research article obtaining thickness maps of corneal...

Research ArticleObtaining Thickness Maps of Corneal Layers Usingthe Optimal Algorithm for Intracorneal Layer Segmentation

Hossein Rabbani1 Rahele Kafieh1 Mahdi Kazemian Jahromi1 Sahar Jorjandi2

Alireza Mehri Dehnavi1 Fedra Hajizadeh3 and Alireza Peyman4

1Department of Bioelectrics and Biomedical Engineering School of Advanced Technologies in MedicineMedical Image and Signal Processing Research Center Isfahan University of Medical Sciences Isfahan 8174673461 Iran2Student Research Center School of Advanced Technologies in Medicine Isfahan University of Medical SciencesIsfahan 8174673461 Iran3Noor Ophthalmology Research Center Noor Eye Hospital Tehran 1968653111 Iran4Isfahan University of Medical Sciences Isfahan 817467346 Iran

Correspondence should be addressed to Rahele Kafieh r kafiehyahoocom

Received 30 November 2015 Revised 11 March 2016 Accepted 6 April 2016

Academic Editor Richard H Bayford

Copyright copy 2016 Hossein Rabbani et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Optical Coherence Tomography (OCT) is one of the most informative methodologies in ophthalmology and provides crosssectional images from anterior and posterior segments of the eye Corneal diseases can be diagnosed by these images and cornealthickness maps can also assist in the treatment and diagnosis The need for automatic segmentation of cross sectional images isinevitable since manual segmentation is time consuming and imprecise In this paper segmentation methods such as GaussianMixture Model (GMM) Graph Cut and Level Set are used for automatic segmentation of three clinically important corneal layerboundaries on OCT images Using the segmentation of the boundaries in three-dimensional corneal data we obtained thicknessmaps of the layers which are created by these borders Mean and standard deviation of the thickness values for normal subjects inepithelial stromal and whole cornea are calculated in central superior inferior nasal and temporal zones (centered on the centerof pupil) To evaluate our approach the automatic boundary results are compared with the boundaries segmented manually by twocorneal specialists The quantitative results show that GMMmethod segments the desired boundaries with the best accuracy

1 Introduction

Optical Coherence Tomography (OCT) is one of the mostinformative methodologies in ophthalmology today It worksnoninvasively has no contact and provides cross sectionalimages from anterior and posterior segments of the eyeImaging of the anterior segment is needed in refractivesurgery and contact lens implantation [1]

Cornea was first imaged by OCT in 1994 [2] withsimilar wavelength of the light as retina (830 nm) A longerwavelength of 1310 nm with advantage of better penetrationthrough sclera as well as real-time imaging at 8 frames persecond was proposed in 2001 [3] Specific systems for visual-ization of anterior eye (anterior segment OCT ASOCT) were

commercially available in 2011 [4] and there are three mainproducers for this device SL-OCT (Heidelberg Engineering)the Visante (Carl Zeiss Meditec Inc) and CASIA (TomeyTokyo Japan) Furthermore many devices based on Fourierdomain OCT (FDOCT) obtain images from both anteriorand posterior segments using the shorter wavelength of 830ndash870 nm The main competitor device to OCT in AS imagingis ultrasound biomicroscopy (UBM) The UBM method canvisualize some anatomical structures posterior to iris on theother hand good quality of the images in thismethod is reallydependant on the operatorrsquos skill [5]

The adult cornea is approximately 05 millimeter thickat the center and it gradually increases in thickness towardthe periphery The human cornea is comprised of five layers

Hindawi Publishing CorporationInternational Journal of Biomedical ImagingVolume 2016 Article ID 1420230 11 pageshttpdxdoiorg10115520161420230

2 International Journal of Biomedical Imaging

Epithelium Bowmanrsquos membrane stroma Descemetrsquos mem-brane and the Endothelium [5]

Some corneal diseases need to be diagnosed by preciseevaluation of subcorneal layers A good example for needof thickness mapping in subcorneal layers is diseases likeKeratoconus In this illness the thickness of the Epitheliumbecomes altered to reduce corneal surface irregularity [6] Asa result the presence of an irregular stroma cannot be diag-nosed by observing the thickness map of the whole corneaTherefore analysis of epithelial and stromal thicknesses andshapes separately can improve the diagnosis [7 8]

Several methods like confocal microscopy ultrasoundand OCT have already been used to measure the cornealepithelial thicknessThe average central Epithelium thicknessis used in many studies [9ndash12] Very high-frequency ultra-sound is used to map the corneal Epithelium and stromalthickness [7] The mentioned two methods had their draw-backs namely confocal microscopy is an invasive methodand ultrasound method needs immersion of the eye in acoupling fluid [7 13ndash16]

Accurate segmentation of corneal boundaries is necessaryfor production of correct thickness maps An error of severalmicrometers can lead towrong diagnosisThe large volume ofthese data in clinical evaluation makes manual segmentationtime consuming and impractical [17ndash19]

Current methods for segmentation of cornea can besummarized as below

Graglia et al [20] proposed an approach for contourdetection algorithm for finding Epithelium and Endotheliumpoints and tracing the contour of the cornea pixel by pixelfrom these two points with a weight criterion Eichel etal [21] proposed a semiautomated segmentation algorithmfor extraction of five corneal boundaries using a globaloptimizationmethod Li et al [22ndash24] proposed an automaticmethod for corneal segmentation using a combination of fastactive contour (FAC) and second-order polynomial fittingalgorithm Eichel et al [18 25] proposed a semiautomaticmethod for corneal segmentation by utilizing EnhancedIntelligent Scissors (EIS) and user interaction Shen et al [26]used a threshold-based technique which failed in segmen-tation of posterior surface of the cornea In Williams et alrsquosstudy [27] Level Set segmentation is investigated to obtaingood results with low speed LaRocca et al [19] proposed anautomatic algorithm to segment boundaries of three corneallayers using graph theory and dynamic programming Thismethod segments three clinically important corneal layerboundaries (Epithelium Bowman and Endothelium) Theirresults had good agreement with manual observers only forthe central region of the cornea where the highest signal tonoise ratio was found A 3D approach is also proposed byRobles et al [28] to segment three main corneal boundariesby graph-based method In a more recent work by Williamset al [29] a Graph Cut based segmentation technique isproposed to improve the speed and efficiency of the segmen-tation Previous methods were never a perfect method forsegmentation Some of them suffered from low number ofcorneal images for testing and others lacked precision in lowcontrast to noise ratios Furthermore none of previous worksdemonstrated a thicknessmap of corneal region for sublayers

(a)

