The use of synthetic images is needed for testing the performance of image processing methods in order to establish a ground truth to test performance metrics. However, these synthetic
images do not represent real applications. The aim of this paper is to build a mathematical model to obtain a synthetic noise-free image mimicking a real Optical Coherence Tomography (OCT) B-scan or volume from the human retina,
in order to establish a ground truth for filtering performance metrics in this context. Moreover we also suggest a method to add speckle noise to this image based on the speckle noise
of the given OCT volume. In this way we establish a replicable method to obtain a ground truth for image processing performance metrics that actually mimics a real case.FCTFEDERProgram COMPET

Bernardes, Rui

Maduro, Cristina

Santos, Torcato

Serranho, Pedro

Vaz, José Cunha

Repositório Aberto da Universidade Aberta

SYNTHETIC OCT DATA FOR IMAGE PROCESSING PERFORMANCE TESTINGP. SerranhoIBILI, Faculty of Medicine,University of Coimbra,Azinhaga de Santa Comba, Celas,3000-548 Coimbra, PortugalC. Maduro, T. Santos, J. Cunha-Vaz, R. BernardesIBILI, Faculty of Medicine,University of Coimbra,andAIBILI, Coimbra, PortugalABSTRACTThe use of synthetic images is needed for testing the perfor-mance of image processing methods in order to establish aground truth to test performance metrics. However, these syn-thetic images do not represent real applications. The aim ofthis paper is to build a mathematical model to obtain a syn-thetic noise-free image mimicking a real Optical CoherenceTomography (OCT) B-scan or volume from the human retina,in order to establish a ground truth for filtering performancemetrics in this context. Moreover we also suggest a methodto add speckle noise to this image based on the speckle noiseof the given OCT volume. In this way we establish a repli-cable method to obtain a ground truth for image processingperformance metrics that actually mimics a real case.Index Terms— Optical Coherence Tomography, Retina,Image Processing, Synthetic Image, Synthetic Noise.1. INTRODUCTIONCurrent image processing techniques (eg. despeckling filter-ing methods) with application to optical coherence tomogra-phy (OCT) rely on the respective qualitative evaluation of itsresults. Qualitative evaluation is usually subjective, since itdepends strongly on the expert evaluating the results. On theother hand, quantitative approaches are reduced to using syn-thetic images which consists of an homogeneous backgroundand a set of abstract geometric objects as concentric rings,squares or triangles with smooth or abrupt edges [1, 2] orare accepted by the image processing community as Lena orthe photographer [3, 4, 5]. These solutions are therefore farfrom optimal, since these synthetic images do not representthe features of real medical image data. Approaches for op-tical testing using phantoms mimicking tissue have alreadybeen developed [6], however to the best of our knowledge noapproach has been made in order to obtain a noise-free syn-thetic image of the retinal tissue as a ground truth to test theperformance of image processing tools nor a noise model forOCT speckle.This work was partially funded by PTDC/SAU-BEB/103151/2008 andprogram COMPETE (FCOMP-01-0124 FEDER-010930).The purpose of the paper at hand is to establish a noise-free synthetic image that mimics real OCT data. In this way,we suggest a method to establish a ground truth for the com-putation of performance metrics in the context of OCT im-age processing tools. We stress that it only makes sense thata feature as fundamental as the mean square error is com-puted if a noise-free ground truth is known. Moreover wesuggest a method to mimic the speckle noise present in thereal OCT data (as in most optic based mechanisms [7, 8]),so that noise can be added to the created synthetic image. Inthis way we have a complete model for OCT image process-ing performance metrics, since we establish a realistic groundtruth and noise pattern model.The computation of the synthetic image relies on featuresof the real OCT data. Each of