research article segmentation of choroidal boundary in...

Research ArticleSegmentation of Choroidal Boundary in Enhanced DepthImaging OCTs Using a Multiresolution Texture Based Modelingin Graph Cuts

Hajar Danesh1 Raheleh Kafieh1 Hossein Rabbani1 and Fedra Hajizadeh2

1 Department of Biomedical Engineering Medical Image and Signal Processing Research Center Isfahan University of Medical SciencesIsfahan 81745 Iran

2Noor Ophthalmology Research Center Tehran 1968653111 Iran

Correspondence should be addressed to Hossein Rabbani h rabbanimedmuiacir

Received 20 August 2013 Revised 30 November 2013 Accepted 19 December 2013 Published 11 February 2014

Academic Editor William Crum

Copyright copy 2014 Hajar Danesh et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The introduction of enhanced depth imaging optical coherence tomography (EDI-OCT) has provided the advantage of in vivocross-sectional imaging of the choroid similar to the retina with standard commercially available spectral domain (SD) OCTmachines A texture-based algorithm is introduced in this paper for fully automatic segmentation of choroidal images obtainedfrom an EDI system of Heidelberg 3D OCT Spectralis Dynamic programming is utilized to determine the location of the retinalpigment epithelium (RPE) Bruchrsquos membrane (BM) (the blood-retina barrier which separates the RPE cells of the retina from thechoroid) can be segmented by searching for the pixels with the biggest gradient value below theRPE Furthermore a novelmethod isproposed to segment the choroid-sclera interface (CSI) which employs the wavelet based features to construct a Gaussian mixturemodel (GMM) The model is then used in a graph cut for segmentation of the choroidal boundary The proposed algorithm istested on 100 EDI OCTs and is compared with manual segmentationThe results showed an unsigned error of 248 plusmn 032 pixels forBM extraction and 979 plusmn 329 pixels for choroid detection It implies significant improvement of the proposed method over otherapproaches like 119896-means and graph cut methods

1 Introduction

Optical coherence tomography (OCT) imaging techniquewas introduced by Huang et al in 1991 [1] This technique isemployed for its ability in taking cross-sectional images frommicroscopic structure of the living tissues The device has aresolution on the scale of micrometers In this technique anumber of A-scans or linear scans create B-scan or cross-sectional images [2] OCT images consist of a great amountof data therefore nonautomated and visual analysis ofsuch a great amount of data would be troublesome for theophthalmologist The main goal of automatic segmentationis to assist the ophthalmologist in diagnosis and monitoringof eye diseases

Choroid is one of the structural layers located betweenthe sclera and the retinaThis pigmented layer contains manycapillaries that supply feeding of the iris and retinal light

receptor cells [3] Many diseases such as polypoidal choroidalvasculopathy and choroidal tumors cause changes in thestructure of this layer [4ndash8] therefore segmentation of thislayer has great importance for ophthalmologists In retinalimaging using conventional OCT wavelength of the lightsource is around 800 nanometers which is not appropriatefor imaging of choroid layer due to signal transmissiondifficulty through retinal pigment epithelium (RPE) layer andincreased depth of imaging [9] However increased pixeldensity and high signal-to-noise ratio in SD-OCT (spectral-domain OCT) in comparison to TD-OCT (time-domainOCT) makes choroidal imaging possible In SD-OCT thestructures that are closer to ldquozero delay linerdquo have highersignals than those that are farther away In conventionalOCT the ldquozero delay linerdquo is near the inner surface of retinahowever in EDI-OCT it is placed near the outer retinaand choroid which is the key for EDI imaging In order to

Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2014 Article ID 479268 9 pageshttpdxdoiorg1011552014479268

2 Computational and Mathematical Methods in Medicine

(a)

Retinal layers

Choroid

RPE

CSI

(b)

Figure 1 An example of EDI OCT imagining (b) compared to conventional OCT (a)

increase the quality of EDI-OCT and to reduce ldquospecklesrdquoa high number of images (usually 100 images) are averagedthrough a software that provides high-quality images withsmoother border [9] An example of this imaging methodis compared with conventional OCT in Figure 1 Howeveranother solution for choroidal imaging is a higher wavelengthof approximately 1060 nanometer [10 11]

In several studies EDI-OCT has been used to measurethe thickness of the choroid finding its relation with diseasesand monitoring the treatment process [12ndash14] In most ofthese studies measurement of choroidal thickness is usuallyaccomplished by manual labeling which is a time-consumingand tedious processThis problem is muchmore complicatedwhen the number of images is numerousTherefore the needfor development of an automatic segmentation algorithm onEDI-OCT arises

A limited number of studies have already been conductedabout automatic segmentation of these images Kajic et al[15ndash17] proposed a two-stage statistical model to detect thechoroid boundaries in the 1060 nm OCT images in healthyand pathological eyes This model needed extensive trainingand the mean error is 13 Tian et al [18 19] found thechoroidal boundary by finding the shortest path of the graphformed by valley pixels using dynamic programming (DP)The average of Dicersquos coefficient on 45 EDI-OCT images was905 Lu et al [20] proposed a technique to segment theinner boundary of the choroid using a two-stage fast activecontour model Then a real-time human-supervised auto-mated segmentation on the outer boundary of the choroidwas appliedThe reported Dice similarity coefficient value on30 images captured from patients diagnosed with diabeteswas 927

Many algorithms based on wavelet and graph cut arealready used in segmentation of retinal layers [21] Howeverdue to heterogeneity in the choroid layers such methodscannot be useful in choroid segmentation However becauseof distinct difference between texture of choroid and otherretinal layers an algorithm based on texture classificationcan be effective With this idea we use a combinationof graph-based methods and wavelet-domain features forchoroidal segmentation A description of ourmethod includ-ing detection of Bruchrsquos membrane (BM) and segmentationof choroidal-scleral interface (CSI) is provided in Section 2and the results are presented in Section 3 The results show

the improved robustness of the method compared to otheravailable algorithms Finally the conclusion and suggestionsfor future works are presented in Section 4