(b)

(c)

Figure 1 Examples of corneal images of varying signal to noise ratio(SNR) used in this study (a) High SNR corneal image (b) Low SNRcorneal image (c) Corneal image with central artifact

In this paper we segment the boundaries of corneallayers by utilizing Graph Cut (GC) Gaussian MixtureModel (GMM) and Level Set (LS) methods We evaluatethe performance of segmenting Epithelium Bowman andEndothelium boundaries in OCT images using these seg-mentation methods Finally using the extracted boundariesof 3D corneal data the 3D thickness maps of each layer areobtained

The OCT images captured from high-tech devices mayhave high SNR (Figure 1(a)) but in many cases they have alow SNR (Figure 1(b)) Furthermore some of OCT imagesmay be affected by different types of artifact like centralartifact (Figure 1(c)) The central artifact is the verticalsaturation artifact that occurs around the center of the corneadue to the back-reflections from the corneal apex whichsaturates the spectrometer line camera [19]

2 Theory of Algorithms

In this section we explain the theory of GMM GC and LSalgorithms

21 GMM As we explained in [30] GMM can be usedfor modeling of cornea layers in OCT images For 119863-dimensional Gaussian random vector with mean vector

119894

and covariance matrix Σ119894given below

119887119894 ()

=1

(2120587)1198632 1003816100381610038161003816Σ119894

1003816100381610038161003816

12exp minus1

2( minus

119894)1015840Σminus1

119894( minus

119894)

(1)

International Journal of Biomedical Imaging 3

a weighted mixture of119872 Gaussian distribution would be

119901 ( | 120582) =

119872

sum

119894=1

119901119894119887119894 () (2)

where 119901119894s are the weights of mixture components and

119872

sum

119894=1

119901119894= 1 (3)

Parameters of GMM 120582 = 120583119894 119901119894 Σ119894 are calculated using

iterative expectationmaximization (EM) algorithmas follows(for 119879 training vectors)

119901 (119894 | 119905 120582) =

119901119894119887119894(119905)

sum119872

119896=1119901119896119887119896(119905)

(4)

119901119894=1

119879

119879

sum

119905=1

119901 (119894 | 119905 120582) (5)

997888rarr120583119894=sum119879

119905=1119901 (119894 |

119905 120582) 119905

sum119879

119905=1119901 (119894 |

119905 120582)

(6)

120590119894

2=sum119879

119905=1119901 (119894 |

119905 120582) 119905

2

sum119879

119905=1119901 (119894 |

119905 120582)

minus 119894

2 (7)

22 GC We use normalized cuts for segmentation which isexplained by Shi andMalik [31]This criterionmeasures boththe total dissimilarity between the different groups and thetotal similarity within the groups Suppose we have a graph119866 = (119881 119864) which is composed of two distinct parts of 119860 119861and easily achieved by removing edges between these twosectors and has the following property 119860 119861 119860 cup 119861 = 119881119860 cap 119861 = 120601 Based on the total weight of the edges that areremoved we can calculate the degree of dissimilarity betweenthese two parts which is called cut

cut (119860 119861) = sum

119906isin119860Visin119861119908 (119906 V) (8)

where119908(119906 V) is the edge weight between nodes 119906 and V Herethe graph is divided into two subsections in such a way thatthe total weight of edges connecting these two parts is smallerthan any other division Instead of looking at the value of totaledge weight connecting the two partitions the cut cost as afraction of the total edge connections will be computed to allthe nodes in the graph which is called normalized cut (Ncut)

Ncut (119860 119861) = cut (119860 119861)assoc (119860 119881)

+cut (119860 119861)assoc (119861 119881)

(9)

where assoc(119860 119881) = sum119906isin119860119905isin119881

119908(119906 119905) is the total connectionfrom nodes in 119860 to all nodes in the graph and assoc(119861 119881)is similarly defined Optimal cut is the cut which minimizesthese criteria In other words minimizing the dissimilarity ofthe two subsections is equal to the maximizing of similaritywithin each subsection

Suppose there is an optimal decomposition of a graphwith vertices 119881 to the components 119860 and 119861 based on the

criteria of the optimal cut Consider the following generalizedeigenvalue problem

(119863 minus119882)119910 = 120582119863119910 (10)

where119863 is an119873 times119873 diagonal matrix with 119889 on its diagonal119889(119894) = sum

119895119908(119894 119895) is the total connection from node 119894 to

all other nodes and 119882 is an 119873 times 119873 symmetrical matrixwhich contains the edge weights We solve this equationfor eigenvectors with the smallest eigenvalues Then theeigenvector with the second smallest eigenvalue is used tobipartition the graph The divided parts if necessary will bedivided again

This algorithm has also been used in the processing offundus images [32 33]

23 LS Li et al [34] presented a LSmethod for segmentationin the presence of intensity inhomogeneities Suppose thatΩis the image domain and 119868 Ω rarr 119877 is a gray level image andalso Ω = cup

119873

119894=1Ω119894 Ω119894cap Ω119895= 0 rarr 119894 = 119895 The image can be

modeled as

119868 = 119887119869 + 119899 (11)

where 119869 is the true image 119887 is the component that accounts forthe intensity inhomogeneity and 119899 is additive noise For thelocal intensity clustering consider a circular neighborhoodwith a radius 120588 centered at each point 119910 isin Ω defined by119874119910≜ 119909 |119909 minus 119910| le 120588 The partition Ω

119894119873

119894=1of Ω induces

a partition of the neighborhood119874119910 Therefore the intensities

in the set 119868119894119910= 119868(119909) 119909 isin 119874

119910cap Ω119894 form the clusters where

119868(119909) is the image model Now we define a clustering criterion120576119910for classifying the intensities in 119874

119910 We need to jointly

minimize 120576119910for all 119910 inΩ which is achievable by minimizing

the integral of 120576119910with respect to 119910 over the image domainΩ

So the energy formulation is as below

120576 = int 120576119910119889119910 (12)

It is difficult to solve the expression 120576 to minimize the energyTherefore we express the energy as LS function LS functionis a function that takes positive and negative signs which canbe used to represent a partition of the domainΩ Suppose 120601 Ω rarr 119877 is a Level Set function For example for two disjointregions

Ω1= 119909 120601 (119909) gt 0

Ω2= 119909 120601 (119909) lt 0

(13)

For the case of119873 gt 2 two or more LS functions can be usedto represent 119873 regions Ω

1 Ω

119873 Now we formulate the

expression 120576 as a Level Set function

120576 = int

119873

sum

119894=1

(int119896 (119910 minus 119909)1003816100381610038161003816119868 (119909) minus 119887 (119910) 119888119894

