3D Curvelet-Based Segmentation and Quantification of Drusen ...downloads.hindawi.com/journals/jece/2017/4362603.pdfby applying length filtering and removing elongated short components.IntheextractedROI,possibleholesnearILM

Research Article3D Curvelet-Based Segmentation and Quantification of Drusenin Optical Coherence Tomography Images

M Esmaeili12 A M Dehnavi1 and H Rabbani1

1Department of Bioelectrics and Biomedical Engineering Medical Image amp Signal Processing Research CenterSchool of Advanced Technologies in Medicine Isfahan University of Medical Sciences Isfahan Iran2Department of Advanced Technologies in Medicine Faculty of Medicine Tabriz University of Medical Sciences Tabriz Iran

Correspondence should be addressed to H Rabbani hoss rabyahoocom

Received 26 July 2016 Revised 9 December 2016 Accepted 26 December 2016 Published 31 January 2017

Academic Editor Panajotis Agathoklis

Copyright copy 2017 M Esmaeili 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

Spectral-Domain Optical Coherence Tomography (SD-OCT) is a widely used interferometric diagnostic technique in ophthalmol-ogy that provides novel in vivo information of depth-resolved inner and outer retinal structures This imaging modality can assistclinicians inmonitoring the progression of Age-relatedMacularDegeneration (AMD) by providing high-resolution visualization ofdrusen Quantitative tools for assessing drusen volume that are indicative of AMD progression may lead to appropriate metrics forselecting treatment protocols To address this need a fully automated algorithmwas developed to segment drusen area and volumefrom SD-OCT images The proposed algorithm consists of three parts (1) preprocessing which includes creating binary mask andremoving possible highly reflective posterior hyaloid that is used in accurate detection of inner segmentouter segment (ISOS)junction layer and Bruchrsquos membrane (BM) retinal layers (2) coarse segmentation in which 3D curvelet transform and graphtheory are employed to get the possible candidate drusenoid regions (3) fine segmentation in which morphological operators areused to remove falsely extracted elongated structures and get the refined segmentation resultsThe proposedmethod was evaluatedin 20 publically available volumetric scans acquired by using Bioptigen spectral-domain ophthalmic imaging system The averagetrue positive and false positive volume fractions (TPVF and FPVF) for the segmentation of drusenoid regions were found to be8915plusmn 376 and 017plusmn 18 respectively

1 Introduction

Age-related Macular Degeneration (AMD) is the most com-mon degenerative eye disease that affects the central portionof the retina known as the macula and is the leading causeof vision loss and blindness in patients who are aged 65and over in the developing countries [1] There are twotypes of AMD dry (atrophic or nonneovascular) and wet(neovascular or exudative) [2] Dry form of AMD affectsapproximately 80ndash90 of individuals with AMD [3] and inthis type ofmacular degeneration extracellular small white oryellowish deposits (made up of lipids a type of fatty protein)called drusen accumulated between the Retinal PigmentEpithelium (RPE) and the inner collagenous layer of Bruchrsquosmembrane (vitreous lamina) Drusen are produced when thephotoreceptors of the eye drop off older parts of the celland could cause a protrusion of RPE over Bruchrsquos membrane

which leads to deterioration or degeneration of the maculaover time [4]

Drusen in the macula are a common early sign of AMDthat can be defined as hard and soft Hard drusen aresmall and distinct lesions with sharp borders (this type ofdrusen may not cause vision problems for a long time andis normal with aging and most people over 40 have somehard drusen) In contrast soft drusen are those with largelesions (clusters close together) with indistinct borders thathave been recognized as intermediate to advanced form ofAMD [5]

Most patients with macular degeneration have the dryform of the disease However the dry form of maculardegeneration can lead to the more damaging wet form thatusually leads to more serious vision loss [2]The Age-RelatedEyeDisease Study (AREDS) reported that certain antioxidantvitamins and zinc delay the progression of advanced dry

HindawiJournal of Electrical and Computer EngineeringVolume 2017 Article ID 4362603 12 pageshttpsdoiorg10115520174362603

2 Journal of Electrical and Computer Engineering

Table 1 Four defined categories by AREDS depending on the stages of AMD

Category 1 Category 2 Category 3 Category 4No AMD Early stage AMD Intermediate AMD Advanced AMD

No or a few small drusenSeveral small sized drusen or afew medium-sized drusen in

one or both eyes

Many medium-sized drusen or oneor more large drusen in one or both

eyes

Degeneration of the deepest cells of theretina (in one eye only) or abnormal andfragile blood vessels known as choroidalneovascularization under the retina (wet

form)

AMDor vision loss by about 25 percent over a six-year period[6] The early diagnosis of the patients at higher risk foradvanced AMD allows earlier protective intervention andpreventive treatment to reduce severe vision loss Thus itis more important to identify the main changes in drusenand the RPE morphology to inspect the progression ofnonneovascular AMD [7] As shown in Table 1 AREDSdefines four categories depending on the stages of AMD [8]

The previous studies on the color fundus (CF) imageshave shown that there is strong correlation between themaximum drusen size and total drusen area with the riskof progression of AMD to its advanced form [1 8] Manydifferent approaches and algorithms for automatic soft andhard drusen grading and quantification from CF imageshave been developed [9ndash12] However detecting and locatingthe drusen in a color retinal image are difficult to measurebecause of their differences in size and shape and alsoirregular and blurred boundaries

Spectral-Domain Optical Coherence Tomography (SD-OCT) is a widely used interferometric diagnostic techniquein ophthalmology that provides in vivo novel informationof depth-resolved inner and outer retinal structures Thehigh resolution sensitivity and speed of SD-OCT provides avaluable opportunity for detection and volumemeasurementof drusen from SD-OCT images compared to color fundusphotographs [13] and can be used as amethod of following theAMD development and monitoring retinal changes over thetime [8 14 15] However manual segmentation of maculardrusen area and volume is time consuming and labor inten-sive which limits its use in large-scale population So theautomatic segmentation of drusen becomes more appealingto process SD-OCT data more efficiently

OCT can provide useful information about drusen andresults inmore accurate differentiation of drusenoid depositsincluding cuticular drusen soft drusen and subretinaldrusenoid deposits [16] Soft drusen are yellow-white domeshaped elevations that their central portion appear lighterthan its edge and are typically 63 to ge1000 120583m in diameterSmaller soft drusen have a little effect on the RPE andISOS junction layer morphology Cuticular drusen appearas a round and punctate with saw tooth pattern in an SD-OCT and are typically 50 to 75 120583m in diameter [16] ButOCT subretinal drusenoid deposits are seen in the subretinalspace in similar size to soft drusen above the RPE Soft andcuticular drusen in contrast are under the RPE They oftenhave a more punctate appearance and are interconnected sothat their sizes range from 25 to gt1000 120583m [16]

Subretinal drusenoiddeposit

Soft drusen

Cuticulardrusen

RPE

Figure 1 Different appearance of drusen in OCT image softcuticular and subretinal drusen

As shown in Figure 1 small and medium-size drusenmay cause subtle elevation of discreet areas of RPE withvariable reflectivity indicating the variable accumulations ofthe underlying material Greater elevation of RPE may beseen as the result of larger confluent drusen or DrusenoidPigment EpitheliumDetachment (DPED) with a hyporeflec-tive or medium-reflective deposit separating the RPE fromthe underlying Bruch membrane (BM) [17]

Although a number of fullysemiautomatic techniqueshave been proposed to detect drusen from OCT images(Table 2) only the accuracy of a few methods has beenvalidated and they mainly only identify the absence orpresence of drusen The challenging issues associated withdrusen detection from OCT images include the variation oftexture and intensity distribution (hyporeflective ormedium-reflective) of drusen which prevents accurate segmentationof the RPE and BM for quantification of drusen complex(the distance between the abnormal RPE and the normalestimated RPE floor) and methods which are based onaccurate detection of RPE layer [18 19] may fail due todifficulty in RPE layer segmentation even in normal patientsbecause the RPE layers are often contiguous with the innersegmentouter segment (ISOS) retinal layer