2 Material and Methods

The proposed choroid segmentation method is tested on100 randomly selected two-dimensional EDI-OCT imagesobtained from 10 eyes of 6 normal subjects by an EDI systemof multimodality diagnostic imaging (wavelength 870 nmscan pattern enhanced depth imaging Spectralis HRA +OCT Heidelberg Engineering Heidelberg Germany) [22]The study protocol was reviewed in advance by the reviewboard of Noor Ophthalmology Research Center Each partic-ipant was informed of the purpose of the study and provideda written consent to participate For evaluation and rulingout any ocular pathology all patients underwent thoroughophthalmic examinations including refraction visual acuityslit lamp biomicroscopic examination IOP measurement byGoldmann applanation tonometer and examination of thefundus with plus 90-D lens Each dataset consisted of a SLOimage and limited number of OCT scans with size of 496 times768 (namely for a data with 31 selected OCT slices the wholedata size would be 496 times 768 times 31)The pixel resolutions were39 120583mpixel in axial direction and 14 120583mpixel in transversaldirection

21 Overview of Algorithm In the first step dynamic pro-gramming (DP) was applied for boundary detection of RPElayer The BM is the blood-retina barrier that separates theRPE cells of the retina from the choroid and can be segmentedby searching for the pixels with the biggest gradient valuebelow the RPE In this stage we eliminated the pixels abovethis boundary form our calculations by making them equalto zero and focused on segmentation of the lower boundaryof the choroid

In the next step discrete wavelet transform (DWT)mdashusing filter bank and descriptorsmdashwas employed to extractappropriate features from EDI-OCT images The extractedfeatures from training images were used to construct aGaussian mixture model (GMM) It is assumed that eachextracted descriptor using DWT has a multivariate normal

Computational and Mathematical Methods in Medicine 3

Extraction ofwavelet domain

coefficientsTexture extraction

Dynamic programming

Manualsegmentation

Gaussian mixturemodel

Graph cut segmentation

Choroidal boundary segmentation

RPE segmentation

Finding the biggest gradient below the RPE

BM segmentation

Training images

EDI-OCTImage

Figure 2 Choroid segmentation algorithm overview

1

1 2

(a) (b)

C(xm1 )

C(xm2 )

C(xmi )

C(xmn )

C(xm+1k )

k

n

m Mm+1

Figure 3 Dynamic programming (a) one step of cost calculation (b) graph layers and nodes notation The highlighted pixels show theneighbors

probability density function (pdf) and the number of Gaus-sian distributions (119870) is chosen to be 3 which representthe area above the BM choroid and the area beneath theCSI Finally the relevance of each data to the model is usedin creating the graph for final CSI segmentation A blockdiagram of the algorithm could be found in Figure 2

22 BMDetection Weapplied boundary detection algorithmusing DP to detect boundary of RPE layer which is thebrightest part in EDI OCT images DP is a method based onoptimality [23] which seeks for the best functions in whichthe variables are not simultaneously in conjunction with eachother In simple problem of boundary tracking the goal isto find the best path (least expensive) between one of thepossible starting points and one of the possible ending points

In this step upper bound of choroid (lower bound of RPE)can be segmented

For boundary detection using DP we are looking for adark boundary transmitted from one edge to another edgein an image (eg from column 1 to 119872 minus 1 in Figure 3)DP algorithm associates a cost to each node (brightness ofeach pixel) and the partial paths are set according to the cost(brightness) of the next neighboring node The algorithmstarts through the columns (column 1 to119872minus 1) and for eachnode (from 1 to 119899) the best path with optimized (lowest) costis selected among three neighbor pixels of the neighboringcolumn (119894 = minus1 0 1 in (1)) Therefore a cumulative cost(119862(119909119898+1119896

)) can be made for a pixel in 119898 + 1th column andin the 119896th node according to the cost of previously selectednodes (1)


(a) (b)

Figure 4 (a) EDI-OCT image of the human eye (b) Bruchrsquos membrane

The following algorithm describes the DP method [24]

(1) Specify initial costs 119862(1199091119894) of all nodes in the first

graph layer 119894 = 1 119899 and partial path costs119892119898(119894 119896)119898 = 1 119872 minus 1

(2) Repeat step 3 for all119898 = 1 119872 minus 1(3) Repeat step 4 for all nodes 119896 = 1 119899 in the graph

layer119898(4) Let

119862 (119909119898+1

119896) = min119894=minus101

(119862 (119909119898

119896+119894) + 119892119898

(119894 119896)) (1)

Set pointer from node 119909119898+1119896

back to node 119909119898lowast119896

wherelowast denotes the optimal predecessor Optimality isdefined as minimization of the cost function

(5) Find an optimal node 119909119872lowast119896

in the last graph layer 119872and obtain an optimal path by backtracking throughthe points from 119909

119872lowast

119896to 1199091lowast119896

The positions of a sample node119862(119909119898+1119896

) and its neighborsin the previous (119898th) graph layer are shown in Figures 3(a)and 3(b) The highlighted pixels around 119862(119909119898+1

119896) indicate 119894 =

minus1 0 1 in (1)It should also be noted that the DP boundary detection

is conventionally looking for the darkest boundary in animage and for our application (detection of the brightestboundary) we should inverse the brightness values of theimage After segmentation of RPE layer BM can be locatedby searching for the pixels with the biggest gradient belowthe RPE Figure 4 shows the result of BM segmentation for asample EDI-OCT image From calculative point of view DPis efficient and flexible and can be considered as a powerfultool even in presence of noise

23 CSI Detection A novel combination of algorithms isproposed for discrimination of lower boundary of choroid(CSI) Among many possible texture descriptors used forsegmentation of images with several textures [24] we showthe ability of wavelet texture descriptors in this work

The algorithm can then be stated in three steps

(1) calculate wavelet descriptors for each pixel (Sec-tion 231)

(2) create a model of the classes using training images(Section 232)

(3) take a new image and segment it using the learnedmodel Use graph cut segmentation to obtain spatiallycoherent segmentation (Section 233)

It is assumed that extracted descriptors using DWT havea multivariate normal pdf This assumption can be justifiedby the central limit theorem (CLT) In its classical formthe CLT states that the mean of 119899 independent identicallydistributed random variables with finite mean and variancehas a limiting distribution for 119899 rarr infin that is Gaussian As anapproximation for a finite number of observations (119899 ⋘ infin)it provides a reasonable approximation only close to the peakof the normal distribution rather than stretching into the tails(convergence to the limit)

In our datasets of Heidelberg 3D OCT Spectralis eachimage is calculated from the mean value of 100 images takenat the same timeThemean process dramatically improves thequality of the information in the images without introducingan alteration to the original image or adding any distractingelectronic noise [22] Therefore according to the ldquoconver-gence to the limitrdquo theorem near the peak areas (needed forGMM assumption) and in accord with linear characteristicsof the wavelet transform we can assume that each extracteddescriptor using DWT has a multivariate normal pdf