1003816100381610038161003816

2119889119910)

sdot 119872119894(120601 (119909)) 119889119909

(14)


Figure 2 An example of segmented corneal image The Epitheliumboundary (cyan) the Bowman boundary (red) and the Endothe-lium boundary (green)

where 119872119894(120601) is a membership function For example for

119873 = 2 1198721(120601) = 119867(120601) 119872

2(120601) = 1 minus 119867(120601) and 119867 is the

Heaviside function 119888119894is a constant in each subregion and

119896 is the kernel function defined as a Gaussian function withstandard deviation 120590 This energy is used as the data term inthe energy of the proposed variational LS formulation whichis defined by

F (120601 c 119887) = 120576 (120601 c 119887) + ]L (120601) + 120583R119901(120601) (15)

where L(120601) and R119901(120601) are the regularization terms By

minimizing this energy the segmentation results will beobtained This is achieved by an iterative process As a resultthe LS function encompasses the desired region


3 Segmentation of Intracorneal Layers

The important corneal layers that is Epithelium Bowmanand Endothelium are shown in Figure 2

For production of thickness maps after preprocessingthe implementation method for segmenting the desired

(a)

(b)

Figure 3 (a) Original image (b) Denoised image using a Gaussiankernel [1 times 30] (std of 10)

boundaries using GMM GC and LS is investigated andthe best segmentation method is chosen Finally using thesegmentation results of all B-scans the intracorneal thicknessmaps are produced

31 Preprocessing Duo to the noise of the images andtheir low contrast a preprocessing stage is proposed Thenthe mentioned algorithms are applied for segmenting theboundaries of Epithelium Bowman and Endothelium layers

311 Noise Reduction The presence of noise in the OCTimages causes errors in the final segmentation To overcomethis problem we apply a low-pass filter via a Gaussian kernelto minimize the effect of noise The kernel size of this filterwhich is going to be applied on OCT images and used asGMM inputs is [1 times 30] with std of 10 These kernel sizes inLS and GC are [1 times 20] (std of 203) and [1 times 5] (std of 53)respectivelyThe selected kernel sizes lead to uniformity of theimage noise and prevent oversegmentation These values forthe kernel sizes and stds are obtained based on trial and errorto have best results Figure 3 shows an example of denoisingstep

312 Contrast Enhancement OCT images usually have lowcontrast and we will be faced with a problem of segment-ing the boundaries (especially the Bowman boundary) Toenhance the contrast we modified a method proposed byEsmaeili et al [37] where each pixel 119891(119894 119895) of image ismodified as follows

119892 (119894 119895) = 2 times 119891 (119894 119895) minus 2 times 119891mean (119908)

+ (100 times 119891min (119894 119895)

119891max (119894 119895) + 1)

(16)

where 119891mean 119891min(119894 119895) and 119891max(119894 119895) are respectively themeanminimum andmaximum intensity values of the imagewithin the square 10 times 10 window around each pixel (119894 119895)Figure 4 shows an example of this process As we can see


(a)

(b)

Figure 4 Contrast enhancement of original image for segmentationof Bowman boundary (a) Original image (b) The enhanced image

Figure 5 An example of central artifact positioning

using this method nonuniform background is corrected ontop of contrast enhancement

313 Central Artifact One of the most important artifactsin corneal OCT images is the central artifact that overcastcorneal boundaries So reducing its effect causes the algo-rithm to be more successful This artifact is nonuniform andwe implement an algorithm that is robust to variations inwidth intensity and location of the central artifact At first tofind abrupt changes in the average intensity we accentuate thecentral artifact by median filtering the image with a [40 times 2]kernel Then we break the image into three equal widthregions and suppose that the second region contains thecentral artifact In the next step we plot the average intensityof columns of the middle region After that we look for thecolumn where the difference intensity between this columnand its previous column is more than 6 Figure 5 shows anexample of central artifact positioning

32 Segmentation of Three Corneal Layer Boundarieswith GMM

321 Segmenting the Boundaries of Epithelium and Endothe-lium Layers To obtain these two boundaries we first reducethe image noise using the method introduced in Section 311Then we give the denoised image to the GMM algorithmActually we use univariate distribution for image intensitiesand 2 components where one of themmodels the backgroundand the next one models the main information between

(a)

(b)

(c)

(d)

(e)

Figure 6 Segmentation of Epithelium and Endothelium bound-aries (a) GMM output This is the image used for segmentationof desirable boundaries (b) Segmentation result before correction(c) Zoomed results of extracted Epithelium before correction(d) Epithelium boundary after correction (e) Zoomed results ofextracted Epithelium after correction

Epithelium and Endothelium layers Figure 6 shows the finalresult of GMM-based segmentation We can see the approx-imate location of Epithelium and Endothelium boundarieswhich is obtained by choosingmaximumresponsibility factorin (4) and curve fitting to the boundaries As it can be seen inFigure 6(c) the detected boundary is not exactly fitted to theborder of Epithelium So the horizontal gradient of originalimage is calculated with help of the current boundary choos-ing the lowest gradient in a small neighborhood (Figure 6)

322 Correction of Low SNR Regions As we can see inFigure 6 the obtained Endothelium boundary in peripheralregions is not accurate because the SNR is low in these areasSo extrapolation of central curve in these low SNR regionsis proposed By taking the second derivative of Endotheliumboundary and searching around the middle of this vector thevalues below zero are found It is observed that for low SNRregions there is a positive inflection in the second derivativeAfter finding the location of this positive inflection by findingthe coefficients of best polynomial of degree 4 fitted to correctestimated border a parabolic curve is obtained to estimate theEndothelium boundary in low SNR areas To have a smooth


0 100 200 300 400 500 600 700

0minus0005minus001minus0015minus002minus0025

000500100150020025

(a)

(b)

Figure 7 Extrapolation to low SNR regions (a) The secondderivative plot of Endothelium layer boundary to detect low SNRregions of this boundary (b) Extrapolation result

(a)

(b)

Figure 8 Segmentation of Bowman layer boundary (a) Horizontalgradient of the enhanced image (b) Final Bowman layer segmenta-tion result

enough curve for the final Endothelium boundary a localregression using weighted linear least squares that assignslower weight to outliers is used Figure 7 shows an exampleof extrapolation of low SNR regions using this method