the considered eye scans wasprocessed in order to extract required parameters. For healthysubjects, only the segmentation of the inner limiting mem-brane (ILM), the outer segment layer (OSL) and the retinalpigment epithelium (RPE) is required. We note that for patho-logic eyes, the segmentation of additional structures (cyst,epiretinal membrane, macular hole, etc...) to be preservedmight also be needed. In each segmented region, OCT datais surface fitted using appropriate basis functions. As for thecomputation of the noise distribution, we do not aim at mim-icking the physical process of speckle formation but to mimicthe speckle noise grainy aspect of the given OCT scan. Toachieve this, we study the intensity distribution in the vitre-ous. In this area, all the variability is due to noise, and there-fore the model for the noise distribution is fitted accordingly,having in mind the grainy appearance of speckle noise.The paper is organized as follows. In section 2 we presentin detail the method to obtain the synthetic retina and the syn-thetic noise. In section 3, we illustrate the results obtained,as well as results for the performed statistical tests to supportthe good performance of the proposed methods. Finally, insection 4 we summarize the results with some conclusions.2011 18th IEEE International Conference on Image Processing978-1-4577-1302-6/11/$26.00 ©2011 IEEE 4092. METHODSEye scans of 10 healthy volunteers were used following Cir-rus OCT (Carl Zeiss Meditec, Dublin, CA, USA) scans usingboth the 200x200x1024 and the 512x128x1024 Macular CubeProtocols.2.1. Synthetic imageFor each B-scan we consider the segmentation of the ILM, theinterface of the upper OSL and the interface between the RPEand the choroid, which in our case was performed manually.In this way, the image is divided in four different areas as il-lustrated in figure 1 (red contour in the left image). Each areais then mapped to the unitary square [0, 1]2 such that the left,right, upper and lower boundary of each segmented regionare mapped to the correspondent subsets within the unitarysquare of x = 0, x = 1, y = 0 and y = 1, respectively. Ac-cording to the variability of the signal in each region, a set ofbasis functions is chosen in the unitary square in order to fitthe given data. For the stability of the solution, we consideredTikhonov regularization. For instance, as the vitreous is sup-posed to be almost constant and this region should vary onlyin depth, we considered a linear approximationfvitreous(x, y) = a0 + a1x+ a2y, x, y ∈ [0, 1],where x is the horizontal direction, y is the depth (vertical)one and a0, a1, a2 are the coefficients that best fit the givenOCT data in a least squares sense. The following two regions(upper retina and OSL/RPE) present a much higher variabil-ity, so one needs a higher degree basis. In order to cope withhigh oscillations we considered a trigonometric series in eachof the two regions considered of the formfretina(x, y) =K∑k=0N∑n=0ak,n cos(kpix) cos(npiy)+K∑k=0N∑n=1bk,n cos(kpix) sin(npiy)+K∑k=1N∑n=0ck,n sin(kpix) cos(npiy)+K∑k=1N∑n=1dk,n sin(kpix) sin(npiy), (1)for x, y ∈ [0, 1] with appropriate choices of K and N ,where ak,n, bk,n, ck,n, dk,n are again the coefficients that bestfit to the given OCT data in each of these regions in a leastsquares sense. Finally, for the last region (choroid), it is clearthat the signal is decreasing in depth y (due to absorption)and may vary in the horizontal coordinate x. Hence we chosean approximation of the formfchoroid(x, y) =K∑k=0N∑n=0ak,ne−σx(x−xk)2−σy(2n−1)y, (2)for x, y ∈ [0, 1],with appropriate choices ofK,N, σx and σy ,and xk = k/K, for k = 0, 1, . . . ,K, with ak,n being the co-efficients that best fit the data for this region in a least squaresense.