231 Wavelet Descriptors DWT using filter bank anddescriptors is employed to extract features for each pixel ofthe image In other applications of wavelets transform fortexture analysis most prevalent features are wavelet energysignatures and their second-order statistics [25 26] In thiscase Haar wavelet filters (119867(119911) = (1 + 119911)2 and 119866(119911) =

(119911 minus 1)2) are utilized for ease of use Filter bank stages arerepeated (multiresolution approach) for four levels Since weare using wavelet frame instead of the standard DWT thenumber of levels can optionally grow But with trial and errorwe found that for levels higher than 4 the results did notimprove and we only faced withmore complexityThe energyof each high-pass filter at different stages of subbands and theenergy of the last stage of the low-pass filter are extracted asimage features (5 features) Extracted features and a trainingimage with a known segmentation (mask) are then used toconstruct GMM for the image


232 Gaussian Mixture Model GMM is a parametric pdfrepresented as a weighted sum of Gaussian componentdistributions The idea for clustering with GMMs is the sameas for 119896-means In conventional GMM we make an initialguess formean120583

119896and covariance Γ

119896and then try to iteratively

refine them The number of Gaussian distributions (119870) ischosen to be 3 which represent the area above the BMchoroid and the area beneath CSI

Assume that 119899-dimensional data constituted 119870 Gaussiandistributionalefsym

1 alefsym2 alefsym

119896 in which alefsym

119896with the mean (120583

119896)

and covariance Γ119896is considered as follows

alefsym119896sim 119873 (120583

119896 Γ119896) (2)

Considering the weights of each relevant 119870 as 120587119896

(sum119870119896=1

120587119896= 1) the final pdf is defined as follows

119901 (119909119895) =

119870

sum

119896=1

120587119896119901 (119909119895| alefsym119896) (3)

in which

119901 (119909119895| alefsym119896)

=1

(2120587)11989921003816100381610038161003816

Γ119896

1003816100381610038161003816

12

exp(minus12

(119909119895minus 120583119896)

119879

Γminus1

119896(119909119895minus 120583119896))

(4)

Since we are working on wavelet features describedin Section 231 119899 should be set to 5 We now assumethat actual values of the observed EDI-OCT images 119883 =

1198831 1198832 119883

119894 119883

119872 and value of pixels in each image

1198831

= 1199091 1199092 119909

119895 119909119860times119861

are independent We alsosuppose that EDI images have equal size of 119860 times 119861 Withdefining119873 = 119872times119860times119861 we will have the following equations

119901 (119883) =

119873

prod

119895=1

119901 (119909119895)

=

119873

prod

119895=1

119896

sum

119896=1

120587119896

(2120587)11989921003816100381610038161003816

Γ119896

1003816100381610038161003816

12

times exp(minus12

(119909119895minus 120583119896)

119879

Γminus1

119896(119909119895minus 120583119896))

(5)

where119872 represents the number of EDI-OCT images used fortraining (10 for our case) For each training image amaskwasmade manually which classifies each image into three labelsthe area above the BM choroid and the area beneath CSI

In conventional GMM the parameters are estimatedusing iterative EM algorithm to fit a mixture model to a setof available data [24 27]

EM algorithm is rapidly repeated and at each stageGaussian expectation is estimated for each data sample andthen Gaussian element estimation (maximization) is alteredIf 120583119896and Γ119896are in hand as an estimation we can calculate the

119896th Gaussian probability for 119909119895

119901119895119896=

120587119896119901 (119909119895| alefsym119896)

sum119896

119894=1120587119894119901 (119909119895| alefsym119894)

(6)

in which 119909119895(probability ratio foralefsym

119896) is granted based on sum

of 119909119895(regardless of Gaussian production) balanced with 120587

119894

Therefore the following equation is defined

120587new119896

=1

119873

119873

sum

119895=1

119901119895119896 (7)

In this equation mean 119901119895119896

is calculated in data seriesSimilarly one can estimate corrected values of 120583

119896and Γ119896

120583new119896

=

sum119873

119895=1119901119895119896119909119895

sum119873

119895=1119901119895119896

Γnew119896

=

sum119873

119895=1119901119895119896(119909119895minus 120583

new119896

) (119909119895minus 120583

new119896

)

119879

sum119873

119895=1119901119895119896

(8)

With a slight modification to conventional GMM whichuses EM algorithm to calculate the parameters of eachGaussian function (including mean and covariance in (8))we use the training step for finding the parameters of GMMNamely we use training images with known segmentation(mask) and calculate themean and covariance of each section(for the training data) These parameters are used for allimages in our database (ie there is no need to use EMalgorithm for each image separately which speeds up thealgorithm) Then we only calculate the responsibility factorby (6) to construct a learned model to be fed to graph cutsegmentation

When anew test image is considered for segmentationwecalculate wavelet descriptors for each pixel (and accordingly5-dimensional vectors of 119909

119895and 120583

119896) The probability (119901) of a

pixel belonging to a particular class of the learned model canbe obtained afterward The value of probability (119901) is thenused in the construction of a graph cut segmentation

233 Graph Cut Segmentation Graph cut segmentation isconstructed based on a learned model to obtain spatiallycoherent segmentation

The direct use of optimization algorithms of minimum-cutmaximum flow for graph partitioning was first intro-duced by Greig et al [28] in image processing of binaryimages Using graph optimization algorithms a powerfulmethod of optimal bordering and region classification in119873-dimensional image data was proposed [29 30]

This method starts by one or more points representingldquoobjectrdquo and one or more points representing ldquobackgroundrdquodetermined using interactive or automatic identificationTheoverall shape of cost function119862 is represented as follows [31]

119862 (119891) = 119888data (119891) + 119888smooth (119891) (9)

To minimize 119862(119891) a special class of arc-weighted graphs119866119904119905

= (119881 cup terminal nodes 119864) is employed In additionto the set of nodes 119881 corresponding to pixels of the image119868 (Figure 5(a)) terminal nodes (shown by 1 2 and 3 inFigure 5(b)) are also added to 119866

119904119905 These terminals are hard-

linked with the segmentation seed points (bold links in


1

2

3

(a)

2

31

(b)