In this paper we tackle the above-mentioned challengesand present a novel fully automated drusen segmentationmethod in SD-OCT images For this purpose in order toprevent inaccurate detection of retinal layers we preprocessOCT images and remove highly reflective posterior hyaloidor other reflective layers beneath the BM layer then weuse curvelet transform and modify curvelet coefficientsto enhance and fill the possible appeared vertically blackshadowing effects due to blood vessels These possible gapsdue to large vessels may degrade graph-based segmentation

Journal of Electrical and Computer Engineering 3

Table 2 Available image analysis techniques for AMD

Diagnostic techniques for AMD

Image analysistechniques for AMD

Color fundus imageanalysis

Texture-basedsegmentation

Gabor filter and wavelet analysis [33]Statistical structural information-based texture analysis [34]The Artificial Neural Network (ANN) based supervised

classifiers [35]Expectation Maximization (EM) based unsupervised classifiers

[36]

Thresholding-basedsegmentation

Probability based thresholding [37]Otsu method for background selection and intensity

thresholding [38]Histogram based adaptive local thresholding [39]

Edge based thresholding [11]

Clustering-basedsegmentation

Spatial histogram and similarity based classification [40]Distance based clustering [41]

Wavelet based feature extraction amp SVM based classification[42]

Edge and templatematching

Gaussian template matching [43]Gradient based segmentation [44]

OCT image analysistechniques

Graph-based segmentation Graph and dynamic programming [31]A graph-based multilayer segmentation approach [45]

Active contour-basedsegmentation

Anisotropic noise suppression and deformable splines [46]Based on active contours and Markov random fields [47]

Polynomial curve-fittingbased technique

Local convexity condition and fitting second- or fourth-orderpolynomials [48 49]

Based on the distance between the abnormal RPE and thenormal RPE floor [19 50]

of ISOS and BM layersThe areas located between the shiftedextracted ISOS junction layer and BM pixels by the use ofgraph theory from modified image are marked as drusen

The paper is organized as follows Section 2 provides anintroduction to 3D digital curvelet transform (3DCUT) InSection 3 our proposed method is described and the resultsand performance evaluation are presented in Section 4Finally the conclusions are given in Section 5

2 3D Digital Curvelet Transform

The curvelet transform is a time-frequency analysis of imagesthat gives a sparse representation of objects The basiselements of this transform have good directional selectivityand are highly anisotropic [20] The directional selectivity ofcurvelets and spatially localized property of each curvelet canbe utilized to preserve the image features along certain direc-tions in each subband Following this reasoning curveletsare appropriate basis elements (atoms) for representing d-D objects which are smooth apart from singularities alongsmooth manifolds of codimension 1 [21]

Although the direct analyzing of 3D data as a volume andconsidering the 3D geometrical nature of the data are compu-tationally expensive it has been shown that 3D analysis of 3Ddata outperforms 2D slice-by-slice analyzing of data [22]The

parabolic scaling good directional selectivity tightness andsparse representation properties of 3D curvelet singularitiesprovide new opportunities to analyze and study large data-sets in medical image processing 3D curvelet elements areplate-like shapes of 2minus1198952 in two directions and width about2minus119895 in the orthonormal direction which are smooth withinthe plate and oscillate along the normal direction of the plate

The 3D discrete curvelet transform is an extension to the2D curvelet transform proposed in [21] In 2D the curveletfamily is generated by translation (119887 isin R2) and rotation (120579)of the basic element 12059311988600

120593119886119887120579 (119909) = 12059311988600 (119877120579 (119909 minus 119887)) (1)

where 119877120579 = ( cos 120579 minus sin 120579sin 120579 cos 120579 ) is 2 times 2 rotation matrix with angle120579 and 12059311988600 isin 1198712(R2) is given by its Fourier transform12059311988600(120585) = 119880119886(120585) The 119886-scaled window119880119886 is a polar wedge in

frequency domain that is used for building curvelet functions[23] Since

120593119886119887120579 (120585) = 119890minus119894⟨119887120585⟩12059311988600 (119877120579120585) = 119890minus119894⟨119887120585⟩119880119886 (119877120579120585) (2)


(a) (b) (c)

Figure 2 3D rendering of curvelet atom in (a) space (b) frequency and (c) discrete frequency tiling The shaded area separates 3D wedge

using a suitable sampling at the range of scales 119886119895 = 2minus119895 119895 ge0 orientations 120579119895119897 = 1205871198972minuslceil1198952rceil2 119897 = 0 1 42lceil1198952rceil minus 1(lceil119909rceillfloor119909rfloor denote the smallest integer being greatersmallerthan or equal to 119909) and locations 119887119895119897119896 = 11988711989511989711989611198962 = 119877minus1120579119895119897(11989612119895 119896221198952)119879 1198961 1198962 isin 119885 the curvelet coefficients are definedas

119888119895119896119897 (119891) = int1198772

119891 (120585)119880119895 (119877120579119895119897120585) exp (119894 ⟨119887119895119897119896 120585⟩) 119889120585 (3)

To have Cartesian arrays instead of the polar tilingof the frequency plane the Cartesian window 119895(120585) isdefined [23] that determines the frequencies in the trapezoid(1205851 1205852) 2119895minus1 le 1205851 le 2119895+1 minus2minuslfloor1198952rfloor le (31205852)(21205851) le2minuslfloor1198952rfloor So the Cartesian counterpart of the coefficients canbe defined by

119888119895119896119897 (119891) = int1198772

119891 (120585) 119895 (119878minus1120579119895119897120585) exp (119894 ⟨119895119897119896 120585⟩) 119889120585 (4)

where 119896119895 = (11989612minus119895 11989622minuslfloor1198952rfloor)119879 (1198961 1198962)119879 isin 1198852 and 119895119897119896 =119878minus119879120579119895119897 (11989612minus119895 11989622minuslfloor1198952rfloor) = 119878minus119879120579119895119897119896119895 and 119878120579 = ( 1 0minus tan 120579 1 )

By defining regular rectangular grid instead of tilted gridCartesian curvelets are defined as

119888119895119896119897 (119891) = int1198772

119891 (120585) 119895 (119878minus1120579119895119897120585) 119890119894⟨119896119895 120585⟩119889120585 (5)

119895119897119896 = 119878minus119879120579119895119897119896119895 of formula (4) has been replaced by 119896119895 =(11989612minus119895 11989622minuslfloor1198952rfloor)119879 that is being taken on values on a rectan-gular grid

In 3D similar to 2D case the Cartesian window 119895(120585) isdefined by 119895(120585) = 119895(1205851 1205852 1205853) that isolates the frequenciesin the truncated pyramid

(1205851 1205852 1205853)119879 2119895minus1 le 1205851 le 2119895+1 minus2minuslfloor1198952rfloor le 3120585221205851le 2minuslfloor1198952rfloor minus2minuslfloor1198952rfloor le 3120585321205851 le 2minuslfloor1198952rfloor

(6)

With the angles 120579119895119897 and 120592119895119898 the 3D shear matrix is defined as

119878120579119895119897 120592119895119898 = ( 1 0 0minus tan 120579119895119897 1 0minus tan 120592119895119898 0 1

) wheretan 120579119895119897 = 1198972minuslfloor1198952rfloor 119897 = minus2lfloor1198952rfloor + 1 2lfloor1198952rfloor + 1tan 120592119895119898 = 1198982minuslfloor1198952rfloor 119898 = minus2lfloor1198952rfloor + 1 2lfloor1198952rfloor + 1

119896119895 = (11989612minus119895 11989622minuslfloor1198952rfloor 11989632minuslfloor1198952rfloor)119879

(1198961 1198962 1198963)119879 isin 1198853

(7)

