atherosclerosis is the major cause of cardiovascular morbidity and mortality , with underlying pathological processes that may begin during childhood [ 1 , 2 ] .
although the exact causes of atherosclerosis are not clear , it is thought to involve lipoprotein influx into the wall , across the endothelium , and chronic inflammation . over time , lipids accumulate in the inner wall and plaques develop , resulting in reduction or blockage of blood flow .
eventually , this condition can lead to heart attacks and strokes [ 3 , 4 ] .
this is most evident in regions of branching and curvature and has therefore been attributed to spatial variation in mechanical forces , particularly the haemodynamic wall shear stress exerted on the endothelium by the flow of blood .
near - wall blood velocity , on which shear stress depends , can not be accurately measured by direct techniques . however , ecs form a monolayer between the blood and arterial wall   that is regulated by haemodynamic forces through flow - mediated signal transduction [ 3 , 5 ] .
of relevance to the present study , endothelial cells and their nuclei align with the predominant flow direction and elongate in response to increased shear .
their shape has been used to assess patterns of wall shear stress in previous studies , [ 6 , 25 ] , including our studies aimed at understanding why the pattern of disease around aortic branches changes with age [ 8 , 9 ] . in the present study , we developed methods for automated analysis of ecs morphology .
the first step is to detect the boundaries of the cells against the background of stained images .
this is difficult in cases where the noise level is high and the image contrast is poor .
this has motivated us to use  support vector machines  ( svms ) as a classifier because recent work has shown this approach to outperform many conventional classifiers . in this paper
, we describe the visual features and the subsequent application of the svm as a classifier to detect thin boundaries of endothelial cells .
endothelial monolayers were stripped from the descending thoracic aortas of rabbits by a modification of the hutchen procedure of bond et al .   and
hirsch et al .. this involves pressing the endothelial surface of the opened aorta against double - sided adhesive tape adhered to the surface of a microscope slide .
aortas were obtained from three male new zealand white rabbits ( harlan interfauna strain ) , one mature and two immature , that had been perfused in situ with 10% neutral buffered formalin at physiological pressure for 90  s followed by 20  ml of silver nitrate solution ( 2.5  mg / ml , sigma ) , followed by further formalin fixation for 30  mins .
all animal procedures complied with the animals ( scientific procedures , uk ) act 1986 .
cell boundaries were examined around the origins of seven intercostal arteries from the descending thoracic aortas of the three rabbits .
a montage of images of the area around each branch mouth was obtained using a zeiss axioplan microscope .
the spatially varying sensitivity of the microscope and camera system resulted in shading of the individual images ; in section 3 , we describe the correction of these distortions , though correction is not needed in our final system . each montage
was then divided into subregions ; the subregions each corresponded to an arterial area of approximately 660  1100 pixels , and they were located in a 3  3 grid centred on the branch mouth .
the central element of the 9-element grid was not used , since it was largely occupied by the branch mouth , giving eight regions at each of the seven branches , and hence 56 regions in total .
the images corresponding to these 56 regions comprised the data set to which the current analysis was applied .
one of the sample images ( with a size of 660  1100 pixels ) taken from one of the montages is shown in figure 1(a ) and its manually traced counterpart in figure 1(b ) .
the cell boundary labelling or segmentation of ecs can be described as a binary classification problem in the sense that cell boundary pixels should be labelled as object or foreground and non - boundary pixels should be labelled as background .
each of the 56 datasets contained more than 500 cells , giving > 25,000 cells requiring analysis .
it is extremely tedious to trace the boundaries manually for tens of thousands of cells , and so a number of different methods was applied to attempt the segmentation of boundary pixels automatically . in order to assess the applicability of intensity thresholding to the task , we analysed the intensity distributions of image data after applying intensity correction based on background subtraction using a least - squares polynomial fit to a second - order spatial illumination model . for images that fell across boundaries of a montage
, we also used the average values of intensity on either side of the boundary to perform additive compensation of intensity differences in different acquisitions .
then , by using hand labelling of image and background data , we estimated the parameters of a standard mixture model : 
 ( 1)p(i)=pop(i    o)+pbp  ( i    b ) , 
					 where po and pb are the prior probabilities of the pixels and p(i | o ) and p(i | b ) are conditional probabilities of boundary and background , respectively .