Figure 5 Graph cut classificationmdashexample of simple classification (a) Image with 3 classes (b) Related graph and terminal nodes Greenlines show 119899-links while red yellow and blue curves represent the 119905-links

Figure 5(b)) and represent the segmentation labels (1 2 and3)

The arcs 119864 in 119866119904119905can be classified into two categories 119899-

links and 119905-links The 119899-links connect pairs of neighboringpixels whose costs are derived from the smoothness term119888smooth(119891) The 119905-links connect pixels whose costs are derivedfrom the data term 119888data(119891) Green lines in Figure 5(b) show119899-links while red yellow and blue curves represent the 119905-links A 119904 minus 119905 cut in 119866

119904119905is a set of arcs whose removal

partitions the nodes into three disjoint subsets (1 2 and 3in Figure 5) The cost of a cut is the total cost of arcs inthe cut and a minimum 119904 minus 119905 cut is a cut whose cost isminimal The minimum 119904 minus 119905 cut problem or its dual (themaximumflowproblem) can be solved by various algorithmsIn maximum flow algorithm maximum amount of water tosink is delivered using directed arc graphs and the amountof water flow through each separate arc is determined usingarc capacity or cost The greatest amount of maximum flowfrom 119904 to 119905 saturates a set of graph arcs These saturated arcsdivide nodes into two separate sections of 119878 and 119879 related tominimum cuts [24 32 33]

Let each image pixel 119894119896take a binary label 119871

119896isin 1 2 3

The labeling vector 119871 = (1198711 1198712 119871

|119868|) defines the resulting

binary segmentationIn this paper 119862data(119891) is the distance between each image

pixel and initial class made by GMM in Section 232 For atest image wavelet descriptors are calculated for each pixeland probability (119901) of a pixel belonging to a particular classof the learned model is obtained Then 119862data(119891) is created by

119862data (119891) = minus log (119901 + 119890119901119904) (10)

119862smooth(119891) is a matrix of costs which is related to adjacentpixel values In this work we assigned a square matrix withfixed values (119903 = 4) and with zeros on diagonal as 119862smooth(119891)(9) The increase in fixed term (119903) would enhance adjacency

constraint constant and therefore would result in a finerseparation

119862smooth (119891) =

[[[[[[[[[[[

[

0 119903 119903 sdot sdot sdot sdot sdot sdot 119903

119903 0 119903 119903 d

119903 119903 0 119903 119903

119903 119903 0 119903 119903

d 119903 119903 0 119903

119903 119903 119903 0

]]]]]]]]]]]

]

(11)

3 Results

One hundred two-dimensional EDI-OCT images wereobtained from Heidelberg 3D OCT Spectralis and were usedin statistical analysis to produce the results For our 100 two-dimensional dataset we chose 10 images to train the learnedmodel Actually we can choose any 10 or less images fortraining and calculate means and covariances and weightsof GMM and there would be no considerable differencebetween these parameters This step will expedite our algo-rithm instead of using EM algorithm for each image Theperformance of the method is reported based on its ability incorrect segmentation of the test images For evaluation of theproposedmethod themanual segmentation of two observerswas used as the gold standard

For validation purpose the mean signed and unsignedborder positioning errors for each border were comparedwith other algorithms such as graph cut 119896-means and DPand the results are presented in Tables 1 and 2 for eachboundary We implemented each of these algorithms andtested them on our 90 two-dimensional test set In 119896-meansalgorithm we selected 119896 = 3 and applied 119896-means algorithmon the image directly In graph cutmethodwe used the resultof 119896-means algorithm to create initial prototype for eachclass and 119862data(119891) was calculated by the distance betweeneach image pixel to initial class made by 119896-means algorithm


Table 1 Summary of mean signed border positioning errors (mean plusmn std)

Avg obs versusour alg

Avg obs versusgraph cut alg

Avg obs versus119896-means alg

Avg obs versusDP alg Obs 1 versus obs 2

BM 044 plusmn 118 430 plusmn 072 773 plusmn 335 044 plusmn 118 112 plusmn 129

Choroid 577 plusmn 277 5769 plusmn 693 minus3125 plusmn 1151 965 plusmn 541 765 plusmn 263

Table 2 Summary of mean unsigned border positioning errors (mean plusmn std)






Choroid 979 plusmn 329 6569 plusmn 753 3373 plusmn 1223 1248 plusmn 541 878 plusmn 238

Table 3 Improvement of the proposed method compared with other algorithms

119875 value our alg versus graph cut alg 119875 value our alg versus 119896-means alg 119875 value our alg versus DP algBM ≪0001 ≪0001 mdashChoroid ≪0001 ≪0001 ≪001

119862smooth(119891) was calculated in the same method described inSection 233 by small change of selecting 119903 = 3 which couldgive the best results For DP method the first step is similarto the proposed method in this paper (we applied boundarydetection algorithm using dynamic programming to detectRPE layer boundary and eliminated the pixels above thisboundary bymaking them equal to zero)Thenwe eliminateda region beneath the RPE (7 pixels below) and applied DP tosearch the image for another time The results were based onthe whitest route available after elimination of RPE layer

According to Tables 1 and 2 the signed border positioningerrors were 044 plusmn 118 pixels for BM extraction and 577plusmn 277 pixels for choroid segmentation and the unsignedborder positioning errors were 248 plusmn 032 pixels for BMextraction and 979 plusmn 329 pixels for choroid segmentationrespectively The errors between the proposed algorithmand the reference standard were similar to those computedbetween the observers For example the overall observererror was 264 plusmn 098 pixels and 878 plusmn 238 pixels for BMand CSI respectively which is comparable to the results ofthe algorithmThe border positioning errors of the proposedmethod showed significant improvement over other algo-rithms compared in both of the tables

To show the statistically significant improvement of theproposed method over the compared algorithms Table 3shows the obtained 119875 values The values confirm that ourresults have a significant improvement For instance thealgorithmrsquos overall119875 value against 119896-means and graph cut wasless than 0001 and against dynamic programming it was lessthan 001

The pixel resolution of our datasets in axial directionwas 39 120583mpixel Therefore mean signed positioning errorsfor localization of BM and choroid are 171 and 2250 120583mrespectively In accord with repeatability measurements forchoroidal thickness of EDI-OCT images [12] it can be

concluded that the positioning error has acceptable accuracyFigure 6 demonstrates two samples showing the performanceof the proposed method Furthermore Figure 7 shows theresults of segmentation using the proposed algorithm incomparison with other methods