In 3D every Cartesian corona has six components one foreach face of the unit cube Each component is regularlypartitioned into wedges with same volume as shown inFigure 2

The curvelet functions in the cone (1205851 1205852 1205853) 0 lt1205851 minus1 le 12058521205851 lt 1 minus1 le 12058531205851 lt 1 are given by

120593119895119896119897119898 = 120593119895000 (119878119879120579119895119897 120592119895119898 (119909 minus 119895119897119898119896 )) (8)

So its Fourier transform would be

120593119895119896119897119898 = exp (minus119894 ⟨119895119897119898119896 120585⟩) 120593119895000 (119878minus1120579119895119897 120592119895119898120585)= exp (minus119894 ⟨119895119897119898119896 120585⟩) 119895 (119878minus1120579119895119897 120592119895119898120585) (9)

where 120601119895000(120585) = 119895(120585) Analogously as in (5) the curveletcoefficients are given by

119862119895119896119897119898 (119891) = ⟨119891 120593119895119896119897119898⟩= int1198773

119891 (120585) 119895 (119878minus1120579119895119897 120592119895119898120585) exp (119894 ⟨119895119897119898119896 120585⟩) 119889120585= int1198773

119891(119878120579119895119897 120592119895119898120585) 119895 (120585) exp (119894 ⟨119896119895 120585⟩) 119889120585(10)

In this paper we use a new implementation of the 3D FastCurvelet Transform (3DFCT) [24 25] with strong directional


ILM

BM

Posterior hyaloid

Posterior hyaloid

ISOS

ILM

BMISOS

Figure 3 Presence of detached posterior hyaloid in B-scans ILMinternal limiting membrane ISOS inner segmentouter segmentand BM Bruchrsquos membrane

selectivity property at the finest scale that has a reducedredundancy factor than the wrapping-based implementationproposed in CurveLab Toolbox [20 21] According to thisimplementation 3D curvelet coefficients are obtained asfollows

(1) Cartesian coronization is performed that decomposesthe object into dyadic coronae based on concentriccubes Each corona is subdivided into trapezoidalregions conforming the usual parabolic scaling asshown in Figure 2

(2) The 3D coefficients are obtained by applying aninverse 3D FFT to each wrapped wedge as shown inFigure 2 which appropriately fits into a 3D rectan-gular parallelepipeds of dimensions sim (2119895 21198952 21198952)centered at the origin

3 Proposed Method

31 Preprocessing Theposterior hyaloidmembrane separatesthe vitreous from the retina A Posterior Vitreous Detach-ment (PVD) is a condition of the eye which is common inover 75 of patients who are age 65 and older in whichthe vitreous membrane is separated from the retina [26]As shown in Figure 3 the presence of detached posteriorhyaloid (thin layer above retina) in some B-scans of 3DOCT volumetric data creates an abnormal layer that maybe seen as a thin hyperreflective layer above the internallimiting membrane (ILM) Some previous algorithms [2728] that assume ILM to be the first hyperreflective layermay determine this abnormal detached vitreous membraneas the retinal boundary which results in an inaccuratesegmentation of the remaining layers also overestimation ofretinal thickness

To overcome this problem each OCT image is thresh-olded with an optimal threshold selected efficiently for each

image based on entropy-based thresholding algorithm [29]which takes into account the spatial distribution of gray levelsin order to coarsely extract the Region of Interest (ROI) fromthe nonretinal layer background

Some possible connected pixels due to highly reflectiveposterior hyaloid in thresholded image can be removedby applying length filtering and removing elongated shortcomponents In the extracted ROI possible holes near ILMare also removed by dilating and eroding (morphologicaloperators) with the disk shaped structuring element of radius5

In some cases upper band of ROI is segmented withsome kind of bumps (Figure 4(b) right) In order to segmentthis layer smoothly we fit a third order polynomial to theupper pixels of ROI region We use this boundary to limitthe search region in segmentation process of ISOS and BMand differentiate them from ILM (3 distinct hyperreflectivelayers with similar characteristics) Once the binary maskis generated 10 pixels below the upper detected boundaryin created binary image is used to separate inner and outerportion of retina and reduce the search range which results inan accurate and fine segmentation of BM and ISOS junctionlayer by the use of graph theory

Figure 4(d) shows the created binary mask in two sampleB-scans contain posterior hyaloid and bumps in detectedupper boundary of ROI

32 Drusenoid Region Segmentation The appeared verticallyblack shadowing effects due to blood vessels may degradethe continuity of ISOS junction layer andmethods based onthresholding and graph theorymay fail for accurate detectionof these layers in presence of large vessels So in order toenhance ISOS layer and fill these gaps we modify curveletcoefficients in OCT images Since the curvelet coefficientshave a sparse distribution and the bright objects get largecoefficients in the curvelet domain in order to enhance thebright hyperreflective regions in OCT images similar to onedefined by Starck et al [30] we take curvelet transform ofOCT image andmodifyDCUT coefficients using function 119896119888

119896119888 (119909) =

071199093 if 119909 lt 11987301119909 if 119873 le 119909 lt 611987306119909 if 6119873 le 119909 lt 9119873119909 if 9119873 le 119909

(11)

In this equation 119873 = 01119872 where 119872 is the maximumcurvelet coefficient of the relative bandThen we reconstructthe enhanced image from the modified curvelet coefficientsby applying inverse DCUT Figure 5(b) shows the recon-structed image from modified curvelet coefficients

To delineate the BM we use modified reconstructedimage with upper masked region using the extracted binarymask in previous section (Figure 5(c)) By using this imagethat the upper cropped region is set to zero the BM layerwould be the first light-to-dark boundary (vertically) Thenwe apply the graph theory based segmentationmethod in [31]


Posterior hyaloid

(a)

(b)

(c)

(d)

Figure 4 Created binarymask to accurate segmentation of BM andRPE First and second columns respectively show the results for a sampleB-scan with posterior hyaloid and a sample data with bumps in detected ROI region (a) Original image (b) Thresholded + length filtered +filled ROI image (c) Segmented upper band pixels of ROI (d) Created binary mask by fitting 3rd-order polynomial to upper band pixels ofROI

(a) (b)

(c) (d)

Figure 5 Reconstructed image from modified curvelet coefficients (a) Original image (b) modified image (c) masked image used todelineate the BM and (d) masked image used to delineate the ISOS junction layer


(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 6 Drusenoid region segmentation results (a) Original noisy image (b) detected ISOS junction boundary (c) detected BM layer (d)extracted BM and ISOS boundaries (e) 2nd-order polynomial fitted lines to extracted boundaries in order to calculate themean difference oftwo boundaries (f) created image by shifting the upper detected ISOS junction pixels (g) filled image (h) reconstructed image by applyingmorphological erosion and then dilation operators and (i) segmented drusenoid region

with an adjacency matrix that its weights are calculated usingthe following equation

119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 3 7)+ norm (minus (119892DL

119886 + 119892DL119887 ) 0 05)

+ norm (minus119889119886119887 2 4) + 119908min(12)

In this equation 119908119886119887 is the weight assigned to the edgeconnecting nodes 119886 and b 119892DL

119886 and 119892DL119887 are the vertical dark-

to-light gradients of the image at nodes 119886 and b 119892LD119886 and 119892LD

119887are the vertical light-to-dark gradients of the image at nodes119886 and 119887 and 119889119886119887 is the Euclidian distance from node 119886 to node119887 and 119908min = 1 times 10minus5 is the minimum weight of the graph

The norm notation norm(119860 119886 119887) indicates the normal-ization of the value 119860 to range from 119886 to 119887

For ISOS junction boundary we use modified recon-structed image after setting the upper cropped regions tomaximum intensity of image (Figure 5(d)) By using thisimage the ISOS layer is the first vertical dark-to-light

boundary For this image the adjacencymatrix is constructedby calculating the weights as follows

119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 0 05)+ norm (minus (119892DL

119886 + 119892DL119887 ) 2 3)