(a) (b) (c)Fig. 1. (a) Original B-scan with given segmented areas; (b)obtained synthetic image; (c) Comparison over the retina ofboth A-scan profiles (green dashed line on (a)).2.2. Noise modelFor each B-scan we consider a 100×100 pixel matrixAvitreouswithin the vitreous, in which we consider the distribution ofintensities. We note that in the vitreous no oscillation in thesignal intensities is expected, being therefore all the variabil-ity due to speckle noise. We considerAnoise = Avitreous − µAvitreous ,where µ holds for the mean. It is clear that µAnoise = 0 andthat the standard deviations coincide (σAnoise = σAvitreous ).We stress that the statistical properties of the OCT specklenoise are represented in Anoise and one can easily determineits probability density function.As a starting point we create a random matrix B(0) withthe same dimensions of the original image and the same den-sity probability function of Anoise . In order to get the usualgrainy appearance of OCT speckle noise in the synthetic noisematrix, we considered three different scales, namely the orig-inal matrixB(0) and the matrices obtained by taking the meanin m1 × n1 (denoted by B(1)) and m2 × n2 blocks (denotedby B(2)). We also considered an outlier matrix in each scale,given byO(k)i,j = B(k)i,j ,∣∣∣B(k)i,j ∣∣∣ > 3σB(k)0 otherwise,, k = 0, 1, 2,2011 18th IEEE International Conference on Image Processing410where σB(k) is the standard deviation of the entries of B(k).For each of these scale matrices we considered two low-passGaussian filters h1 and h2 with different standard variation σ1and σ2, respectively. Finally, we computed a weighted com-bination of these matricesC(k) = α1O(k) + α2(B(k) ∗ h1)+ α3(B(k) ∗ h2), (3)for k = 0, 1, 2, where ∗ holds for the discrete convolution,considerM = β1C(0) + β2C(1) + β3C(2). (4)We note that the sum of both the triplets of the coeffi-cients αi and βi, i = 1, 2, 3, should be equal to one. Weconsider M˜ =M − µM and makeAsynthetic−noise =σAnoiseσM˜M˜,in order to the synthetic noise matrix Asynthetic−noise to havethe same global statistics as the real noise matrix Anoise fromthe OCT data. The results are illustrated in figure 2, show-ing that both the statistics and the visual appearance of theoriginal and synthetic noise are similar.(a) (b) (c)(d) (e) (f)(g) (h) (i)Fig. 2. Original noise (top), synthetic noise (middle) andcomparison of both probability density functions (bottom)with several signal-to-noise ratios, namely SNR=3 dB (left),SNR=7 dB (center) and SNR=10 dB (right).3. RESULTSA total of 10 B-scans from 10 healthy eyes were processedresulting in the synthetic data representing the major charac-teristics of the respective real OCT scans.Having in mind the characteristic of the OCT signal ineach region, we considered K = N = 8 for both regions re-ferring to fretina in (1) and K = 8, N = 3, σx = 8, σy = 36for fchoroid in (2).Moreover, for the construction of the matrices B(1)and B(2) we considered block of size 1 × 2 and 1 × 5,respectively. We also considered two low-pass Gaussian fil-ters h1 and h2 such that the first is anisotropic with standardvariation σ1 = [0.15, 1.5] and the second is isotropic withstandard variation σ2 = [0.5, 0.5].Finally, in equations (3) and (4) we consideredα1 = 0.2, α2 = 0.2, α3 = 0.6,β1 = 0.6, β2 = 0.3, β3 = 0.1.In figure 3 we present the sum of the synthetic B-scan andthe synthetic noise in order to compare with the original scan.The main visible difference between the synthetic and orig-inal data is at the beginning of the choroid, which is not aproblem for the intended application, since the region of in-terest is the retina.(a) (b) (c)Fig. 3. (a) Original OCT B-scan; (b) Synthetic OCT B-scanwith synthetic noise added; (c) Comparison of the probabilitydensity function of the intensities of the original (red dashed)and synthetic (blue) B-scan.We note that the standard variation for the differencebetween the original and the noise-free synthetic imageis 14.29 ± 0.34 (mean ± std. dev.) while the noise levelin the vitreous is 10.88 ± 0.27. This shows that the error ofour approximation is of the same order of magnitude as thenoise level.We have also compared the probability density functionsof the intensities of both the original and noisy synthetic im-ages, which are illustrated in figure 3(c). A Rank-sum test forthe comparison of both probability functions for the sample ofdimension 10 gave p-values 0.37±0.28, which shows that thedistribution of intensities