The computational complexity of the proposed algorithmis around 13 seconds in the case of using the saved parametersfor constructed models otherwise if the computation con-sists of the model construction for one image it takes around21 seconds on a PC with Microsoft Windows XP x32 editionIntel core 2 Duo CPU at 300GHz 4GB RAM

4 Conclusion

In this paper a new method for choroid segmentation inEDI-OCT is introduced In the first step RPE boundary wassegmented using DP method and the area above RPE waseliminated from next steps Then the wavelet descriptorswere calculated for each pixel of the training images andassuming that the pdf of these descriptors are normal theirparameters were calculated to construct a model

When a new test image is considered for segmentationwavelet descriptors were calculated for each pixel and prob-ability (119901) of a pixel belonging to a particular class of thelearned model was obtainedThe value of probability (119901) wasthen used in the construction of a graph cut segmentation

The main limitation of this method is the need formanual segmentation to construct the model Despite thefact that only a few training images are sufficient to producegood results the manual labeling may be troublesome andreplacing this step with an automatic method can be studiedin future works For example in this work we chooseseveral images as known data and extracted their mixturemodelrsquos parameters for using as parameters of all new data


(a) (b)

(c) (d)

Figure 6 Two samples showing performance of the proposed methodThe green line shows the BM boundary and the red line indicates theSCI boundary

(a) (b) (c)

(d) (e) (f)

Figure 7 (a) EDI-OCT image (b) graph cut result (c) 119896-means result (d) dynamic programming result (e) our algorithm and (f) manualsegmentation

in the database For each database arbitrary sample datacan be used for constructing this mixture model (withknown parameters) and then used for all data in databaseHowever the automatic version of this method can also beenconsidered without using a predefinedmixture model and byusing EM algorithm for each image

The new method has better accuracy than previousmethods and the algorithm is tested on a larger dataset com-pared to older algorithms The performance of the methodis also fast and the implementation is relatively simple incomparison to more complicated algorithms

As a future work the proposed method should betested on EDI images taken from other modalities to proveits robustness to the imaging technique Furthermore a3D choroidal thickness map can be constructed using 3DOCT dataset which can assist the ophthalmologist in the

diagnosis of the choroidal diseases We also like to workon segmentation of the blood vessels in choroidal layer andproduce a 3D vascular structure to give more informationabout distribution of the vessels

Conflict of Interests

The authors disclose that there is no conflict of interestsincluding any financial and personal relationships with otherpeople or organizations that could inappropriately influence(bias) their work

References

[1] D Huang E A Swanson C P Lin et al ldquoOptical coherencetomographyrdquo Science vol 254 no 5035 pp 1178ndash1181 1991


[2] D Huang E A Swanson C P Lin et al Optical CoherenceTomography Massachusetts Institute of Technology WhitakerCollege of Health Sciences and Technology 1993

[3] G A Cioffi E Granstam and A Alm ldquoOcular circulationrdquo inAdlerrsquos Physiology of the Eye Mosby St Louis Mo USA 2003

[4] G Barteselli J Chhablani S El-Emamet al ldquoChoroidal volumevariations with age axial length and sex in healthy subjects athree-dimensional analysisrdquoOphthalmology vol 119 no 12 pp2572ndash2578 2012

[5] S E Chung S W Kang J H Lee and Y T Kim ldquoChoroidalthickness in polypoidal choroidal vasculopathy and exudativeage-related macular degenerationrdquo Ophthalmology vol 118 no5 pp 840ndash845 2011

[6] P Jirarattanasopa S Ooto A Tsujikawa et al ldquoAssessment ofmacular choroidal thickness by optical coherence tomographyand angiographic changes in central serous chorioretinopathyrdquoOphthalmology vol 119 no 8 pp 1666ndash1678 2012

[7] J R Ehrlich J Peterson G Parlitsis K Y Kay S Kiss andN M Radcliffe ldquoPeripapillary choroidal thickness in glaucomameasured with optical coherence tomographyrdquo ExperimentalEye Research vol 92 no 3 pp 189ndash194 2011

[8] J Yeoh W Rahman F Chen et al ldquoChoroidal imaging ininherited retinal disease using the technique of enhanced depthimaging optical coherence tomographyrdquo Graefersquos Archive forClinical and Experimental Ophthalmology vol 248 no 12 pp1719ndash1728 2010

[9] R F Spaide H Koizumi and M C Pozonni ldquoEnhanced depthimaging spectral-domain optical coherence tomographyrdquo TheAmerican Journal of Ophthalmology vol 146 no 4 pp 496ndash500 2008

[10] R F Spaide ldquoEnhanced depth imaging optical coherencetomography of retinal pigment epithelial detachment in age-related macular degenerationrdquo The American Journal of Oph-thalmology vol 147 no 4 pp 644ndash652 2009

[11] B Povazay B Hermann A Unterhuber et al ldquoThree-dimensional optical coherence tomography at 1050 nm versus800mn in retinal pathologies enhanced performance andchoroidal penetration in cataract patientsrdquo Journal of Biomed-ical Optics vol 12 no 4 Article ID 041211 2007

[12] W Rahman F K Chen J Yeoh P Patel A Tufail andL Da Cruz ldquoRepeatability of manual subfoveal choroidalthicknessmeasurements in healthy subjects using the techniqueof enhanced depth imaging optical coherence tomographyrdquoInvestigative Ophthalmology and Visual Science vol 52 no 5pp 2267ndash2271 2011

[13] T Fujiwara Y Imamura R Margolis J S Slakter and R FSpaide ldquoEnhanced depth imaging optical coherence tomogra-phy of the choroid in highlymyopic eyesrdquoTheAmerican Journalof Ophthalmology vol 148 no 3 pp 445ndash450 2009

[14] R L Wong P Zhao and W W Lai ldquoChoroidal thickness inrelation to hypercholesterolemia on enhanced depth imagingoptical coherence tomographyrdquo Retina vol 33 no 2 pp 423ndash428 2013

[15] V Kajic M Esmaeelpour B Povazay D Marshall P L RosinandWDrexler ldquoAutomated choroidal segmentation of 1060 nmOCT in healthy and pathologic eyes using a statistical modelrdquoBiomedical Optics Express vol 3 no 1 pp 86ndash103 2012

[16] M Esmaeelpour S Brunner S Ansari-Shahrezaei et al ldquoCho-roidal thinning in diabetes type 1 detected by 3-dimensional1060 nm optical coherence tomographyrdquo Investigative Ophthal-mology and Visual Science vol 53 no 11 pp 6803ndash6809 2012