+ norm (minus119889119886119887 0 05) + 119908min

(13)

Figures 6(b) and 6(c) illustrate the results of applying thementioned graph-based method on the masked images for asample B-scan (Figure 6(a))

In order to estimate RPEDC (RPE + drusen complex)thickness at first we apply two 2nd order polynomial fittingfunctions to the detected ISOS and BM (Figure 6(d)) thenthemean difference of these two 2nd order polynomial curvesis calculated The calculated mean value is used to estimateRPEDC thickness (Figure 6(e)) and to shift upper detectedISOS pixels toward detected BM (Figure 6(f))

For extraction of drusenoid regions we produce an imagethat in each columnof this image if row location (inMATLABcoordinate system) of ISOS pixel + mean difference is lessthan or equal to the row location of detected BM we setthe row location of shifted ISOS (row location of ISOSpixel + mean difference) and row location of BM in thatcolumn to 1 otherwise this column is set to zero (Figure 6(f))


OCT image (I)

Apply length filtering and remove elongated short components

Dilate and erode D with the disk shaped structuring element to fill

possible holes

Take curvelet transform of image and collect curvelet coefficients

Take inverse curvelet transform of modified coefficients

Use upper detected pixels of ROI and limit the search region forgraph-based segmentation of ISOS junction layer and BM layer from reconstructed image

Apply 2nd-order order polynomial fitting functions to the detected ISOS and BM

Calculate the mean difference (m) of these two 2nd-order polynomial curves

Shift upper detected ISOS by m pixels toward detected BM

Fill the holes in produced image by shifting ISOS toward BM

Remove miss extracted line shape structures by morphological erosion and dilation of image with disk shape structure element

Apply threshold

T is selected threshold based on entropy-based thresholding

=

1 if I(i j) gt T

0 others

kc (x) =

07x3 if x lt N

01x if N le x lt 6N

06x if 6N le x lt 9N

x if 9N le x

Modify curvelet coefficients with

Fit 3rd-order polynomial to upperpixels of ROI

BW (i j)

kc

Figure 7 The block diagram of the proposed method

The created holes between connected layers (shifted ISOSand BM) are filled by performing a flood-fill morphologicaloperation on the pixels of the binary image (Figure 6(g))Then we remove miss extracted liny shape structures bymorphological erosion and dilation of image with disk shapestructure element (Figure 6(h)) Figure 6(i) shows the finalresults of our proposed method

A sketch of the proposed algorithm after detecting ISOSand BM layers with the use of graph theory is as inAlgorithm 1

Figure 7 illustrates the general block diagram of ourproposed approach

4 Results

For this study we use 20 volumetric scans acquired by usingBioptigen spectral-domain ophthalmic imaging system (thedataset is publicly available at httppeopledukeedusimsf59Chiu IOVS 2011 datasethtm) [31] Two independent expert

graders performed manual segmentation of the drusenoidregions using the 3D Slicer software (the software is freelyavailable at httpswwwslicerorg) We then performed au-tomatic segmentation using the algorithm described earlierwhich was implemented in MATLAB

To test the accuracy of proposed algorithm automaticsegmentation results for 220 B-scans across 20 patients werecompared against the available results from two graders

Segmentation results are quantitatively measured usingDice Coefficient (DC) and true positive and false positivevolume fractions (TPVF and FPVF) [32] are defined asfollows

Dice coefficient = 210038161003816100381610038161003816119881seg cap 119881ref

1003816100381610038161003816100381610038161003816100381610038161003816119881seg10038161003816100381610038161003816 + 1003816100381610038161003816119881ref

1003816100381610038161003816 (14)

where119881seg and119881ref are the extracted volume in the automaticsegmented image and in the reference ground truth imageThemaximum possible value for DC is 1 (indicating a perfectmatch between the result of the algorithm and ground truth)


Input I I is an image119898 times 119899 with extracted locations of ISOS and BM (Figure 6(d))Output DR Create the image DR for extraction of drusenoid regionsDR = zeros(size(I))For 119897 = 1 119899119860 = 119868( 119897)[119894 119895] = Find(119860 == 1)If 119898119894119899(119894) + mean diff-max(i)lt=0mean diff is obtained from I (Figure 6(e))DR(min(i) + mean diffl) = 1DR(119898119886119909(119894) 119897) = 1EndEnd

Algorithm 1 The proposed algorithm for drusenoid region segmentation

Table 3 Comparison of automatic versus manual results of drusenoid region segmentation

In comparison to Dice coefficient (DC) TPVF FPVFGrader 1 8945plusmn 346 8921plusmn 461 015plusmn 021Grader 2 8985plusmn 434 9012plusmn 443 012plusmn 026Graders 1 amp 2 9023plusmn 412 8915plusmn 376 017plusmn 018

and DC is zero for a slice when no drusenoid region isdetected or when there is no overlap between 119881seg and 119881ref

The mean and standard deviation of DC for all thevolumes with ground truth taken as Graders 1 and 2 andunion of Graders 1 and 2 are mentioned in Table 3

TPVF also indicates the fraction of the total amount oftissue inside the reference delineation and FPVF denotes theamount of tissue falsely identifiedThey are defined as follows

TPVF =10038161003816100381610038161003816119881seg cap 119881ref

100381610038161003816100381610038161003816100381610038161003816119881ref1003816100381610038161003816

FPVF =10038161003816100381610038161003816119881seg

10038161003816100381610038161003816 minus 10038161003816100381610038161003816119881seg cap 119881ref100381610038161003816100381610038161003816100381610038161003816119881119905V minus 119881ref

1003816100381610038161003816 (15)

where 119881119905V denotes the volume in the whole image betweenILM and BM

In order to show the effect of applying 3D curvelettransform in the proposed method in this paper we canimplement the different stages of proposed segmentationalgorithm without applying 3D curvelet transform and com-pare the results As an example Figure 8 shows the effectof applying 3D curvelet transform in accurate detection ofBM In comparison to the proposed method in [18] which isbased on assuming the RPE layer to be constant in thickness(20120583m) and using the threshold-based method to identifyRPE layer our proposed method can robustly identify RPEand ISOS layer for drusen quantification Figure 9 illustratesthe final results of proposed drusenoid region segmentationmethod in this paper for different B-scans

(a)

(b)

Figure 8 The results of detected BM by applying the graph-basedsegmentation method on (a) modified image by curvelet transformand (b) original image without modification

5 Conclusion

SD-OCT provides high axial resolution and dense 3D imag-ing of the pathological changes in the eye which makes itan appropriate device for detection of abnormal elevationsof the RPE and ISOS layer in various pathologies such asdrusenoid pigment epithelial detachment Previous methodsthat are based on difference between detected normal andabnormal RPE layer may fail due to difficulty in RPE layersegmentation even in normal patients because the RPE layerare often contiguous with the ISOS retinal layer

This paper presents a new fully automatic method tosegment and quantify the drusen volume from OCT imagesin order to provide a metric that can assist clinicians inmonitoring the progression of AMD The previous studies


(a) (b)

(c) (d)

(e) (f)

Figure 9 Experimental results for three examples of drusen segmentation The first column shows the original image and the 2nd columnshows the final fine segmentation results

show that there are good agreement of drusen diameter andmean drusen area on SD-OCT with those identified on colorfundus photographs In this base drusen detection using3D SD-OCT may be a potentially useful alternative methodto drusen assessment by human graders using color fundusphotographs

In order to prevent inaccurate detection of retinal layersby graph-based intraretinal layer segmentation methods wepreprocessed OCT images and removed highly reflectiveposterior hyaloid (or other reflective layers above RPE)and then we applied 3D curvelet transform and modifiedcurvelet coefficients to enhance and fill the possible appearedvertically black shadowing effects due to blood vessels Thesepossible gaps due to large vessels may degrade graph-basedsegmentation of ISOS and BM layers