is similar in the synthetic and orig-inal images. A comparison within each segmented layer isalso presented in figure 4. As expected, the main differencesare presented within the retina, since we force the syntheticretina to be smoother than the original signal in order to havea smooth ground truth.In order to validate the synthetic noise model alone, weconsidered 100 × 100 pixel regions of the vitreous of theoriginal and the correspondent synthetic data. A Rank-sumTest for the comparison of the two distribution gave p-valuesof 0.83 ± 0.12 in our 10-dimensional sample, showing thatthe speckle synthetic model mimics the real one with high ac-curacy. Moreover, the same 20 images were shown to 3 OCT2011 18th IEEE International Conference on Image Processing411(a) (b)(c) (d)Fig. 4. Comparison of the probability density function of theintensities of the original (red dashed) and synthetic (blue) B-scan in each region ((a) Vitreous, (b) Upper Retina, (c) OSLand RPE, (d) choroid) for the example shown in figure 3.technicians in order for them to classify them into original orsynthetic noise. Results demonstrate the difficulty in correctclassification, with 52 misclassifications and only 8 correctclassifications out of 60, that is, 86.6% and 13.3%, respec-tively. Additionally, out of the 30 classifications of syntheticnoise images, 22 were classified as original (73.3%) and only8 were classified as synthetic (26.7%). No original noise im-age was classified as such, illustrating that the synthetic noiseimages were very close to the original ones.4. DISCUSSIONS AND CONCLUSIONSWe propose a method to generate synthetic OCT data thatmimics real one. The approach is two-folded. We obtain anoise-free synthetic B-scan that mimics the main features ofa given original one with an appropriate segmentation, in or-der to establish a ground truth for processing methods. Themethod is designed so that for healthy eyes one only needsthe segmentation of 4 areas (that is, 3 interfaces), which canbe easily accomplished.Moreover, we showed the statistic validation of an OCTspeckle noise model, based on the characteristics of the givenreal OCT data. If one adds the synthetic noise and the syn-thetic noise-free B-scan generated by our methods, one hasan adequate synthetic image in the context of OCT processingmethods. In this way, this process makes it possible to have aquantitative evaluation of the performance of any image pro-cessing procedure (eg. filtering) by providing adequate syn-thetic data as ground truth.These results have been used for testing the performanceof an improved complex diffusion despeckling method [1]subsequently to its publication. We also intend to apply thismethod to pathologic eyes. This extension is straighforward,given that the segmentation of additional structures (eg. cysts,epiretinal membranes, macular holes, etc...) is provided. Thepossibility of using less smooth approximation spaces in eachsegmented region will also be considered.AcknowledgmentsThe authors would like to thank Dr. Melissa Horne and CarlZeiss Meditec (Dublin, CA, USA) for their support on get-ting access to OCT data, and AIBILI Clinical Trial Centertechnicians for their support in managing data, working withpatients and performing scans.5. REFERENCES[1] R. Bernardes, C. Maduro, P. Serranho, A. Arau´jo, S. Bar-beiro, and J. Cunha-Vaz, “Improved adaptive complexdiffusion despeckling filter,” Opt. Express, vol. 18, no.23, pp. 24048–24059, 2010.[2] H. Salinas and D. Ferna´ndez, “Comparison of pde-basednonlinear diffusion approaches for image enhancementand denoising in optical coherence tomography,” IEEETrans Med Imaging, vol. 26 (6), pp. 761–771, 2007.[3] G. Gilboa, N. Sochen, and Y. Zeeni, “Image enhancementand denoising by complex diffusion processes,” IEEETrans Pattern Anal Mach Intell, vol. 26, no. 8, pp. 1020–1036, 2004.[4] P. Perona and J. Malik, “Scale-space and edge detectionusing anisotropic diffusion,” Pattern Analysis and Ma-chine Intelligence, IEEE Transactions on, vol. 12, no. 7,pp. 629 –639, July 1990.