323 Bowman Layer Segmentation Since in most cases theBowman boundary is very weak we first enhance this bound-ary employing the contrast enhancement method explainedin Section 312 After enhancement the horizontal edges areobtained by applying Sobel gradient Figure 8 shows thisprocedure which can extract the Bowman boundary Sincewe have obtained the Epithelium boundary (as describedin Section 31) the Bowman boundary can be obtained bytracing Epithelium toward down to get a white to blackchange in brightness However unlike themiddle of the Bow-man boundary the periphery may be corrupted by noise Toovercome this problem similar to the proposed extrapolationmethod for low SNR areas in previous subsection the outliersare corrected

(a)

(b)

Figure 9 (a) Primary segmentation of Epithelium boundary thathas failed in the central artifact (b) The corrected Epitheliumboundary

(a)

(b)

Figure 10 (a) Output of Level Set (b)The estimated Epithelium andEndothelium boundaries

324 Interpolation into the Central Artifact Location Centralartifact causes the estimated boundary to be imprecise So wefirst find the artifact location with the method elaborated inSection 313 and then we make a linear interpolation on theestimated boundary in this location as shown in Figure 9

33 Segmentation of Three Corneal Layer Boundaries with LS

331 Segmenting the Boundaries of Epithelium and Endothe-lium Layers To obtain these boundaries we first denoise theimages according to the method described in Section 311then the LS algorithm is applied to the denoised image Theparameters are configured in this way suppose 119860 is equal to255 then ] = 001 times 1198602 120590 = 5 and 120583 = 1 The final result ofLS shows the approximate location of these two boundariesExtrapolation and interpolation are performed according towhat we explained for GMM (Figure 10)

332 Segmenting the Boundary of Bowman Layer For thispurpose to have an enhanced Bowman boundary the pre-sented contrast enhancement method in Section 312 isperformed In the next step we apply LS to this imagewith ] =


(a)

(b)

Figure 11 (a) Output of Level Set (b) The estimated Bowmanboundary

(a)

(b)

Figure 12 (a) Output of Graph Cut (b) The estimated boundaries

0001 times 1198602 and there is no change in other parameters This

value causes segmentation ofmuchmore details in particularBowman boundary Figure 11(a) is the output of LS and usingthis image we can localize the Bowman boundary similarto what we did in GMM Bowman boundary can be finallydetected with the help of Epithelium boundary (Figure 11(b))

34 Segmentation ofThree Corneal Layer Boundaries with GC

341 Segmenting the Boundaries of Epithelium and Endothe-lium Layers To obtain these boundaries we first denoise theimages according to the proposed method in Section 311Then we apply GC considering the cutting area of 10Figure 12(a) shows the output image and we can achievethe desired boundaries by looking for a change in intensitystarting from the first row and the last oneThe extrapolationto low SNR regions and interpolation for the central artifactare like what was performed for GMM

342 Segmenting the Boundary of Bowman Layer For thispurpose similar to other two algorithms we first enhance theoriginal image In the next step we flatten this image basedon the obtained Epithelium boundary from the previous step

(a)

(b)

Figure 13 (a)Themethod to flattening the image using a horizontalline and Epithelium boundary (b) Flat image

(a)

(b)

Figure 14 (a) Output of Graph Cut for the restricted area to theBowman boundary (b) Bowman boundary estimation in themiddlebased on the Epithelium boundary

and with respect to a horizontal line as shown in Figure 13(a)The flattening algorithm works by shifting the pixel positionswhich are under the Epithelium boundary to be fitted on ahorizontal line (Figure 13(b)) The Bowman boundary can betracked better in horizontal setup Applying the algorithm tothe entire flattened image is both time consuming and lessreliable So the image is divided into three parts and thealgorithm is applied to the restricted area to the Bowmanboundary and based on the Epithelium boundary the desiredboundary is achieved (Figure 14) The estimated boundary inthemiddle area is accurate and the linear extrapolation of thisboundary to the image width is then performed as shown inFigure 15 (the estimated boundaries in the two other partsusually are not accurate)

4 Three-Dimensional Thickness Maps ofCorneal Layers

In the previous section 3 methods for intracorneal layersegmentation were explained In this section these methods


(a) (b)

Figure 15 (a) Linear extrapolation of estimated Bowman boundary in the middle of the image (b) Final result of Bowman boundarysegmentation

Table 1 Mean and standard deviation of unsigned error in corneallayer boundary segmentation between automatic and manual seg-mentation using GMM

Corneal layer boundary Mean difference(120583m)

Standard deviation(120583m)

Epithelium boundary 299464 20746Bowman boundary 379742 289542Endothelium boundary 71709 674696

are compared and the best one is picked to produce theintracorneal thickness maps by employing the segmentationresults of all B-scans

41 Comparing Segmentation Results of GMM LS and GCMethods In this study we used corneal OCT images takenfrom 15 normal subjects Each 3D OCT includes 40 B-scans of the whole cornea The images were taken from theHeidelberg OCT-Spectralis HRA imaging system in NOORophthalmology center Tehran To evaluate the robustnessand accuracy of the proposed algorithms we use manualsegmentation by two corneal specialists For this purpose20 images were selected randomly from all subjects Wecalculated the unsigned and signed error of each algorithmagainst manual results

The boundaries were segmented automatically using aMATLAB (R2011a) implementation of our algorithm Acomputer with Microsoft Windows 7 x32 edition intel corei5 CPU at 25 GHZ 6GB RAM was used for the processingThe average computation times for GMM LS and GC were799 1938 and 17022 seconds per image respectively Themean and std of unsigned and signed error of the mentionedalgorithms were calculated and are shown in Tables 1ndash6 Themean and std of unsigned error are defined as follows

119898error = mean(119899

sum

119894=1

1003816100381610038161003816119887manual (119894) minus 119887auto (119894)1003816100381610038161003816)

120590error

= standard deviation(119899

sum

119894=1


(17)

where119898error and 120590error are themean and std of unsigned errorbetween manual and automatic methods 119899 is the numberof points to calculate the layer error (width of the image)

Table 2 Mean and standard deviation of signed error in corneallayer boundary segmentation between automatic and manual seg-mentation using GMM




Table 3 Mean and standard deviation of unsigned error in corneallayer boundary segmentation between automatic and manual seg-mentation using level set




Table 4 Mean and standard deviation of signed error in corneallayer boundary segmentation between automatic and manual seg-mentation using level set



Epithelium boundary minus322014 325622Bowman boundary minus56375 470844Endothelium boundary minus014432 869528

and 119887manual and 119887auto are the boundary layers which areobtained manually and automatically respectively The meanvalue of manual segmentation by two independent cornealspecialists is considered as 119887manual in the above equationsand the interobserver errors are also provided in Tables 1ndash6 The direct comparison of these values with the reportederrors shows that the performance of GMM algorithm ismore acceptable in comparison with manual segmentation