The shifted upper detected ISOS pixels that are aboveBM are considered as a possible candidate region and domeshaped regions are considered as a drusenoid regions Theproposedmethod for drusen segmentation is not able to iden-tify small size drusen (approximately less than 8 pixels) Theinformation about the drusenoid area can be better assessedby creatingOCT fundus images as an enface projection imagefrom the SD-OCT dataset and registering these images to

corresponding color fundus photographs and mapping thedelineated drusen area on each color fundus photograph

Competing Interests

The authors declare that they have no competing interests

References

[1] R Klein B E K Klein S C Jensen and S MMeuer ldquoThe five-year incidence and progression of age-related maculopathy thebeaver dam eye studyrdquo Ophthalmology vol 104 no 1 pp 7ndash211997

[2] J Z Nowak ldquoAge-relatedmacular degeneration (AMD) patho-genesis and therapyrdquo Pharmacological Reports vol 58 no 3 pp353ndash363 2006

[3] Y Kanagasingam A Bhuiyan M D Abramoff R T SmithL Goldschmidt and T Y Wong ldquoProgress on retinal imageanalysis for age related macular degenerationrdquo Progress inRetinal and Eye Research vol 38 pp 20ndash42 2014

[4] I Barbazetto and U Schmidt-Erfurth ldquoPhotodynamic therapya novel approach to the treatment of AMDrdquo in Age-RelatedMacular Degeneration pp 143ndash158 Springer Berlin Germany2004


[5] NM Bressler S B Bressler and S L Fine ldquoAge-relatedmaculardegenerationrdquo Survey of Ophthalmology vol 32 no 6 pp 375ndash413 1988

[6] Age-Related Eye Disease Study Research Group ldquoA random-ized placebo-controlled clinical trial of high-dose supplemen-tation with vitamins C and E and beta carotene for age-relatedcataract and vision lossrdquoArchives of Ophthalmology vol 119 no10 p 1439 2001

[7] K I Hartmann M L Gomez D-U G Bartsch A K Schusterand W R Freeman ldquoEffect of change in drusen evolution onphotoreceptor inner segmentouter segment junctionrdquo Retinavol 32 no 8 pp 1492ndash1499 2012

[8] Age-Related Eye Disease Study Research Group ldquoThe Age-Related Eye Disease Study severity scale for age-relatedmaculardegeneration AREDS report no 17rdquoArchives of Ophthalmologyvol 123 no 11 pp 1484ndash1498 2005

[9] M Niemeijer B Van Ginneken S R Russell M S A Suttorp-Schulten andMDAbramoff ldquoAutomated detection and differ-entiation of drusen exudates and cotton-wool spots in digitalcolor fundus photographs for diabetic retinopathy diagnosisrdquoInvestigative Ophthalmology amp Visual Science vol 48 no 5 pp2260ndash2267 2007

[10] A Guven ldquoAutomatic detection of age-related macular degen-eration pathologies in retinal fundus imagesrdquo Computer Meth-ods in Biomechanics and Biomedical Engineering vol 16 no 4pp 425ndash434 2013

[11] Z Liang D W K Wong J Liu K L Chan and T YWong ldquoTowards automatic detection of age-related maculardegeneration in retinal fundus imagesrdquo in Proceedings of the32nd Annual International Conference of the IEEE Engineeringin Medicine and Biology Society (EMBC rsquo10) pp 4100ndash4103Buenos Aires Argentina September 2010

[12] 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

[13] Z Yehoshua G Gregori S R Sadda et al ldquoComparison ofdrusen area detected by spectral domain optical coherencetomography and color fundus imagingrdquo Investigative Ophthal-mology amp Visual Science vol 54 no 4 pp 2429ndash2434 2013

[14] T E Clemons L-Y Lee E Y Chew R C Milton S B BresslerandR Klein ldquoA simplified severity scale for age-relatedmaculardegenerationrdquo Archives of Ophthalmology vol 123 no 11 pp1570ndash1574 2005

[15] R Klein B E K Klein M D Knudtson S M Meuer MSwift and R E Gangnon ldquoFifteen-year cumulative incidence ofage-related macular degeneration the Beaver Dam Eye StudyrdquoOphthalmology vol 114 no 2 pp 253ndash262 2007

[16] R F Spaide and C A Curcio ldquoDrusen characterization withmultimodal imagingrdquo Retina vol 30 no 9 pp 1441ndash1454 2010

[17] P A Keane P J Patel S Liakopoulos F M Heussen SR Sadda and A Tufail ldquoEvaluation of age-related maculardegeneration with optical coherence tomographyrdquo Survey ofOphthalmology vol 57 no 5 pp 389ndash414 2012

[18] Q Chen T Leng L Zheng et al ldquoAutomated drusen segmen-tation and quantification in SD-OCT imagesrdquo Medical ImageAnalysis vol 17 no 8 pp 1058ndash1072 2013

[19] G Gregori FWang P J Rosenfeld et al ldquoSpectral domain opti-cal coherence tomography imaging of drusen in nonexudativeage-related macular degenerationrdquo Ophthalmology vol 118 no7 pp 1373ndash1379 2011

[20] L Ying L Demanet and E Candes ldquo3D discrete curvelettransformrdquo Applied and Computational Mathematics vol 502005

[21] E Candes L Demanet D Donoho and L Ying ldquoFast discretecurvelet transformsrdquo Multiscale Modeling amp Simulation vol 5no 3 pp 861ndash899 2006

[22] H Rabbani M Sonka andM D Abramoff ldquoOptical coherencetomography noise reduction using anisotropic local bivariategaussian mixture prior in 3D complex wavelet domainrdquo Inter-national Journal of Biomedical Imaging vol 2013 Article ID417491 23 pages 2013

[23] J Ma and G Plonka ldquoA review of curvelets and recent applica-tionsrdquo IEEE Signal Processing gazine vol 27 no 2 pp 118ndash1332010

[24] A Woiselle J-L Starck and J Fadili ldquo3-D data denoising andinpainting with the low-redundancy fast curvelet transformrdquoJournal of Mathematical Imaging and Vision vol 39 no 2 pp121ndash139 2011

[25] A Woiselle J-L Starck and J Fadili ldquo3D curvelet transformsand astronomical data restorationrdquo Applied and ComputationalHarmonic Analysis vol 28 no 2 pp 171ndash188 2010

[26] J Yonemoto Y Noda N Masuhara and S Ohno ldquoAge ofonset of posterior vitreous detachmentrdquo Current Opinion inOphthalmology vol 7 no 3 pp 73ndash76 1996

[27] S J Chiu X T Li P Nicholas C A Toth J A Izatt andS Farsiu ldquoAutomatic segmentation of seven retinal layers inSDOCT images congruent with expert manual segmentationrdquoOptics Express vol 18 no 18 pp 19413ndash19428 2010

[28] M Salarian R Ansari J Wanek and M Shahidi ldquoAcuuratesegmentation of retina nerve fiber layer in OCT imagesrdquoin Proceedings of the IEEE International Conference on Elec-troInformation Technology (EIT rsquo15) pp 653ndash656 IEEEDekalb Ill USA May 2015

[29] W-T Chen C-H Wen and C-W Yang ldquoA fast two-dimensional entropic thresholding algorithmrdquo Pattern Recogni-tion vol 27 no 7 pp 885ndash893 1994

[30] J-L Starck F Murtagh E J Candes and D L Donoho ldquoGrayand color image contrast enhancement by the curvelet trans-formrdquo IEEE Transactions on Image Processing vol 12 no 6 pp706ndash717 2003

[31] S J Chiu J A Izatt R V OrsquoConnell K P Winter C AToth and S Farsiu ldquoValidated automatic segmentation of AMDpathology including drusen and geographic atrophy in SD-OCT imagesrdquo InvestigativeOphthalmologyampVisual Science vol53 no 1 pp 53ndash61 2012

[32] J K Udupa V R LaBlanc H Schmidt et al ldquoMethodology forevaluating image-segmentation algorithmsrdquo inMedical Imaging2002 pp 266ndash277 2002