[5] J. Rajan and M.R. Kaimal, “Image denoising usingwavelet embedded anisotropic diffusion (wead),” IETConference Publications, vol. 2006, no. CP522, pp. 589–593, 2006.[6] D.C. Fernandez and H.M. Salinas, “A tissue phantomfor investigating volume quantification on retinal imagesobtained with the stratus oct system,” in Engineer-ing in Medicine and Biology Society, 2004. IEMBS ’04.26th Annual International Conference of the IEEE, 2004,vol. 1, pp. 1225 –1228.[7] J. Dainty, A. Ennos, M. Franc¸on, J. Goodman, T. McK-echnie, G. Parry, and J. Goodman, “Statistical prop-erties of laser speckle patterns,” in Laser Speckleand Related Phenomena, vol. 9 of Topics in AppliedPhysics, pp. 9–75. Springer Berlin / Heidelberg, 1975,10.1007/BFb0111436.[8] J. W. Goodman, “Some fundamental properties ofspeckle,” J. Opt. Soc. Am., vol. 66, no. 11, pp. 1145–1150, Nov 1976.2011 18th IEEE International Conference on Image Processing412

Synthtic OCT Data for image processing performance testing

The Repositório Aberto

SYNTHETIC OCT DATA FOR IMAGE PROCESSING PERFORMANCE TESTING
P. Serranho
IBILI, Faculty of Medicine,
University of Coimbra,
Azinhaga de Santa Comba, Celas,
3000-548 Coimbra, Portugal
C. Maduro, T. Santos, J. Cunha-Vaz, R. Bernardes
IBILI, Faculty of Medicine,
University of Coimbra,
and
AIBILI, Coimbra, Portugal
ABSTRACT
The use of synthetic images is needed for testing the perfor-
mance of image processing methods in order to establish a
ground truth to test performance metrics. However, these syn-
thetic images do not represent real applications. The aim of
this paper is to build a mathematical model to obtain a syn-
thetic noise-free image mimicking a real Optical Coherence
Tomography (OCT) B-scan or volume from the human retina,
in order to establish a ground truth for filtering performance
metrics in this context. Moreover we also suggest a method
to add speckle noise to this image based on the speckle noise
of the given OCT volume. In this way we establish a repli-
cable method to obtain a ground truth for image processing
performance metrics that actually mimics a real case.
Index Terms— Optical Coherence Tomography, Retina,
Image Processing, Synthetic Image, Synthetic Noise.
1. INTRODUCTION
Current image processing techniques (eg. despeckling filter-
ing methods) with application to optical coherence tomogra-
phy (OCT) rely on the respective qualitative evaluation of its
results. Qualitative evaluation is usually subjective, since it
depends strongly on the expert evaluating the results. On the
other hand, quantitative approaches are reduced to using syn-
thetic images which consists of an homogeneous background
and a set of abstract geometric objects as concentric rings,
squares or triangles with smooth or abrupt edges [1, 2] or
are accepted by the image processing community as Lena or
the photographer [3, 4, 5]. These solutions are therefore far
from optimal, since these synthetic images do not represent
the features of real medical image data. Approaches for op-
tical testing using phantoms mimicking tissue have already
been developed [6], however to the best of our knowledge no
approach has been made in order to obtain a noise-free syn-
thetic image of the retinal tissue as a ground truth to test the
performance of image processing tools nor a noise model for
OCT speckle.
This work was partially funded by PTDC/SAU-BEB/103151/2008 and
program COMPETE (FCOMP-01-0124 FEDER-010930).
The purpose of the paper at hand is to establish a noise-
free synthetic image that mimics real OCT data. In this way,
we suggest a method to establish a ground truth for the com-
putation of performance metrics in the context of OCT im-
age processing tools. We stress that it only makes sense that
a feature as fundamental as the mean square error is com-
puted if a noise-free ground truth is known. Moreover we
suggest a method to mimic the speckle noise present in the
real OCT data (as in most optic based mechanisms [7, 8]),
so that noise can be added to the created synthetic image. In
this way we have a complete model for OCT image process-
ing performance metrics, since we establish a realistic ground
truth and noise pattern model.