With study of the presented results such as the lowersegmentation error for each of the layer boundaries and timespent for segmenting the borders it is observed that GMMmethod compared to the position differences between twoexpert manual graders (Table 7) give better results comparedwith two other methods


Table 5 Mean and standard deviation of unsigned error in corneal layer boundary segmentation between automatic and manualsegmentation using graph cut




Table 6 Mean and standard deviation of signed error in corneallayer boundary segmentation between automatic and manual seg-mentation using graph cut



Epithelium boundary minus276012 334642Bowman boundary minus032472 655754Endothelium boundary 718894 79376

Table 7 The position differences between the two expert manualgraders




42 Producing Intracorneal Thickness Maps According towhat is described above GMM was selected as the optimalmethod for segmentation of corneal layers Therefore usingGMMmethod the corneal layer boundaries in the volumet-ric images of each subject are segmented The segmentedvalues are then interpolated (as described below) to create thethickness maps To illustrate the layer thickness we first sub-tract the boundaries which create a layer and an interpolationis performed between two consecutive volumetric imagesThe number of pixels between two successive images forinterpolation is calculated as shown in Figure 16 Consideringpixel values of 119862 and 119883 the equation between 119862 and 119861 andscale signs in right and left images the value pixels whichcorrespond to of 119860 can be found This value () should beused in interpolation and the number of interpolation pixelsis equal to number of slices It can be shown that the OCTslices cover an area of 6 millimeters in width and heightFigure 17 shows the 3D thickness maps of corneal layers ofa normal subject

Mean and standard deviation of the thickness values fornormal subjects in epithelial stromal and whole cornea arecalculated in central superior inferior nasal and temporalzones (cantered on the centre of pupil)The zones are definedin concentric circles with diameters equal to 2 and 5 millime-ters (Figure 17(c)) The thickness averages (plusmnpopulation SD)are shown in Table 8

B

A

C

X

Figure 16 The method to calculate the number of pixels forinterpolation

Table 8

Corneal layers Central Superior Inferior Nasal TemporalEpithelial layerAverages 429352 436568 429352 41943 439274SD 42394 29766 93808 65846 3157

Stromal layerAverages 4632672 4819386 5072848 4883428 497904SD 337348 38335 389664 321112 376134

Whole corneaAverages 4899664 5292034 5350664 5298348 5346154SD 393272 439274 381546 348172 375232

5 Conclusion

In this paper we compared three different segmentationmethods for segmentation of three important corneal layersof normal eyes using OCT devices According to goodperformance of the GMM method in this application wechose GMM as the optimal method to calculate the bound-aries The proposed method is able to eliminate the artifactsand is capable of automatic segmentation of three cornealboundaries

In the next step we obtained the thickness maps ofcorneal layers by interpolating the layer information Meanand standard deviation of the thickness values in epithelialstromal and whole cornea are calculated in 3 central supe-rior and inferior zones (cantered on the centre of pupil)To the best of our knowledge this is the first work to findthe thickness maps from a set of parallel B-scans and all ofthe previous methods in construction of thickness map fromOCT data use pachymetry scan pattern [13 14 16]

Competing Interests

The authors declare that they have no competing interests


50

25

0(a)

300

150

0(b)

350

200

0700600500400300200100

700

600

500

400

300

200

100

NasalTemporal

Superior

Inferior

Central

(c)

Figure 17 3D thicknessmaps of a normal subject (a)Whole cornea (b) layer 1 (c) the layer created by Bowman andEndotheliumboundaries(the zones are defined in concentric circles with diameters equal to 2 and 5 millimeters as central superior inferior nasal and temporalzones)

References

[1] V Hurmeric S H Yoo and F M Mutlu ldquoOptical coherencetomography in cornea and refractive surgeryrdquo Expert Review ofOphthalmology vol 7 no 3 pp 241ndash250 2012

[2] J A Izatt M R Hee E A Swanson et al ldquoMicrometer-scaleresolution imaging of the anterior eye in vivo with opticalcoherence tomographyrdquoArchives of Ophthalmology vol 112 no12 pp 1584ndash1589 1994

[3] S Radhakrishnan A M Rollins J E Roth et al ldquoReal-time optical coherence tomography of the anterior segment at1310 nmrdquo Archives of Ophthalmology vol 119 no 8 pp 1179ndash1185 2001

[4] httpeyewikiaaoorgAnterior Segment Optical CoherenceTomographyTechnology

[5] httpsneinihgovhealthcornealdisease

[6] D Z Reinstein M Gobbe T J Archer R H Silverman andJ Coleman ldquoEpithelial stromal and total corneal thickness inkeratoconus three-dimensional display with artemis very-highfrequency digital ultrasoundrdquo Journal of Refractive Surgery vol26 no 4 pp 259ndash271 2010

[7] Y Li O Tan R Brass J L Weiss and D Huang ldquoCornealepithelial thickness mapping by fourier-domain optical coher-ence tomography in normal and keratoconic eyesrdquoOphthalmol-ogy vol 119 no 12 pp 2425ndash2433 2012

[8] C Temstet O Sandali N Bouheraoua et al ldquoCorneal epithe-lial thickness mapping by fourier-domain optical coherencetomography in normal keratoconic and forme fruste kerato-conus eyesrdquo Investigative Ophthalmology amp Visual Science vol55 pp 2455ndash2455 2014

[9] H F Li W M Petroll T Moslashller-Pedersen J K Maurer HD Cavanagh and J V Jester ldquoEpithelial and corneal thicknessmeasurements by in vivo confocal microscopy through focus-ing (CMTF)rdquo Current Eye Research vol 16 no 3 pp 214ndash2211997

[10] J C Erie S V Patel J W McLaren et al ldquoEffect of myopiclaser in situ keratomileusis on epithelial and stromal thicknessa confocalmicroscopy studyrdquoOphthalmology vol 109 no 8 pp1447ndash1452 2002

[11] S Sin and T L Simpson ldquoThe repeatability of corneal andcorneal epithelial thickness measurements using optical coher-ence tomographyrdquo Optometry amp Vision Science vol 83 no 6pp 360ndash365 2006


[12] J Wang D Fonn T L Simpson and L Jones ldquoThe measure-ment of corneal epithelial thickness in response to hypoxiausing optical coherence tomographyrdquo American Journal ofOphthalmology vol 133 no 3 pp 315ndash319 2002