[17] V Kajic M Esmaeelpour C Glittenberg et al ldquoAuto-mated three-dimensional choroidal vessel segmentation of 3D1060 nmOCT retinal datardquoBiomedical Optics Express vol 4 no1 pp 134ndash150 2013

[18] J Tian P Marziliano M Baskaran T A Tun and T AungldquoAutomatic measurements of choroidal thickness in EDI-OCTimagesrdquo in Proceedings of the Annual International Conferenceof the IEEE Engineering in Medicine and Biology Society (EMBCrsquo12) pp 5360ndash5363 San Diego Calif USA September 2012

[19] J Tian P Marziliano M Baskaran T A Tun and T AungldquoAutomatic segmentation of the choroid in enhanced depthimaging optical coherence tomography imagesrdquo BiomedicalOptics Express vol 4 no 3 pp 397ndash411 2013

[20] H Lu N Boonarpha M T Kwong and Y Zheng ldquoAutomatedsegmentation of the choroid in retinal optical coherence tomog-raphy imagesrdquo in Proceedings of the 35th Annual InternationalConference of the IEEE Engineering in Medicine and BiologySociety (EMBC rsquo13) pp 5869ndash5872 Osaka Japan July 2013

[21] M K Garvin M D Abramoff R Kardon S R Russell XWu and M Sonka ldquoIntraretinal layer segmentation of macularoptical coherence tomography images using optimal 3-D graphsearchrdquo IEEE Transactions on Medical Imaging vol 27 no 10pp 1495ndash1505 2008

[22] httpwwwheidelbergengineeringcomuswp-contentuploadshra2-aquire-the-perfect-imagepdf

[23] R Bellman ldquoThe theory of dynamic programmingrdquo Bulletin ofthe American Mathematical Society vol 60 pp 503ndash515 1954

[24] M Sonka V Hlavac and R Boyle Image Processing Analysisand Machine Vision BrooksCole Albany NY USA 1999

[25] S Arivazhagan and L Ganesan ldquoTexture classification usingwavelet transformrdquo Pattern Recognition Letters vol 24 no 9-10 pp 1513ndash1521 2003

[26] G van de Wouwer P Scheunders and D van Dyck ldquoStatisticaltexture characterization from discrete wavelet representationsrdquoIEEE Transactions on Image Processing vol 8 no 4 pp 592ndash598 1999

[27] C E Rasmussen ldquoThe infinite Gaussian mixture modelrdquoAdvances in Neural Information Processing Systems vol 12 pp554ndash560 2000

[28] D Greig B Porteous and A H Seheult ldquoExact maximum aposteriori estimation for binary imagesrdquo Journal of the RoyalStatistical Society B vol 51 no 2 pp 271ndash279 1989

[29] Y Boykov and G Funka-Lea ldquoGraph cuts and efficient N-Dimage segmentationrdquo International Journal of Computer Visionvol 70 no 2 pp 109ndash131 2006

[30] Y Boykov and V Kolmogorov ldquoComputing geodesics andminimal surfaces via graph cutsrdquo in Proceedings of the 9thIEEE International Conference on Computer Vision pp 26ndash33October 2003

[31] S Geman and D Geman ldquoStochastic relaxation Gibbs distri-butions and the Bayesian restoration of imagesrdquo IEEE Transac-tions on Pattern Analysis and Machine Intelligence vol 6 no 6pp 721ndash741 1984

[32] A V Goldberg and R E Tarjan ldquoNew approach to themaximum-flow problemrdquo Journal of the ACM vol 35 no 4 pp921ndash940 1988

[33] L R Ford and D R Fulkerson ldquoMaximal flow through anetworkrdquoCanadian Journal ofMathematics vol 8 pp 399ndash4041956

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


MEDIATORSINFLAMMATION

of


Behavioural Neurology

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of



Computational and Mathematical Methods in Medicine

OphthalmologyJournal of


Diabetes ResearchJournal of



Research and TreatmentAIDS


Gastroenterology Research and Practice


Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom


(a)

Retinal layers

Choroid

RPE

CSI

(b)

Figure 1 An example of EDI OCT imagining (b) compared to conventional OCT (a)

increase the quality of EDI-OCT and to reduce ldquospecklesrdquoa high number of images (usually 100 images) are averagedthrough a software that provides high-quality images withsmoother border [9] An example of this imaging methodis compared with conventional OCT in Figure 1 Howeveranother solution for choroidal imaging is a higher wavelengthof approximately 1060 nanometer [10 11]

In several studies EDI-OCT has been used to measurethe thickness of the choroid finding its relation with diseasesand monitoring the treatment process [12ndash14] In most ofthese studies measurement of choroidal thickness is usuallyaccomplished by manual labeling which is a time-consumingand tedious processThis problem is muchmore complicatedwhen the number of images is numerousTherefore the needfor development of an automatic segmentation algorithm onEDI-OCT arises

A limited number of studies have already been conductedabout automatic segmentation of these images Kajic et al[15ndash17] proposed a two-stage statistical model to detect thechoroid boundaries in the 1060 nm OCT images in healthyand pathological eyes This model needed extensive trainingand the mean error is 13 Tian et al [18 19] found thechoroidal boundary by finding the shortest path of the graphformed by valley pixels using dynamic programming (DP)The average of Dicersquos coefficient on 45 EDI-OCT images was905 Lu et al [20] proposed a technique to segment theinner boundary of the choroid using a two-stage fast activecontour model Then a real-time human-supervised auto-mated segmentation on the outer boundary of the choroidwas appliedThe reported Dice similarity coefficient value on30 images captured from patients diagnosed with diabeteswas 927

Many algorithms based on wavelet and graph cut arealready used in segmentation of retinal layers [21] Howeverdue to heterogeneity in the choroid layers such methodscannot be useful in choroid segmentation However becauseof distinct difference between texture of choroid and otherretinal layers an algorithm based on texture classificationcan be effective With this idea we use a combinationof graph-based methods and wavelet-domain features forchoroidal segmentation A description of ourmethod includ-ing detection of Bruchrsquos membrane (BM) and segmentationof choroidal-scleral interface (CSI) is provided in Section 2and the results are presented in Section 3 The results show

the improved robustness of the method compared to otheravailable algorithms Finally the conclusion and suggestionsfor future works are presented in Section 4