The computation of the synthetic image relies on features
of the real OCT data. Each of the considered eye scans was
processed in order to extract required parameters. For healthy
subjects, only the segmentation of the inner limiting mem-
brane (ILM), the outer segment layer (OSL) and the retinal
pigment epithelium (RPE) is required. We note that for patho-
logic eyes, the segmentation of additional structures (cyst,
epiretinal membrane, macular hole, etc...) to be preserved
might also be needed. In each segmented region, OCT data
is surface fitted using appropriate basis functions. As for the
computation of the noise distribution, we do not aim at mim-
icking the physical process of speckle formation but to mimic
the speckle noise grainy aspect of the given OCT scan. To
achieve this, we study the intensity distribution in the vitre-
ous. In this area, all the variability is due to noise, and there-
fore the model for the noise distribution is fitted accordingly,
having in mind the grainy appearance of speckle noise.
The paper is organized as follows. In section 2 we present
in detail the method to obtain the synthetic retina and the syn-
thetic noise. In section 3, we illustrate the results obtained,
as well as results for the performed statistical tests to support
the good performance of the proposed methods. Finally, in
section 4 we summarize the results with some conclusions.
2011 18th IEEE International Conference on Image Processing978-1-4577-1302-6/11/$26.00 ©2011 IEEE 409
2. METHODS
Eye scans of 10 healthy volunteers were used following Cir-
rus OCT (Carl Zeiss Meditec, Dublin, CA, USA) scans using
both the 200x200x1024 and the 512x128x1024 Macular Cube
Protocols.
2.1. Synthetic image
For each B-scan we consider the segmentation of the ILM, the
interface of the upper OSL and the interface between the RPE
and the choroid, which in our case was performed manually.
In this way, the image is divided in four different areas as il-
lustrated in figure 1 (red contour in the left image). Each area
is then mapped to the unitary square [0, 1]2 such that the left,
right, upper and lower boundary of each segmented region
are mapped to the correspondent subsets within the unitary
square of x = 0, x = 1, y = 0 and y = 1, respectively. Ac-
cording to the variability of the signal in each region, a set of
basis functions is chosen in the unitary square in order to fit
the given data. For the stability of the solution, we considered
Tikhonov regularization. For instance, as the vitreous is sup-
posed to be almost constant and this region should vary only
in depth, we considered a linear approximation
fvitreous(x, y) = a0 + a1x+ a2y, x, y ∈ [0, 1],
where x is the horizontal direction, y is the depth (vertical)
one and a0, a1, a2 are the coefficients that best fit the given
OCT data in a least squares sense. The following two regions
(upper retina and OSL/RPE) present a much higher variabil-
ity, so one needs a higher degree basis. In order to cope with
high oscillations we considered a trigonometric series in each
of the two regions considered of the form
fretina(x, y) =
K∑
k=0
N∑
n=0
ak,n cos(kpix) cos(npiy)
+
K∑
k=0
N∑
n=1
bk,n cos(kpix) sin(npiy)
+
K∑
k=1
N∑
n=0
ck,n sin(kpix) cos(npiy)
+
K∑
k=1
N∑
n=1
dk,n sin(kpix) sin(npiy), (1)
for x, y ∈ [0, 1] with appropriate choices of K and N ,
where ak,n, bk,n, ck,n, dk,n are again the coefficients that best
fit to the given OCT data in each of these regions in a least
squares sense. Finally, for the last region (choroid), it is clear
that the signal is decreasing in depth y (due to absorption)
and may vary in the horizontal coordinate x. Hence we chose
an approximation of the form
fchoroid(x, y) =
K∑
k=0
N∑
n=0
ak,ne
−σx(x−xk)2−σy(2n−1)y, (2)
for x, y ∈ [0, 1],with appropriate choices ofK,N, σx and σy ,
and xk = k/K, for k = 0, 1, . . . ,K, with ak,n being the co-
efficients that best fit the data for this region in a least square
sense.