p(i | b )   and  explains  the histograms of all pixel intensities pooled together . as shown in figure 2 , the conditional probability density functions of background and cell boundary pixels overlap with each other strongly .
it is thus hard to set a global threshold which distinguishes between background and boundary pixels ; we have previously described results of our initial work on the same data using adaptive thresholding following quadratic - based trend removal , a type of adaptive high - pass filtering .
we therefore developed a technique with the help of a class of machine learning algorithms known as support vector machines ( svms ) to computationally detect the boundaries of the images .
the method is attractive in that it is able to handle the weak boundary signals in our data , and does not require explicit edge - linking or explicit illumination correction 
these latter two modules of classical segmentation are implicit properties in the choice of features .
once such labellings are obtained , it is fairly straightforward to apply a variety of shape analysis techniques on the boundary representations to study the morphology of cells under the effects of biological flow .
the rest of the paper describes the method we have developed for automatically detecting the cell boundaries using svms and some evaluations of its performance .
features are extracted from the cell boundary image and mapped into feature space . to train the classifier ,
then , using the input feature space generated from the training image and an svm kernel , a decision model is generated ; this model is then applied to segment other boundary images .
the svm classifies image pixels into two different classes : boundary and non - boundary .
it is useful to consider the complexity of this problem , and why the selection of patch - based features , though increasing feature space dimensions , helps solve the segmentation problem . 

figure 4 illustrates the complexity of learning to detect boundary pixels . since we can not rely purely on the image intensity of a single pixel in order to classify it  the basis of thresholding approaches
 the decision - making process on the correct classification for each pixel needs to consider the intensity of its neighbours as well .
figure 4 shows four different configurations of pixels , similar to the  cliques  of markov - random fields ( mrfs ) , and considers a subspace of the full 9-dimensional space of the 3  3 patch represented by the intensities along a horizontal line of three pixels centred on the pixel to be classified .
three of these pixels are valid boundary points , and the fourth ( b ) is an isolated pixel that has a boundary - like intensity , but contains no neighbouring pixels to  support  it .
the consideration of three pixels is not enough to allow a correct decision to be made concerning pixel a ( boundary ) and pixel b ( non - boundary ) , as they lie in the same place in 3-dimensional feature space .
including all the eight nearest neighbours of a pixel to be classified provides a partial solution , but the separation of classes in a 9-dimensional space is more difficult , and almost impossible using a linear classifier such as a fisher criterion .
this is the motivation for using svms . through the use of kernels that generate nonlinear combinations of variables , svms
are able to find decision boundaries for the classes that are not easily separable in the original space .
other approaches to this problem might include algorithms to perform boundary linking , based on directions of gradients .
such approaches might work for images in which the object boundaries correspond to edges of regions which contain different average pixel intensities on either side of the boundary ; for the case of thin structures , second - order directional derivatives or phase - invariant measures of orientation are more appropriate for estimating structure direction to perform edge linking .
even so , creating an edge - linking algorithm to correctly handle the very complex spatial patterns formed by junctions between cells is no trivial task , and it is better to pursue a training approach which can learn how to appropriately classify pixels based on spatial configurations of neighbours .
however , given the nature of the poor signal - to - noise levels in the images , even a 3  3 neighbourhood of pixel values is not sufficient as a feature vector ; and whilst a 5  5 neighbourhood might provide more information that would allow , say , pixels lying on gaps in boundaries to be correctly classified , it would require an increase in the dimensions of the feature vector , more training and testing data , and also would incur higher computational cost in training and classification .
instead , we resort to generating features that group information from a wider area , for example , through spatial filtering , to compactly capture information over a larger neighbourhood which explicitly describes local orientations . we have taken an intuitive approach to selecting features , but have validated it using a feature selection approach .
we have explored a rich set of possible feature vector combinations , using up to 75 components in the feature vector , but do not reproduce them all here .
rather , we take the strongest feature vector components to illustrate the process of feature selection using the principle of minimum redundancy , maximum relevance ( mrmr ) .
this is illustrative , as it shows that some features are much more informative than others .
although we have used feature selection to assess some possible features , one has to be careful in assessing features individually .
as illustrated by figure 4 , some features provide strong discriminating power only when included as a collection over space  a patch - based approach , whereby some components of the feature vector are taken from a property that is estimated at different locations over neighbourhood space .