[13] S Haque L Jones and T Simpson ldquoThickness mapping of thecornea and epithelium using optical coherence tomographyrdquoOptometry amp Vision Science vol 85 no 10 pp E963ndashE9762008

[14] Y Li O Tan and D Huang ldquoNormal and keratoconic cornealepithelial thickness mapping using Fourier-domain opticalcoherence tomographyrdquo in Medical Imaging 2011 BiomedicalApplications in Molecular Structural and Functional Imaging796508 vol 7965 6 pages March 2011

[15] D Alberto and R Garello ldquoCorneal sublayers thickness esti-mation obtained by high-resolution FD-OCTrdquo InternationalJournal of Biomedical Imaging vol 2013 Article ID 989624 7pages 2013

[16] W Zhou and A Stojanovic ldquoComparison of corneal epithelialand stromal thickness distributions between eyes with kerato-conus and healthy eyes with corneal astigmatism ge 20Drdquo PLoSONE vol 9 no 1 Article ID e85994 2014

[17] D W DelMonte and T Kim ldquoAnatomy and physiology of thecorneardquo Journal of Cataract and Refractive Surgery vol 37 no3 pp 588ndash598 2011

[18] J A Eichel A K Mishra D A Clausi P W Fieguth and K KBizheva ldquoA novel algorithm for extraction of the layers of thecorneardquo in Proceedings of the Canadian Conference on ComputerandRobotVision (CRV rsquo09) pp 313ndash320 Kelowna CanadaMay2009

[19] F LaRocca S J Chiu R P McNabb A N Kuo J A Izattand S Farsiu ldquoRobust automatic segmentation of corneal layerboundaries in SDOCT images using graph theory and dynamicprogrammingrdquoBiomedicalOptics Express vol 2 no 6 pp 1524ndash1538 2011

[20] F Graglia J-L Mari G Baikoff and J Sequeira ldquoContourdetection of the cornea fromOCT radial imagesrdquo in Proceedingsof the 29th Annual International Conference of the IEEE Engi-neering in Medicine and Biology Society pp 5612ndash5615 LyonFrance August 2007

[21] J A Eichel A K Mishra P W Fieguth D A Clausi and K KBizheva ldquoA novel algorithm for extraction of the layers of thecorneardquo in Proceedings of the Canadian Conference on Computerand Robot Vision (CRV rsquo09) pp 313ndash320 IEEE 2009

[22] Y Li M V Netto R Shekhar R R Krueger and D HuangldquoA longitudinal study of LASIK flap and stromal thickness withhigh-speed optical coherence tomographyrdquoOphthalmology vol114 no 6 pp 1124ndash1132e1 2007

[23] Y Li R Shekhar and D Huang ldquoSegmentation of 830-and1310-nm LASIK corneal optical coherence tomography images[4684-18]rdquo in Proceedings of the International Society for OpticalEngineering vol 4684 of Proceedings of SPIE pp 167ndash178 SanDiego Calif USA 2002

[24] Y Li R Shekhar and D Huang ldquoCorneal pachymetrymappingwith high-speed optical coherence tomographyrdquo Ophthalmol-ogy vol 113 no 5 pp 792ndash799e2 2006

[25] N Hutchings T L Simpson C Hyun et al ldquoSwelling of thehuman cornea revealed by high-speed ultrahigh-resolutionoptical coherence tomographyrdquo Investigative Ophthalmology ampVisual Science vol 51 no 9 pp 4579ndash4584 2010

[26] M Shen L Cui M Li D Zhu M R Wang and J WangldquoExtended scan depth optical coherence tomography for evalu-ating ocular surface shaperdquo Journal of Biomedical Optics vol 16no 5 Article ID 056007 10 pages 2011

[27] D Williams Y Zheng F Bao and A Elsheikh ldquoAutomatic seg-mentation of anterior segment optical coherence tomographyimagesrdquo Journal of Biomedical Optics vol 18 no 5 Article ID056003 2013

[28] V A Robles B J Antony D R Koehn M G Andersonand M K Garvin ldquo3D graph-based automated segmenta-tion of corneal layers in anterior-segment optical coherencetomography images of micerdquo in Medical Imaging BiomedicalApplications in Molecular Structural and Functional Imagingvol 9038 of Proceedings of SPIE pp 1ndash7 March 2014

[29] D Williams Y Zheng F Bao and A Elsheikh ldquoFast segmenta-tion of anterior segment optical coherence tomography imagesusing graph cutrdquo Eye and Vision vol 2 p 1 2015

[30] M K Jahromi R Kafieh H Rabbani et al ldquoAn automatic algo-rithm for segmentation of the boundaries of corneal layers inoptical coherence tomography images using gaussian mixturemodelrdquo Journal of Medical Signals and Sensors vol 4 article 1712014

[31] J Shi and J Malik ldquoNormalized cuts and image segmentationrdquoIEEE Transactions on Pattern Analysis andMachine Intelligencevol 22 no 8 pp 888ndash905 2000

[32] X Chen M Niemeijer L Zhang K Lee M D Abramoffand M Sonka ldquoThree-dimensional segmentation of fluid-associated abnormalities in retinal OCT probability con-strained graph-search-graph-cutrdquo IEEE Transactions on Medi-cal Imaging vol 31 no 8 pp 1521ndash1531 2012

[33] Z Hu M Niemeijer K Lee M D Abramoff M Sonkaand M K Garvin ldquoAutomated segmentation of the optic discmargin in 3-D optical coherence tomography images usinga graph-theoretic approachrdquo in Medical Imaging BiomedicalApplications in Molecular Structural and Functional Imagingvol 7262 of Proceedings of SPIE pp 1ndash11 February 2009

[34] C Li R Huang Z Ding J Gatenby D N Metaxas and JC Gore ldquoA level set method for image segmentation in thepresence of intensity inhomogeneities with application toMRIrdquoIEEE Transactions on Image Processing vol 20 no 7 pp 2007ndash2016 2011

[35] DWKWong J Liu J H Lim et al ldquoLevel-set based automaticcup-to-disc ratio determination using retinal fundus imagesin ARGALIrdquo in Proceedings of the 30th Annual InternationalConference of the IEEE Engineering in Medicine and BiologySociety (EMBS rsquo08) pp 2266ndash2269 Vancouver Canada August2008

[36] A Yazdanpanah G Hamarneh B R Smith andM V SarunicldquoSegmentation of intra-retinal layers from optical coherencetomography images using an active contour approachrdquo IEEETransactions on Medical Imaging vol 30 no 2 pp 484ndash4962011