(a) (b) (c)
Fig. 1. (a) Original B-scan with given segmented areas; (b)
obtained synthetic image; (c) Comparison over the retina of
both A-scan profiles (green dashed line on (a)).
2.2. Noise model
For each B-scan we consider a 100×100 pixel matrixAvitreous
within the vitreous, in which we consider the distribution of
intensities. We note that in the vitreous no oscillation in the
signal intensities is expected, being therefore all the variabil-
ity due to speckle noise. We consider
Anoise = Avitreous − µAvitreous ,
where µ holds for the mean. It is clear that µAnoise = 0 and
that the standard deviations coincide (σAnoise = σAvitreous ).
We stress that the statistical properties of the OCT speckle
noise are represented in Anoise and one can easily determine
its probability density function.
As a starting point we create a random matrix B(0) with
the same dimensions of the original image and the same den-
sity probability function of Anoise . In order to get the usual
grainy appearance of OCT speckle noise in the synthetic noise
matrix, we considered three different scales, namely the orig-
inal matrixB(0) and the matrices obtained by taking the mean
in m1 × n1 (denoted by B(1)) and m2 × n2 blocks (denoted
by B(2)). We also considered an outlier matrix in each scale,
given by
O
(k)
i,j =
 B
(k)
i,j ,
∣∣∣B(k)i,j ∣∣∣ > 3σB(k)
0 otherwise,
, k = 0, 1, 2,
2011 18th IEEE International Conference on Image Processing410
where σB(k) is the standard deviation of the entries of B(k).
For each of these scale matrices we considered two low-pass
Gaussian filters h1 and h2 with different standard variation σ1
and σ2, respectively. Finally, we computed a weighted com-
bination of these matrices
C(k) = α1O
(k) + α2
(
B(k) ∗ h1
)
+ α3
(
B(k) ∗ h2
)
, (3)
for k = 0, 1, 2, where ∗ holds for the discrete convolution,
consider
M = β1C
(0) + β2C
(1) + β3C
(2). (4)
We note that the sum of both the triplets of the coeffi-
cients αi and βi, i = 1, 2, 3, should be equal to one. We
consider M˜ =M − µM and make
Asynthetic−noise =
σAnoise
σM˜
M˜,
in order to the synthetic noise matrix Asynthetic−noise to have
the same global statistics as the real noise matrix Anoise from
the OCT data. The results are illustrated in figure 2, show-
ing that both the statistics and the visual appearance of the
original and synthetic noise are similar.
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Fig. 2. Original noise (top), synthetic noise (middle) and
comparison of both probability density functions (bottom)
with several signal-to-noise ratios, namely SNR=3 dB (left),
SNR=7 dB (center) and SNR=10 dB (right).
3. RESULTS
A total of 10 B-scans from 10 healthy eyes were processed
resulting in the synthetic data representing the major charac-
teristics of the respective real OCT scans.
Having in mind the characteristic of the OCT signal in
each region, we considered K = N = 8 for both regions re-
ferring to fretina in (1) and K = 8, N = 3, σx = 8, σy = 36
for fchoroid in (2).
Moreover, for the construction of the matrices B(1)
and B(2) we considered block of size 1 × 2 and 1 × 5,
respectively. We also considered two low-pass Gaussian fil-
ters h1 and h2 such that the first is anisotropic with standard
variation σ1 = [0.15, 1.5] and the second is isotropic with
standard variation σ2 = [0.5, 0.5].
Finally, in equations (3) and (4) we considered
α1 = 0.2, α2 = 0.2, α3 = 0.6,
β1 = 0.6, β2 = 0.3, β3 = 0.1.
In figure 3 we present the sum of the synthetic B-scan and
the synthetic noise in order to compare with the original scan.