[33] N Lee A F Laine andT R Smith ldquoLearning non-homogenoustextures and the unlearning problemwith application to drusendetection in retinal imagesrdquo in Proceedings of the 5th IEEEInternational Symposium on Biomedical Imaging From Nano toMacro (ISBI rsquo08) pp 1215ndash1218 Paris France May 2008

[34] C Kose U Sevik OGencalioglu C Ikibas andT KayıkıcıogluldquoA statistical segmentation method for measuring age-relatedmacular degeneration in retinal fundus imagesrdquo Journal ofMedical Systems vol 34 no 1 pp 1ndash13 2010

[35] L Brandon and A Hoover ldquoDrusen detection in a retinalimage using multi-level analysisrdquo in Medical Image Computingand Computer-Assisted Intervention-MICCAI 2003 pp 618ndash625 Springer Berlin Germany 2003


[36] D E Freund N Bressler and P Burlina ldquoAutomated detectionof drusen in the maculardquo in Proceedings of the IEEE Interna-tional Symposium on Biomedical Imaging From Nano to Macro(ISBI rsquo09) pp 61ndash64 Boston Mass USA July 2009

[37] P SolizM PWilson S C Nemeth and P Nguyen ldquoComputer-aided methods for quantitative assessment of longitudinalchanges in retinal images presenting with maculopathyrdquo inMedical Imaging 2002 pp 159ndash170 2002

[38] R T Smith J K Chan T Nagasaki et al ldquoAutomated detectionof macular drusen using geometric background leveling andthreshold selectionrdquo Archives of Ophthalmology vol 123 no 2pp 200ndash206 2005

[39] K Rapantzikos and M Zervakis ldquoNonlinear enhancement andsegmentation algorithm for the detection of Age-related Macu-lar Degeneration (AMD) in human eyersquos retinardquo in Proceedingsof the IEEE International Conference on Image Processing (ICIPrsquo01) pp 1055ndash1058 Thessaloniki Greece October 2001

[40] M H A Hijazi F Coenen and Y Zheng ldquoRetinal imageclassification for the screening of age-relatedmacular degenera-tionrdquo in Research and Development in Intelligent Systems XXVIIIncorporating Applications and Innovations in Intelligent SystemsXVIII Proceedings of AI-2010 The Thirtieth SGAI InternationalConference on Innovative Techniques and Applications of Artifi-cial Intelligence pp 325ndash338 Springer Berlin Germany 2011

[41] G Quellec S R Russell and M D Abramoff ldquoOptimal filterframework for automated instantaneous detection of lesions inretinal imagesrdquo IEEE Transactions on Medical Imaging vol 30no 2 pp 523ndash533 2011

[42] S Lahmiri C S Gargour andM Gabrea ldquoAutomated patholo-gies detection in retina digital images based on complex con-tinuous wavelet transform phase anglesrdquoHealthcare TechnologyLetters vol 1 no 4 pp 104ndash108 2014

[43] B Remeseiro N Barreira D Calvo M Ortega and M GPenedo ldquoAutomatic drusen detection from digital retinalimages Amd preventionrdquo in Computer Aided Systems Theory-EUROCAST 2009 12th International Conference Las Palmasde Gran Canaria Spain February 15ndash20 2009 Revised SelectedPapers vol 5717 of Lecture Notes in Computer Science pp 187ndash194 Springer Berlin Germany 2009

[44] A D Mora P M Vieira A Manivannan and J M FonsecaldquoAutomated drusen detection in retinal images using analyticalmodelling algorithmsrdquo Biomedical Engineering Online vol 10article 59 2011

[45] M K Garvin M D Abramoff XWu S R Russell T L Burnsand M Sonka ldquoAutomated 3-D intraretinal layer segmentationof macular spectral-domain optical coherence tomographyimagesrdquo IEEE Transactions on Medical Imaging vol 28 no 9pp 1436ndash1447 2009

[46] M Mujat R C Chan B Cense et al ldquoRetinal nerve fiber layerthickness map determined from optical coherence tomographyimagesrdquo Optics Express vol 13 no 23 pp 9480ndash9491 2005

[47] I Ghorbel F Rossant I Bloch S Tick and M PaquesldquoAutomated segmentation ofmacular layers inOCT images andquantitative evaluation of performancesrdquo Pattern Recognitionvol 44 no 8 pp 1590ndash1603 2011

[48] S Farsiu S J Chiu J A Izatt et al ldquoFast detection and seg-mentation of drusen in retinal optical coherence tomographyimagesrdquo in Proceedings of the Ophthalmic Technologies XVIII68440D vol 6844 of Proceedings of SPIE February 2008

[49] C Toth S Farsiu S Chiu A Khanifar and J Izatt ldquoAutomaticDrusen segmentation and characterization in spectral domainoptical coherence tomography (SDOCT) images of AMD eyesrdquo

Investigative Ophthalmology amp Visual Science vol 49 p 53942008

[50] D Iwama M Hangai S Ooto et al ldquoAutomated assessmentof drusen using three-dimensional spectral-domain opticalcoherence tomographyrdquo Investigative Ophthalmology amp VisualScience vol 53 no 3 pp 1576ndash1583 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 athttpswwwhindawicom

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



Table 1 Four defined categories by AREDS depending on the stages of AMD

Category 1 Category 2 Category 3 Category 4No AMD Early stage AMD Intermediate AMD Advanced AMD

No or a few small drusenSeveral small sized drusen or afew medium-sized drusen in

one or both eyes

Many medium-sized drusen or oneor more large drusen in one or both

eyes

Degeneration of the deepest cells of theretina (in one eye only) or abnormal andfragile blood vessels known as choroidalneovascularization under the retina (wet

form)

AMDor vision loss by about 25 percent over a six-year period[6] The early diagnosis of the patients at higher risk foradvanced AMD allows earlier protective intervention andpreventive treatment to reduce severe vision loss Thus itis more important to identify the main changes in drusenand the RPE morphology to inspect the progression ofnonneovascular AMD [7] As shown in Table 1 AREDSdefines four categories depending on the stages of AMD [8]

The previous studies on the color fundus (CF) imageshave shown that there is strong correlation between themaximum drusen size and total drusen area with the riskof progression of AMD to its advanced form [1 8] Manydifferent approaches and algorithms for automatic soft andhard drusen grading and quantification from CF imageshave been developed [9ndash12] However detecting and locatingthe drusen in a color retinal image are difficult to measurebecause of their differences in size and shape and alsoirregular and blurred boundaries

Spectral-Domain Optical Coherence Tomography (SD-OCT) is a widely used interferometric diagnostic techniquein ophthalmology that provides in vivo novel informationof depth-resolved inner and outer retinal structures Thehigh resolution sensitivity and speed of SD-OCT provides avaluable opportunity for detection and volumemeasurementof drusen from SD-OCT images compared to color fundusphotographs [13] and can be used as amethod of following theAMD development and monitoring retinal changes over thetime [8 14 15] However manual segmentation of maculardrusen area and volume is time consuming and labor inten-sive which limits its use in large-scale population So theautomatic segmentation of drusen becomes more appealingto process SD-OCT data more efficiently

OCT can provide useful information about drusen andresults inmore accurate differentiation of drusenoid depositsincluding cuticular drusen soft drusen and subretinaldrusenoid deposits [16] Soft drusen are yellow-white domeshaped elevations that their central portion appear lighterthan its edge and are typically 63 to ge1000 120583m in diameterSmaller soft drusen have a little effect on the RPE andISOS junction layer morphology Cuticular drusen appearas a round and punctate with saw tooth pattern in an SD-OCT and are typically 50 to 75 120583m in diameter [16] ButOCT subretinal drusenoid deposits are seen in the subretinalspace in similar size to soft drusen above the RPE Soft andcuticular drusen in contrast are under the RPE They oftenhave a more punctate appearance and are interconnected sothat their sizes range from 25 to gt1000 120583m [16]

