than EIS and IS for themiddle layers, as shown in Figure 5. The proposed algo-rithm provides a smoother curve that is less prone to noiseand artifacts present in many of the images, as shown in Fig-ure 4. The proposed method also requires significantly lessuser interaction. As a consequence, more accurate bound-aries can be measured from minimal user input.

Proposed method EIS [12] IS [5]

Figure 4. Demonstration of the performance of proposed method compared to other published meth-ods across five cornea images. Column 1: results obtained using proposed approach. Column 2-3:results obtained using enhanced intelligent scissor (EIS) and intelligent scissor (IS). From top tobottom the images contain the following artifacts: multiple white bands distributed over the entireimage, a single white band on the left side of the image, a dark artifact located at the apex of theepithelium layer, typical image with good contrast, and typical image with very low contrast.

Figure 5. Performance index of proposed approach compared to enhanced intelligent scissor (EIS)and intelligent scissor (IS). The layers 1-5 corresponds to epithelium, Bowman’s membrane, stroma,Descemet’s membrane and the endothelium layers of the cornea respectively. The proposed algo-rithm performs as well or better than EIS and IS for all layers and images in the test set. Level set(LS) and Gradient vector flow based snake (GVFS) are not shown because their errors exceeded 200pixels.

5 Conclusion and Future work

This paper establishes and evaluates a novel algorithmfor segmentation of the layers of the cornea. The algorithmaccurately determines layer boundaries of the cornea im-ages for a variety of corneal imaging techniques. For im-ages with large numbers of artifacts, on average, the algo-rithm is able to determine the boundaries to be within 1.5pixels of the actual boundaries. The proposed algorithmis able to produce these results with significantly less userinput than fully manual segmentation. The proposed algo-rithm is capable of segmenting images with large artifactsor speckle noise. The use of a corneal model and minimaluser input allows the cornea to be segmented without ex-plicitly denoising the image. Consequently, the algorithmis robust to low signal to noise ratios. Future work will at-tempt to fully automate the segmentation process and willconsider additional parameters, such as scale and rotation,to improve the local optimization process when fitting thespline boundaries to the image data.

6 Acknowledgement

This research has been sponsored by the Natural Sci-ences and Engineering Research Council (NSERC) ofCanada through individual Discovery Grants as well asGEOIDE (GEOmatics for Informed Decisions) which is aNetwork of Centres of Excellence under NSERC.

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