[37] M Esmaeili H Rabbani A M Dehnavi and A DehghanildquoAutomatic detection of exudates and optic disk in retinalimages using curvelet transformrdquo IET Image Processing vol 6no 7 pp 1005ndash1013 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Epithelium Bowmanrsquos membrane stroma Descemetrsquos mem-brane and the Endothelium [5]

Some corneal diseases need to be diagnosed by preciseevaluation of subcorneal layers A good example for needof thickness mapping in subcorneal layers is diseases likeKeratoconus In this illness the thickness of the Epitheliumbecomes altered to reduce corneal surface irregularity [6] Asa result the presence of an irregular stroma cannot be diag-nosed by observing the thickness map of the whole corneaTherefore analysis of epithelial and stromal thicknesses andshapes separately can improve the diagnosis [7 8]

Several methods like confocal microscopy ultrasoundand OCT have already been used to measure the cornealepithelial thicknessThe average central Epithelium thicknessis used in many studies [9ndash12] Very high-frequency ultra-sound is used to map the corneal Epithelium and stromalthickness [7] The mentioned two methods had their draw-backs namely confocal microscopy is an invasive methodand ultrasound method needs immersion of the eye in acoupling fluid [7 13ndash16]

Accurate segmentation of corneal boundaries is necessaryfor production of correct thickness maps An error of severalmicrometers can lead towrong diagnosisThe large volume ofthese data in clinical evaluation makes manual segmentationtime consuming and impractical [17ndash19]

Current methods for segmentation of cornea can besummarized as below

Graglia et al [20] proposed an approach for contourdetection algorithm for finding Epithelium and Endotheliumpoints and tracing the contour of the cornea pixel by pixelfrom these two points with a weight criterion Eichel etal [21] proposed a semiautomated segmentation algorithmfor extraction of five corneal boundaries using a globaloptimizationmethod Li et al [22ndash24] proposed an automaticmethod for corneal segmentation using a combination of fastactive contour (FAC) and second-order polynomial fittingalgorithm Eichel et al [18 25] proposed a semiautomaticmethod for corneal segmentation by utilizing EnhancedIntelligent Scissors (EIS) and user interaction Shen et al [26]used a threshold-based technique which failed in segmen-tation of posterior surface of the cornea In Williams et alrsquosstudy [27] Level Set segmentation is investigated to obtaingood results with low speed LaRocca et al [19] proposed anautomatic algorithm to segment boundaries of three corneallayers using graph theory and dynamic programming Thismethod segments three clinically important corneal layerboundaries (Epithelium Bowman and Endothelium) Theirresults had good agreement with manual observers only forthe central region of the cornea where the highest signal tonoise ratio was found A 3D approach is also proposed byRobles et al [28] to segment three main corneal boundariesby graph-based method In a more recent work by Williamset al [29] a Graph Cut based segmentation technique isproposed to improve the speed and efficiency of the segmen-tation Previous methods were never a perfect method forsegmentation Some of them suffered from low number ofcorneal images for testing and others lacked precision in lowcontrast to noise ratios Furthermore none of previous worksdemonstrated a thicknessmap of corneal region for sublayers

(a)

(b)

(c)

Figure 1 Examples of corneal images of varying signal to noise ratio(SNR) used in this study (a) High SNR corneal image (b) Low SNRcorneal image (c) Corneal image with central artifact

In this paper we segment the boundaries of corneallayers by utilizing Graph Cut (GC) Gaussian MixtureModel (GMM) and Level Set (LS) methods We evaluatethe performance of segmenting Epithelium Bowman andEndothelium boundaries in OCT images using these seg-mentation methods Finally using the extracted boundariesof 3D corneal data the 3D thickness maps of each layer areobtained

The OCT images captured from high-tech devices mayhave high SNR (Figure 1(a)) but in many cases they have alow SNR (Figure 1(b)) Furthermore some of OCT imagesmay be affected by different types of artifact like centralartifact (Figure 1(c)) The central artifact is the verticalsaturation artifact that occurs around the center of the corneadue to the back-reflections from the corneal apex whichsaturates the spectrometer line camera [19]

2 Theory of Algorithms

In this section we explain the theory of GMM GC and LSalgorithms

21 GMM As we explained in [30] GMM can be usedfor modeling of cornea layers in OCT images For 119863-dimensional Gaussian random vector with mean vector

119894

and covariance matrix Σ119894given below

119887119894 ()

=1

(2120587)1198632 1003816100381610038161003816Σ119894

1003816100381610038161003816

12exp minus1

2( minus

119894)1015840Σminus1

119894( minus

119894)

(1)



119901 ( | 120582) =

119872

sum

119894=1

119901119894119887119894 () (2)


119872

sum

119894=1

119901119894= 1 (3)



119901 (119894 | 119905 120582) =

119901119894119887119894(119905)

sum119872

119896=1119901119896119887119896(119905)

(4)

119901119894=1

119879

119879

sum

119905=1

119901 (119894 | 119905 120582) (5)

997888rarr120583119894=sum119879

119905=1119901 (119894 |

119905 120582) 119905

sum119879

119905=1119901 (119894 |

119905 120582)

(6)

120590119894

2=sum119879

119905=1119901 (119894 |

119905 120582) 119905

2

sum119879

119905=1119901 (119894 |

119905 120582)

minus 119894

2 (7)


cut (119860 119861) = sum

119906isin119860Visin119861119908 (119906 V) (8)


Ncut (119860 119861) = cut (119860 119861)assoc (119860 119881)

+cut (119860 119861)assoc (119861 119881)

(9)





(119863 minus119882)119910 = 120582119863119910 (10)






119873


modeled as

119868 = 119887119869 + 119899 (11)


119894119873



in the set 119868119894119910= 119868(119909) 119909 isin 119874







120576 = int 120576119910119889119910 (12)


Ω1= 119909 120601 (119909) gt 0

Ω2= 119909 120601 (119909) lt 0

(13)


1 Ω



120576 = int

119873

sum

119894=1

(int119896 (119910 minus 119909)1003816100381610038161003816119868 (119909) minus 119887 (119910) 119888119894

1003816100381610038161003816

2119889119910)

sdot 119872119894(120601 (119909)) 119889119909

(14)




119873 = 2 1198721(120601) = 119867(120601) 119872

2(120601) = 1 minus 119867(120601) and 119867 is the



F (120601 c 119887) = 120576 (120601 c 119887) + ]L (120601) + 120583R119901(120601) (15)







(a)

(b)







+ (100 times 119891min (119894 119895)

119891max (119894 119895) + 1)

(16)



(a)

(b)







(a)

(b)

(c)

(d)

(e)





0 100 200 300 400 500 600 700


000500100150020025

(a)