Subretinal drusenoiddeposit

Soft drusen

Cuticulardrusen

RPE

Figure 1 Different appearance of drusen in OCT image softcuticular and subretinal drusen

As shown in Figure 1 small and medium-size drusenmay cause subtle elevation of discreet areas of RPE withvariable reflectivity indicating the variable accumulations ofthe underlying material Greater elevation of RPE may beseen as the result of larger confluent drusen or DrusenoidPigment EpitheliumDetachment (DPED) with a hyporeflec-tive or medium-reflective deposit separating the RPE fromthe underlying Bruch membrane (BM) [17]

Although a number of fullysemiautomatic techniqueshave been proposed to detect drusen from OCT images(Table 2) only the accuracy of a few methods has beenvalidated and they mainly only identify the absence orpresence of drusen The challenging issues associated withdrusen detection from OCT images include the variation oftexture and intensity distribution (hyporeflective ormedium-reflective) of drusen which prevents accurate segmentationof the RPE and BM for quantification of drusen complex(the distance between the abnormal RPE and the normalestimated RPE floor) and methods which are based onaccurate detection of RPE layer [18 19] may fail due todifficulty in RPE layer segmentation even in normal patientsbecause the RPE layers are often contiguous with the innersegmentouter segment (ISOS) retinal layer

In this paper we tackle the above-mentioned challengesand present a novel fully automated drusen segmentationmethod in SD-OCT images For this purpose in order toprevent inaccurate detection of retinal layers we preprocessOCT images and remove highly reflective posterior hyaloidor other reflective layers beneath the BM layer then weuse curvelet transform and modify curvelet coefficientsto enhance and fill the possible appeared vertically blackshadowing effects due to blood vessels These possible gapsdue to large vessels may degrade graph-based segmentation









[36]
























120593119886119887120579 (119909) = 12059311988600 (119877120579 (119909 minus 119887)) (1)



120593119886119887120579 (120585) = 119890minus119894⟨119887120585⟩12059311988600 (119877120579120585) = 119890minus119894⟨119887120585⟩119880119886 (119877120579120585) (2)


(a) (b) (c)



119888119895119896119897 (119891) = int1198772

119891 (120585)119880119895 (119877120579119895119897120585) exp (119894 ⟨119887119895119897119896 120585⟩) 119889120585 (3)


119888119895119896119897 (119891) = int1198772

119891 (120585) 119895 (119878minus1120579119895119897120585) exp (119894 ⟨119895119897119896 120585⟩) 119889120585 (4)



119888119895119896119897 (119891) = int1198772

119891 (120585) 119895 (119878minus1120579119895119897120585) 119890119894⟨119896119895 120585⟩119889120585 (5)




(6)





(1198961 1198962 1198963)119879 isin 1198853

(7)



120593119895119896119897119898 = 120593119895000 (119878119879120579119895119897 120592119895119898 (119909 minus 119895119897119898119896 )) (8)




119862119895119896119897119898 (119891) = ⟨119891 120593119895119896119897119898⟩= int1198773

119891 (120585) 119895 (119878minus1120579119895119897 120592119895119898120585) exp (119894 ⟨119895119897119898119896 120585⟩) 119889120585= int1198773

119891(119878120579119895119897 120592119895119898120585) 119895 (120585) exp (119894 ⟨119896119895 120585⟩) 119889120585(10)



ILM

BM

Posterior hyaloid

Posterior hyaloid

ISOS

ILM

BMISOS





3 Proposed Method








119896119888 (119909) =


(11)




Posterior hyaloid

(a)

(b)

(c)

(d)


(a) (b)

(c) (d)



(a) (b) (c)

(d) (e) (f)

(g) (h) (i)



119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 3 7)+ norm (minus (119892DL

119886 + 119892DL119887 ) 0 05)

+ norm (minus119889119886119887 2 4) + 119908min(12)








119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 0 05)+ norm (minus (119892DL

119886 + 119892DL119887 ) 2 3)

+ norm (minus119889119886119887 0 05) + 119908min

(13)





OCT image (I)



possible holes









Apply threshold


=

1 if I(i j) gt T

0 others

kc (x) =

07x3 if x lt N

01x if N le x lt 6N


x if 9N le x



BW (i j)

kc





4 Results






1003816100381610038161003816100381610038161003816100381610038161003816119881seg10038161003816100381610038161003816 + 1003816100381610038161003816119881ref

1003816100381610038161003816 (14)










TPVF =10038161003816100381610038161003816119881seg cap 119881ref

100381610038161003816100381610038161003816100381610038161003816119881ref1003816100381610038161003816

FPVF =10038161003816100381610038161003816119881seg


1003816100381610038161003816 (15)



(a)

(b)


5 Conclusion




(a) (b)

(c) (d)

(e) (f)






Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















[36]
























120593119886119887120579 (119909) = 12059311988600 (119877120579 (119909 minus 119887)) (1)



120593119886119887120579 (120585) = 119890minus119894⟨119887120585⟩12059311988600 (119877120579120585) = 119890minus119894⟨119887120585⟩119880119886 (119877120579120585) (2)


(a) (b) (c)



119888119895119896119897 (119891) = int1198772

119891 (120585)119880119895 (119877120579119895119897120585) exp (119894 ⟨119887119895119897119896 120585⟩) 119889120585 (3)


119888119895119896119897 (119891) = int1198772

119891 (120585) 119895 (119878minus1120579119895119897120585) exp (119894 ⟨119895119897119896 120585⟩) 119889120585 (4)



119888119895119896119897 (119891) = int1198772

119891 (120585) 119895 (119878minus1120579119895119897120585) 119890119894⟨119896119895 120585⟩119889120585 (5)




(6)





(1198961 1198962 1198963)119879 isin 1198853

(7)



120593119895119896119897119898 = 120593119895000 (119878119879120579119895119897 120592119895119898 (119909 minus 119895119897119898119896 )) (8)




119862119895119896119897119898 (119891) = ⟨119891 120593119895119896119897119898⟩= int1198773

119891 (120585) 119895 (119878minus1120579119895119897 120592119895119898120585) exp (119894 ⟨119895119897119898119896 120585⟩) 119889120585= int1198773

119891(119878120579119895119897 120592119895119898120585) 119895 (120585) exp (119894 ⟨119896119895 120585⟩) 119889120585(10)



ILM

BM

Posterior hyaloid

Posterior hyaloid

ISOS

ILM

BMISOS





3 Proposed Method








119896119888 (119909) =


(11)




Posterior hyaloid

(a)

(b)

(c)

(d)


(a) (b)

(c) (d)



(a) (b) (c)

(d) (e) (f)

(g) (h) (i)



119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 3 7)+ norm (minus (119892DL

119886 + 119892DL119887 ) 0 05)

+ norm (minus119889119886119887 2 4) + 119908min(12)








119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 0 05)+ norm (minus (119892DL

119886 + 119892DL119887 ) 2 3)

+ norm (minus119889119886119887 0 05) + 119908min

(13)





OCT image (I)



possible holes









Apply threshold


=

1 if I(i j) gt T

0 others

kc (x) =

07x3 if x lt N

01x if N le x lt 6N


x if 9N le x



BW (i j)

kc





4 Results






1003816100381610038161003816100381610038161003816100381610038161003816119881seg10038161003816100381610038161003816 + 1003816100381610038161003816119881ref

1003816100381610038161003816 (14)










TPVF =10038161003816100381610038161003816119881seg cap 119881ref

100381610038161003816100381610038161003816100381610038161003816119881ref1003816100381610038161003816

FPVF =10038161003816100381610038161003816119881seg


1003816100381610038161003816 (15)



(a)

(b)


5 Conclusion




(a) (b)

(c) (d)

(e) (f)






Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c)