this is the case for the patch - based information such as the intensity and orientation dominance field . whilst linear classifiers can not learn the tortuous decision boundaries suggested by the training data in , say , 9-dimensional space that are required to satisfy orientation invariance ,
the svm is able to find separating hyperplanes which generalise well   from relatively few examples .
each pixel in the image is mapped to a 33-dimensional feature vector by extracting information from a 3  3 neighborhood of the central pixel : nine intensity elements extracted from 3  3 nearest neighbors ; eighteen features extracted from 3  3 nearest neighbors of an orientation dominance field ; the magnitude of the vectors in this field ranges from 0 to 1 .
the magnitude of the values can be used as an indication of anisotropy , in which strongly isotropic neighbors will produce values near to 0 and strongly anisotropic neighbors will produce values near to 1 ; an example of this field over a 3  3 patch is shown in figure 5 .
these features are quasi - invariant to slow background illumination changes because they are generated from band pass filters ; six statistical features generated from the 3  3 intensity neighborhood of a candidate pixel , given in table 1 .
the 33-dimensional feature vector given in ( 2 ) is then described for each pixel in the image in both the training and testing phases of the svm 
 ( 2)fvn=[i(33),o(33),med , range , e , m2,3,4 ] . 
 
the feature vector components are normalised by removing the mean of each feature and dividing the result by the standard deviation of each feature .
we used the minimum redundancy , maximum relevance ( mrmr ) measure to evaluate the importance of , and thereby select , the components of the feature vector input to the svm .
as implied by figure 4 , some features should not be separated or assessed on their own .
the result of mrmr is not repeated here , because it is performed against a very large number of neighbourhood features , including edge filters , statistical moments of intensities , and order - statistic neighbourhood measures . as a general rule
, we found that orientation dominance , pixel intensities , and statistical moments were the most discriminating , ( table 2 ) , and so we included these in the feature vector we have used for segmentation .
a certain degree of caution is required in interpreting mrmr results : individual neighbourhood pixels may be split apart in ranking of mrmr methods .
thus , for example , if pixels from an 3  3 patch are all included in the mrmr , they may be separated in the ranked list of relevance obtained from the standard mrmr algorithm .
when such features , obtained from different pixel locations in a feature space image around the candidate pixel , are included in an mrmr analysis , one should note the frequency with which the different locations of one property occur in , say , the top k ranked relevance measures .
if a large proportion of features of   one property occur close to the top of the list , then   all the neighbouring pixels over the 3  3 grid in that property should be included in the vector .
this algorithm is trained with a sample image of size 62  62 pixels taken from one of the 56 regions , as illustrated in figure 6 .
the 33-dimensional feature vectors generated over this region are used as an input to the svm that classifies image pixels into boundary and non - boundary pixels .
a binary image is generated after classification with each black pixel corresponding to a boundary and each white pixel corresponding to a non - boundary pixel [ 13 , 18 ] . for training
, we used the rbf kernel [ 19 , 20 ] with the maximum cost function / parameter set at 1 and  = 0.14 . with these settings , 2144
the algorithm was written with the help of the libsvm package   in matlab r2009b , and it took 13.38 seconds on a desktop pc with pentium(r)4 2.8  ghz processor running windows . the time taken to classify an image of size 512
the algorithm provided usable boundary data in 43 out of the 56 regions . in the remaining 13 regions , image data are very noisy .
one such image is shown in figure 7 , and it may be noted that even discerning the boundaries by eye is difficult ; high - pass filtering such an image does not improve matters . the binary images in figures 8(b ) and 8(d ) show classifications of pixels into boundaries and background by the svm algorithm .
the performance of the svm approach in segmenting cell boundaries was evaluated on four images containing manually traced boundaries ; one of these images is shown in figure 1(b ) .
the manually traced boundaries provide   ground - truth data that allows the accuracy of the segmentation to be evaluated on a pixel - by - pixel basis .
four trained svm kernels were applied to each of these test images , and the results were used to determine performance . in total , the performance of the algorithm was assessed on 3.9 million pixels .
the parameter ,  , was varied from 0.02 to 0.14 across all four svm kernels in step sizes of 0.01 .
the rbf kernel reached its best accuracy of 93% at  = 0.14 and the worst result it achieved on a single image was 80% .