2 Material and Methods

The proposed choroid segmentation method is tested on100 randomly selected two-dimensional EDI-OCT imagesobtained from 10 eyes of 6 normal subjects by an EDI systemof multimodality diagnostic imaging (wavelength 870 nmscan pattern enhanced depth imaging Spectralis HRA +OCT Heidelberg Engineering Heidelberg Germany) [22]The study protocol was reviewed in advance by the reviewboard of Noor Ophthalmology Research Center Each partic-ipant was informed of the purpose of the study and provideda written consent to participate For evaluation and rulingout any ocular pathology all patients underwent thoroughophthalmic examinations including refraction visual acuityslit lamp biomicroscopic examination IOP measurement byGoldmann applanation tonometer and examination of thefundus with plus 90-D lens Each dataset consisted of a SLOimage and limited number of OCT scans with size of 496 times768 (namely for a data with 31 selected OCT slices the wholedata size would be 496 times 768 times 31)The pixel resolutions were39 120583mpixel in axial direction and 14 120583mpixel in transversaldirection

21 Overview of Algorithm In the first step dynamic pro-gramming (DP) was applied for boundary detection of RPElayer The BM is the blood-retina barrier that separates theRPE cells of the retina from the choroid and can be segmentedby searching for the pixels with the biggest gradient valuebelow the RPE In this stage we eliminated the pixels abovethis boundary form our calculations by making them equalto zero and focused on segmentation of the lower boundaryof the choroid

In the next step discrete wavelet transform (DWT)mdashusing filter bank and descriptorsmdashwas employed to extractappropriate features from EDI-OCT images The extractedfeatures from training images were used to construct aGaussian mixture model (GMM) It is assumed that eachextracted descriptor using DWT has a multivariate normal




Dynamic programming

Manualsegmentation




RPE segmentation


BM segmentation

Training images

EDI-OCTImage


1

1 2

(a) (b)

C(xm1 )

C(xm2 )

C(xmi )

C(xmn )

C(xm+1k )

k

n

m Mm+1








(a) (b)






layer119898(4) Let

119862 (119909119898+1

119896) = min119894=minus101

(119862 (119909119898

119896+119894) + 119892119898

(119894 119896)) (1)






119872lowast

119896to 1199091lowast119896



119896) indicate 119894 =


















1 alefsym2 alefsym



119896)


alefsym119896sim 119873 (120583

119896 Γ119896) (2)


(sum119870119896=1


119901 (119909119895) =

119870

sum

119896=1

120587119896119901 (119909119895| alefsym119896) (3)

in which

119901 (119909119895| alefsym119896)

=1

(2120587)11989921003816100381610038161003816

Γ119896

1003816100381610038161003816

12

exp(minus12

(119909119895minus 120583119896)

119879

Γminus1

119896(119909119895minus 120583119896))

(4)


1198831 1198832 119883

119894 119883


1198831

= 1199091 1199092 119909

119895 119909119860times119861


119901 (119883) =

119873

prod

119895=1

119901 (119909119895)

=

119873

prod

119895=1

119896

sum

119896=1

120587119896

(2120587)11989921003816100381610038161003816

Γ119896

1003816100381610038161003816

12

times exp(minus12

(119909119895minus 120583119896)

119879

Γminus1

119896(119909119895minus 120583119896))

(5)





119901119895119896=

120587119896119901 (119909119895| alefsym119896)

sum119896

119894=1120587119894119901 (119909119895| alefsym119894)

(6)




119894


120587new119896

=1

119873

119873

sum

119895=1

119901119895119896 (7)



119896and Γ119896

120583new119896

=

sum119873

119895=1119901119895119896119909119895

sum119873

119895=1119901119895119896

Γnew119896

=

sum119873

119895=1119901119895119896(119909119895minus 120583

new119896

) (119909119895minus 120583

new119896

)

119879

sum119873

119895=1119901119895119896

(8)



119895and 120583






119862 (119891) = 119888data (119891) + 119888smooth (119891) (9)






1

2

3

(a)

2

31

(b)








119896isin 1 2 3





119862data (119891) = minus log (119901 + 119890119901119904) (10)



119862smooth (119891) =

[[[[[[[[[[[

[


119903 0 119903 119903 d

119903 119903 0 119903 119903

119903 119903 0 119903 119903

d 119903 119903 0 119903

119903 119903 119903 0

]]]]]]]]]]]

]

(11)

3 Results


























4 Conclusion





(a) (b)

(c) (d)


(a) (b) (c)

(d) (e) (f)








References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















Dynamic programming

Manualsegmentation




RPE segmentation


BM segmentation

Training images

EDI-OCTImage


1

1 2

(a) (b)

C(xm1 )

C(xm2 )

C(xmi )

C(xmn )

C(xm+1k )

k

n

m Mm+1








(a) (b)






layer119898(4) Let

119862 (119909119898+1

119896) = min119894=minus101

(119862 (119909119898

119896+119894) + 119892119898

(119894 119896)) (1)






119872lowast

119896to 1199091lowast119896



119896) indicate 119894 =


















1 alefsym2 alefsym



119896)


alefsym119896sim 119873 (120583

119896 Γ119896) (2)


(sum119870119896=1


119901 (119909119895) =

119870

sum

119896=1

120587119896119901 (119909119895| alefsym119896) (3)

in which

119901 (119909119895| alefsym119896)

=1

(2120587)11989921003816100381610038161003816

Γ119896

1003816100381610038161003816

12

exp(minus12

(119909119895minus 120583119896)

119879

Γminus1

119896(119909119895minus 120583119896))

(4)


1198831 1198832 119883

119894 119883


1198831

= 1199091 1199092 119909

119895 119909119860times119861


119901 (119883) =

119873

prod

119895=1

119901 (119909119895)

=

119873

prod

119895=1

119896

sum

119896=1

120587119896

(2120587)11989921003816100381610038161003816

Γ119896

1003816100381610038161003816

12

times exp(minus12

(119909119895minus 120583119896)

119879

Γminus1

119896(119909119895minus 120583119896))

(5)





119901119895119896=

120587119896119901 (119909119895| alefsym119896)

sum119896

119894=1120587119894119901 (119909119895| alefsym119894)

(6)




119894


120587new119896

=1

119873

119873

sum

119895=1

119901119895119896 (7)