(b)


(a)

(b)




(a)

(b)


(a)

(b)







(a)

(b)


(a)

(b)







(a)

(b)


(a)

(b)






(a) (b)









119898error = mean(119899

sum

119894=1


120590error


sum

119894=1


(17)































B

A

C

X


Table 8




5 Conclusion



Competing Interests



50

25

0(a)

300

150

0(b)

350

200

0700600500400300200100

700

600

500

400

300

200

100

NasalTemporal

Superior

Inferior

Central

(c)


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119901 ( | 120582) =

119872

sum

119894=1

119901119894119887119894 () (2)


119872

sum

119894=1

119901119894= 1 (3)



119901 (119894 | 119905 120582) =

119901119894119887119894(119905)

sum119872

119896=1119901119896119887119896(119905)

(4)

119901119894=1

119879

119879

sum

119905=1

119901 (119894 | 119905 120582) (5)

997888rarr120583119894=sum119879

119905=1119901 (119894 |

119905 120582) 119905

sum119879

119905=1119901 (119894 |

119905 120582)

(6)

120590119894

2=sum119879

119905=1119901 (119894 |

119905 120582) 119905

2

sum119879

119905=1119901 (119894 |

119905 120582)

minus 119894

2 (7)


cut (119860 119861) = sum

119906isin119860Visin119861119908 (119906 V) (8)


Ncut (119860 119861) = cut (119860 119861)assoc (119860 119881)

+cut (119860 119861)assoc (119861 119881)

(9)





(119863 minus119882)119910 = 120582119863119910 (10)






119873


modeled as

119868 = 119887119869 + 119899 (11)


119894119873



in the set 119868119894119910= 119868(119909) 119909 isin 119874







120576 = int 120576119910119889119910 (12)


Ω1= 119909 120601 (119909) gt 0

Ω2= 119909 120601 (119909) lt 0

(13)


1 Ω



120576 = int

119873

sum

119894=1

(int119896 (119910 minus 119909)1003816100381610038161003816119868 (119909) minus 119887 (119910) 119888119894

1003816100381610038161003816

2119889119910)

sdot 119872119894(120601 (119909)) 119889119909

(14)




119873 = 2 1198721(120601) = 119867(120601) 119872

2(120601) = 1 minus 119867(120601) and 119867 is the



F (120601 c 119887) = 120576 (120601 c 119887) + ]L (120601) + 120583R119901(120601) (15)







(a)

(b)







+ (100 times 119891min (119894 119895)

119891max (119894 119895) + 1)

(16)



(a)

(b)







(a)

(b)

(c)

(d)

(e)





0 100 200 300 400 500 600 700


000500100150020025

(a)

(b)


(a)

(b)




(a)

(b)


(a)

(b)







(a)

(b)


(a)

(b)







(a)

(b)


(a)

(b)






(a) (b)









119898error = mean(119899

sum

119894=1


120590error


sum

119894=1


(17)































B

A

C

X


Table 8




5 Conclusion



Competing Interests



50

25

0(a)

300

150

0(b)

350

200

0700600500400300200100

700

600

500

400

300

200

100

NasalTemporal

Superior

Inferior

Central

(c)


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119873 = 2 1198721(120601) = 119867(120601) 119872

2(120601) = 1 minus 119867(120601) and 119867 is the



F (120601 c 119887) = 120576 (120601 c 119887) + ]L (120601) + 120583R119901(120601) (15)







(a)

(b)







+ (100 times 119891min (119894 119895)

119891max (119894 119895) + 1)

(16)



(a)

(b)







(a)

(b)

(c)

(d)

(e)





0 100 200 300 400 500 600 700


000500100150020025

(a)

(b)


(a)

(b)




(a)

(b)


(a)

(b)







(a)

(b)


(a)

(b)







(a)

(b)


(a)

(b)






(a) (b)









119898error = mean(119899

sum

119894=1


120590error


sum

119894=1


(17)































B

A

C

X


Table 8




5 Conclusion



Competing Interests



50

25

0(a)

300

150

0(b)

350

200

0700600500400300200100

700

600

500

400

300

200

100

NasalTemporal

Superior

Inferior

Central

(c)


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

(b)







(a)

(b)

(c)

(d)

(e)





0 100 200 300 400 500 600 700


000500100150020025

(a)

(b)


(a)

(b)




(a)

(b)


(a)

(b)







(a)

(b)


(a)

(b)







(a)

(b)


(a)

(b)






(a) (b)









119898error = mean(119899

sum

119894=1


120590error


sum

119894=1


(17)































B

A

C

X


Table 8




5 Conclusion



Competing Interests



50

25

0(a)

300

150

0(b)

350

200

0700600500400300200100

700

600

500

400

300

200

100

NasalTemporal

Superior

Inferior

Central

(c)


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 100 200 300 400 500 600 700


000500100150020025

(a)

(b)


(a)

(b)




(a)

(b)


(a)

(b)







(a)

(b)


(a)

(b)







(a)

(b)


(a)

(b)






(a) (b)









119898error = mean(119899

sum

119894=1


120590error


sum

119894=1


(17)































B

A

C

X


Table 8




5 Conclusion



Competing Interests



50

25

0(a)

300

150

0(b)

350

200

0700600500400300200100

700

600

500

400

300

200

100

NasalTemporal

Superior

Inferior

Central

(c)


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

(b)


(a)

(b)







(a)

(b)


(a)

(b)






(a) (b)









119898error = mean(119899

sum

119894=1


120590error


sum

119894=1


(17)































B

A

C

X


Table 8




5 Conclusion



Competing Interests



50

25

0(a)

300

150

0(b)

350

200

0700600500400300200100

700

600

500

400

300

200

100

NasalTemporal

Superior

Inferior

Central

(c)


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)









119898error = mean(119899

sum

119894=1


120590error


sum

119894=1


(17)































B

A

C

X


Table 8




5 Conclusion



Competing Interests



50

25

0(a)

300

150

0(b)

350

200

0700600500400300200100

700

600

500

400

300

200

100

NasalTemporal

Superior

Inferior

Central

(c)


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
























B

A

C

X


Table 8




5 Conclusion



Competing Interests



50

25

0(a)

300

150

0(b)

350

200

0700600500400300200100

700

600

500

400

300

200

100

NasalTemporal

Superior

Inferior

Central

(c)


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










50

25

0(a)

300

150

0(b)

350

200

0700600500400300200100

700

600

500

400

300

200

100

NasalTemporal

Superior

Inferior

Central

(c)


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article obtaining thickness maps of corneal...

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