The main visible difference between the synthetic and orig-
inal data is at the beginning of the choroid, which is not a
problem for the intended application, since the region of in-
terest is the retina.
(a) (b) (c)
Fig. 3. (a) Original OCT B-scan; (b) Synthetic OCT B-scan
with synthetic noise added; (c) Comparison of the probability
density function of the intensities of the original (red dashed)
and synthetic (blue) B-scan.
We note that the standard variation for the difference
between the original and the noise-free synthetic image
is 14.29 ± 0.34 (mean ± std. dev.) while the noise level
in the vitreous is 10.88 ± 0.27. This shows that the error of
our approximation is of the same order of magnitude as the
noise level.
We have also compared the probability density functions
of the intensities of both the original and noisy synthetic im-
ages, which are illustrated in figure 3(c). A Rank-sum test for
the comparison of both probability functions for the sample of
dimension 10 gave p-values 0.37±0.28, which shows that the
distribution of intensities is similar in the synthetic and orig-
inal images. A comparison within each segmented layer is
also presented in figure 4. As expected, the main differences
are presented within the retina, since we force the synthetic
retina to be smoother than the original signal in order to have
a smooth ground truth.
In order to validate the synthetic noise model alone, we
considered 100 × 100 pixel regions of the vitreous of the
original and the correspondent synthetic data. A Rank-sum
Test for the comparison of the two distribution gave p-values
of 0.83 ± 0.12 in our 10-dimensional sample, showing that
the speckle synthetic model mimics the real one with high ac-
curacy. Moreover, the same 20 images were shown to 3 OCT
2011 18th IEEE International Conference on Image Processing411
(a) (b)
(c) (d)
Fig. 4. Comparison of the probability density function of the
intensities of the original (red dashed) and synthetic (blue) B-
scan in each region ((a) Vitreous, (b) Upper Retina, (c) OSL
and RPE, (d) choroid) for the example shown in figure 3.
technicians in order for them to classify them into original or
synthetic noise. Results demonstrate the difficulty in correct
classification, with 52 misclassifications and only 8 correct
classifications out of 60, that is, 86.6% and 13.3%, respec-
tively. Additionally, out of the 30 classifications of synthetic
noise images, 22 were classified as original (73.3%) and only
8 were classified as synthetic (26.7%). No original noise im-
age was classified as such, illustrating that the synthetic noise
images were very close to the original ones.
4. DISCUSSIONS AND CONCLUSIONS
We propose a method to generate synthetic OCT data that
mimics real one. The approach is two-folded. We obtain a
noise-free synthetic B-scan that mimics the main features of
a given original one with an appropriate segmentation, in or-
der to establish a ground truth for processing methods. The
method is designed so that for healthy eyes one only needs
the segmentation of 4 areas (that is, 3 interfaces), which can
be easily accomplished.
Moreover, we showed the statistic validation of an OCT
speckle noise model, based on the characteristics of the given
real OCT data. If one adds the synthetic noise and the syn-
thetic noise-free B-scan generated by our methods, one has
an adequate synthetic image in the context of OCT processing
methods. In this way, this process makes it possible to have a
quantitative evaluation of the performance of any image pro-
cessing procedure (eg. filtering) by providing adequate syn-
thetic data as ground truth.
These results have been used for testing the performance
of an improved complex diffusion despeckling method [1]
subsequently to its publication. We also intend to apply this
method to pathologic eyes. This extension is straighforward,
given that the segmentation of additional structures (eg. cysts,
epiretinal membranes, macular holes, etc...) is provided. The
possibility of using less smooth approximation spaces in each
segmented region will also be considered.
Acknowledgments
The authors would like to thank Dr. Melissa Horne and Carl
Zeiss Meditec (Dublin, CA, USA) for their support on get-
ting access to OCT data, and AIBILI Clinical Trial Center
technicians for their support in managing data, working with
patients and performing scans.
5. REFERENCES
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2011 18th IEEE International Conference on Image Processing412


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Synthtic OCT Data for image processing performance testing

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