119896and Γ119896

120583new119896

=

sum119873

119895=1119901119895119896119909119895

sum119873

119895=1119901119895119896

Γnew119896

=

sum119873

119895=1119901119895119896(119909119895minus 120583

new119896

) (119909119895minus 120583

new119896

)

119879

sum119873

119895=1119901119895119896

(8)



119895and 120583






119862 (119891) = 119888data (119891) + 119888smooth (119891) (9)






1

2

3

(a)

2

31

(b)








119896isin 1 2 3





119862data (119891) = minus log (119901 + 119890119901119904) (10)



119862smooth (119891) =

[[[[[[[[[[[

[


119903 0 119903 119903 d

119903 119903 0 119903 119903

119903 119903 0 119903 119903

d 119903 119903 0 119903

119903 119903 119903 0

]]]]]]]]]]]

]

(11)

3 Results


























4 Conclusion





(a) (b)

(c) (d)


(a) (b) (c)

(d) (e) (f)








References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















(a) (b)






layer119898(4) Let

119862 (119909119898+1

119896) = min119894=minus101

(119862 (119909119898

119896+119894) + 119892119898

(119894 119896)) (1)






119872lowast

119896to 1199091lowast119896



119896) indicate 119894 =


















1 alefsym2 alefsym



119896)


alefsym119896sim 119873 (120583

119896 Γ119896) (2)


(sum119870119896=1


119901 (119909119895) =

119870

sum

119896=1

120587119896119901 (119909119895| alefsym119896) (3)

in which

119901 (119909119895| alefsym119896)

=1

(2120587)11989921003816100381610038161003816

Γ119896

1003816100381610038161003816

12

exp(minus12

(119909119895minus 120583119896)

119879

Γminus1

119896(119909119895minus 120583119896))

(4)


1198831 1198832 119883

119894 119883


1198831

= 1199091 1199092 119909

119895 119909119860times119861


119901 (119883) =

119873

prod

119895=1

119901 (119909119895)

=

119873

prod

119895=1

119896

sum

119896=1

120587119896

(2120587)11989921003816100381610038161003816

Γ119896

1003816100381610038161003816

12

times exp(minus12

(119909119895minus 120583119896)

119879

Γminus1

119896(119909119895minus 120583119896))

(5)





119901119895119896=

120587119896119901 (119909119895| alefsym119896)

sum119896

119894=1120587119894119901 (119909119895| alefsym119894)

(6)




119894


120587new119896

=1

119873

119873

sum

119895=1

119901119895119896 (7)



119896and Γ119896

120583new119896

=

sum119873

119895=1119901119895119896119909119895

sum119873

119895=1119901119895119896

Γnew119896

=

sum119873

119895=1119901119895119896(119909119895minus 120583

new119896

) (119909119895minus 120583

new119896

)

119879

sum119873

119895=1119901119895119896

(8)



119895and 120583






119862 (119891) = 119888data (119891) + 119888smooth (119891) (9)






1

2

3

(a)

2

31

(b)








119896isin 1 2 3





119862data (119891) = minus log (119901 + 119890119901119904) (10)



119862smooth (119891) =

[[[[[[[[[[[

[


119903 0 119903 119903 d

119903 119903 0 119903 119903

119903 119903 0 119903 119903

d 119903 119903 0 119903

119903 119903 119903 0

]]]]]]]]]]]

]

(11)

3 Results


























4 Conclusion





(a) (b)

(c) (d)


(a) (b) (c)

(d) (e) (f)








References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of






















1 alefsym2 alefsym



119896)


alefsym119896sim 119873 (120583

119896 Γ119896) (2)


(sum119870119896=1


119901 (119909119895) =

119870

sum

119896=1

120587119896119901 (119909119895| alefsym119896) (3)

in which

119901 (119909119895| alefsym119896)

=1

(2120587)11989921003816100381610038161003816

Γ119896

1003816100381610038161003816

12

exp(minus12

(119909119895minus 120583119896)

119879

Γminus1

119896(119909119895minus 120583119896))

(4)


1198831 1198832 119883

119894 119883


1198831

= 1199091 1199092 119909

119895 119909119860times119861


119901 (119883) =

119873

prod

119895=1

119901 (119909119895)

=

119873

prod

119895=1

119896

sum

119896=1

120587119896

(2120587)11989921003816100381610038161003816

Γ119896

1003816100381610038161003816

12

times exp(minus12

(119909119895minus 120583119896)

119879

Γminus1

119896(119909119895minus 120583119896))

(5)





119901119895119896=

120587119896119901 (119909119895| alefsym119896)

sum119896

119894=1120587119894119901 (119909119895| alefsym119894)

(6)




119894


120587new119896

=1

119873

119873

sum

119895=1

119901119895119896 (7)



119896and Γ119896

120583new119896

=

sum119873

119895=1119901119895119896119909119895

sum119873

119895=1119901119895119896

Γnew119896

=

sum119873

119895=1119901119895119896(119909119895minus 120583

new119896

) (119909119895minus 120583

new119896

)

119879

sum119873

119895=1119901119895119896

(8)



119895and 120583






119862 (119891) = 119888data (119891) + 119888smooth (119891) (9)






1

2

3

(a)

2

31

(b)








119896isin 1 2 3





119862data (119891) = minus log (119901 + 119890119901119904) (10)



119862smooth (119891) =

[[[[[[[[[[[

[


119903 0 119903 119903 d

119903 119903 0 119903 119903

119903 119903 0 119903 119903

d 119903 119903 0 119903

119903 119903 119903 0

]]]]]]]]]]]

]

(11)

3 Results


























4 Conclusion





(a) (b)

(c) (d)


(a) (b) (c)

(d) (e) (f)








References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















1

2

3

(a)

2

31

(b)








119896isin 1 2 3





119862data (119891) = minus log (119901 + 119890119901119904) (10)



119862smooth (119891) =

[[[[[[[[[[[

[


119903 0 119903 119903 d

119903 119903 0 119903 119903

119903 119903 0 119903 119903

d 119903 119903 0 119903

119903 119903 119903 0

]]]]]]]]]]]

]

(11)

3 Results


























4 Conclusion





(a) (b)

(c) (d)


(a) (b) (c)

(d) (e) (f)








References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of







































4 Conclusion





(a) (b)

(c) (d)


(a) (b) (c)

(d) (e) (f)








References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















(a) (b)

(c) (d)


(a) (b) (c)

(d) (e) (f)








References








































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of






















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















research article segmentation of choroidal boundary in...

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