accuracy of segmentation was assessed by noting the number of correctly classified pixels ( either boundary or background ) and is defined by 
 ( 3)accuracy%=(tp+tn)(tp+tn+fp+fn ) , 
							 where tp , fp , tn , and fn are true positive , false positive , true negative , and false negative , respectively .   in another experiment ,
we compared  ground truth  , an svm with rbf kernel and two conventional segmentation algorithms , canny   and kittler , in four image patches of size 128  128  pixels .
different thresholds were set for the decision in order to obtain a number of points along a receiver operating characteristics ( roc ) curve , which describes the performance of a classification method and feature space in addressing a discrimination task as one alters the balance between type i and type ii errors .
for the canny and kittler algorithms , 961 and 63 possible detection thresholds were applied to each image , respectively .
the svm model accuracy is largely based on the selection of the model parameters so , to find points along a roc , a search algorithm was used to attempt training and classification as values of the most significant parameters are altered across a wide range .
for example , as the rbf kernel depends on two main parameters ( c and  ) , a range of 4   to + 4 with interval of 0.1 for c and from 0.1 to 2 with an interval of 0.001 for  was selected . however , since each image to be assessed might have different statistical characteristics , generating an roc might require slightly different parameter settings . for a given image ,
the model was further evaluated with 5-fold cross - validation to find the best possible combination of parameters .  
table 4 and figure 9 present the classical segmentation technique results in comparison to the svm with rbf kernel , and the roc plots are given in figure 10 .  
table 4 also includes a comparison with the otsu method , which employs an automatic thresholding and is therefore not easily amenable to roc analysis .
this paper presents a method for detecting ec boundaries that reduces the need for human intervention .
previously , cell boundaries have been segmented manually [ 9 , 25 ] , since noise and unclear or faint boundaries would have led to the failure of traditional automated segmentation techniques .
previous reports have described computational work on corneal endothelial cell boundary detection [ 2629 ] , but the detection of cell boundaries was not as challenging as the ec boundaries in our images . in our previous work , we suggested some approaches to automatic cell boundary detection .
to address issues of accurately finding edge maps with this previous method , we developed the current method , which has successfully worked on image data with a poor signal - to - noise ratio ( snr ) .
our algorithm uses small neighbourhood patches in intensity , and orientation dominance patches of each candidate pixel in the image , and successfully segmented 43 out of 56 available regions to an acceptable level of accuracy
our method has some limitations : it does not perform well on image patches where the brightness variation is very large or where cell boundaries are not visible by eye .
we have found that illumination correction , such as by high - pass filtering , does not improve results and may even worsen them slightly if pixel noise is amplified .
the method requires good manual labelling of one example as input in the training process .
this necessitates selecting a patch with a representative variation in intensity to yield a satisfactory generalised model .
we have only worked on kernels already available in libsvm , but performance might be improved by developing a new kernel for such data , which was beyond the scope this research .   tests in other types of biomedical image data , such as retinal images , have suggested that with a comparable training process and comparable features , similar promising segmentation results can be achieved with minimal effort . future work will seek to extend the segmentation method to other biomedical image problems .
the method we developed will enable us to explore the relationships between blood flow and cell behavior , between cell nuclear shape and cell boundary shape , and between length  :  width ratio and cell orientation in different regions around arterial branches , by allowing large numbers of cells to be analysed .
 this paper presents an automatic detection method for thin boundaries of silver - stained endothelial cells ( ecs ) imaged using light microscopy of endothelium mono - layers from rabbit aortas . to achieve this , 
 a segmentation technique was developed , which relies on a rich feature space to describe the spatial neighbourhood of each pixel and employs a support vector machine ( svm ) as a classifier . 
 this segmentation approach is compared , using hand - labelled data , to a number of standard segmentation / thresholding methods commonly applied in microscopy . 
 the importance of different features is also assessed using the method of minimum redundancy , maximum relevance ( mrmr ) , and the effect of different svm kernels is also considered . 
 the results show that the approach suggested in this paper attains much greater accuracy than standard techniques ; in our comparisons with manually labelled data , our proposed technique is able to identify boundary pixels to an accuracy of 93% . 
 more significantly , out of a set of 56 regions of image data , 43 regions were binarised to a useful level of accuracy . 
 the results obtained from the image segmentation technique developed here may be used for the study of shape and alignment of ecs , and hence patterns of blood flow , around arterial branches . 
1. Introduction
2. Data Acquisition
3. Segmentation of Endothelial Cell Boundaries
4. A Segmentation Algorithm for Cell Boundaries
5. Results
6. Discussion