119888119895119896119897 (119891) = int1198772

119891 (120585)119880119895 (119877120579119895119897120585) exp (119894 ⟨119887119895119897119896 120585⟩) 119889120585 (3)


119888119895119896119897 (119891) = int1198772

119891 (120585) 119895 (119878minus1120579119895119897120585) exp (119894 ⟨119895119897119896 120585⟩) 119889120585 (4)



119888119895119896119897 (119891) = int1198772

119891 (120585) 119895 (119878minus1120579119895119897120585) 119890119894⟨119896119895 120585⟩119889120585 (5)




(6)





(1198961 1198962 1198963)119879 isin 1198853

(7)



120593119895119896119897119898 = 120593119895000 (119878119879120579119895119897 120592119895119898 (119909 minus 119895119897119898119896 )) (8)




119862119895119896119897119898 (119891) = ⟨119891 120593119895119896119897119898⟩= int1198773

119891 (120585) 119895 (119878minus1120579119895119897 120592119895119898120585) exp (119894 ⟨119895119897119898119896 120585⟩) 119889120585= int1198773

119891(119878120579119895119897 120592119895119898120585) 119895 (120585) exp (119894 ⟨119896119895 120585⟩) 119889120585(10)



ILM

BM

Posterior hyaloid

Posterior hyaloid

ISOS

ILM

BMISOS





3 Proposed Method








119896119888 (119909) =


(11)




Posterior hyaloid

(a)

(b)

(c)

(d)


(a) (b)

(c) (d)



(a) (b) (c)

(d) (e) (f)

(g) (h) (i)



119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 3 7)+ norm (minus (119892DL

119886 + 119892DL119887 ) 0 05)

+ norm (minus119889119886119887 2 4) + 119908min(12)








119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 0 05)+ norm (minus (119892DL

119886 + 119892DL119887 ) 2 3)

+ norm (minus119889119886119887 0 05) + 119908min

(13)





OCT image (I)



possible holes









Apply threshold


=

1 if I(i j) gt T

0 others

kc (x) =

07x3 if x lt N

01x if N le x lt 6N


x if 9N le x



BW (i j)

kc





4 Results






1003816100381610038161003816100381610038161003816100381610038161003816119881seg10038161003816100381610038161003816 + 1003816100381610038161003816119881ref

1003816100381610038161003816 (14)










TPVF =10038161003816100381610038161003816119881seg cap 119881ref

100381610038161003816100381610038161003816100381610038161003816119881ref1003816100381610038161003816

FPVF =10038161003816100381610038161003816119881seg


1003816100381610038161003816 (15)



(a)

(b)


5 Conclusion




(a) (b)

(c) (d)

(e) (f)






Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










ILM

BM

Posterior hyaloid

Posterior hyaloid

ISOS

ILM

BMISOS





3 Proposed Method








119896119888 (119909) =


(11)




Posterior hyaloid

(a)

(b)

(c)

(d)


(a) (b)

(c) (d)



(a) (b) (c)

(d) (e) (f)

(g) (h) (i)



119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 3 7)+ norm (minus (119892DL

119886 + 119892DL119887 ) 0 05)

+ norm (minus119889119886119887 2 4) + 119908min(12)








119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 0 05)+ norm (minus (119892DL

119886 + 119892DL119887 ) 2 3)

+ norm (minus119889119886119887 0 05) + 119908min

(13)





OCT image (I)



possible holes









Apply threshold


=

1 if I(i j) gt T

0 others

kc (x) =

07x3 if x lt N

01x if N le x lt 6N


x if 9N le x



BW (i j)

kc





4 Results






1003816100381610038161003816100381610038161003816100381610038161003816119881seg10038161003816100381610038161003816 + 1003816100381610038161003816119881ref

1003816100381610038161003816 (14)










TPVF =10038161003816100381610038161003816119881seg cap 119881ref

100381610038161003816100381610038161003816100381610038161003816119881ref1003816100381610038161003816

FPVF =10038161003816100381610038161003816119881seg


1003816100381610038161003816 (15)



(a)

(b)


5 Conclusion




(a) (b)

(c) (d)

(e) (f)






Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Posterior hyaloid

(a)

(b)

(c)

(d)


(a) (b)

(c) (d)



(a) (b) (c)

(d) (e) (f)

(g) (h) (i)



119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 3 7)+ norm (minus (119892DL

119886 + 119892DL119887 ) 0 05)

+ norm (minus119889119886119887 2 4) + 119908min(12)








119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 0 05)+ norm (minus (119892DL

119886 + 119892DL119887 ) 2 3)

+ norm (minus119889119886119887 0 05) + 119908min

(13)





OCT image (I)



possible holes









Apply threshold


=

1 if I(i j) gt T

0 others

kc (x) =

07x3 if x lt N

01x if N le x lt 6N


x if 9N le x



BW (i j)

kc





4 Results






1003816100381610038161003816100381610038161003816100381610038161003816119881seg10038161003816100381610038161003816 + 1003816100381610038161003816119881ref

1003816100381610038161003816 (14)










TPVF =10038161003816100381610038161003816119881seg cap 119881ref

100381610038161003816100381610038161003816100381610038161003816119881ref1003816100381610038161003816

FPVF =10038161003816100381610038161003816119881seg


1003816100381610038161003816 (15)



(a)

(b)


5 Conclusion




(a) (b)

(c) (d)

(e) (f)






Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c)

(d) (e) (f)

(g) (h) (i)



119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 3 7)+ norm (minus (119892DL

119886 + 119892DL119887 ) 0 05)

+ norm (minus119889119886119887 2 4) + 119908min(12)








119908119886119887 = norm (minus (119892LD119886 + 119892LD

119887 ) 0 05)+ norm (minus (119892DL

119886 + 119892DL119887 ) 2 3)

+ norm (minus119889119886119887 0 05) + 119908min

(13)





OCT image (I)



possible holes









Apply threshold


=

1 if I(i j) gt T

0 others

kc (x) =

07x3 if x lt N

01x if N le x lt 6N


x if 9N le x



BW (i j)

kc





4 Results






1003816100381610038161003816100381610038161003816100381610038161003816119881seg10038161003816100381610038161003816 + 1003816100381610038161003816119881ref

1003816100381610038161003816 (14)










TPVF =10038161003816100381610038161003816119881seg cap 119881ref

100381610038161003816100381610038161003816100381610038161003816119881ref1003816100381610038161003816

FPVF =10038161003816100381610038161003816119881seg


1003816100381610038161003816 (15)



(a)

(b)


5 Conclusion




(a) (b)

(c) (d)

(e) (f)






Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










OCT image (I)



possible holes









Apply threshold


=

1 if I(i j) gt T

0 others

kc (x) =

07x3 if x lt N

01x if N le x lt 6N


x if 9N le x



BW (i j)

kc





4 Results






1003816100381610038161003816100381610038161003816100381610038161003816119881seg10038161003816100381610038161003816 + 1003816100381610038161003816119881ref

1003816100381610038161003816 (14)










TPVF =10038161003816100381610038161003816119881seg cap 119881ref

100381610038161003816100381610038161003816100381610038161003816119881ref1003816100381610038161003816

FPVF =10038161003816100381610038161003816119881seg


1003816100381610038161003816 (15)



(a)

(b)


5 Conclusion




(a) (b)

(c) (d)

(e) (f)






Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















TPVF =10038161003816100381610038161003816119881seg cap 119881ref

100381610038161003816100381610038161003816100381610038161003816119881ref1003816100381610038161003816

FPVF =10038161003816100381610038161003816119881seg


1003816100381610038161003816 (15)



(a)

(b)


5 Conclusion




(a) (b)

(c) (d)

(e) (f)






Competing Interests


References
























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c) (d)

(e) (f)






Competing Interests


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




























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









Documents

3D Curvelet-Based Segmentation and Quantification of Drusen ...downloads.hindawi.com/journals/jece/2017/4362603.pdfby applying length filtering and removing elongated short components.IntheextractedROI,possibleholesnearILM