Blood Vessel Segmentation in Retinal Imagesusing Lattice Neural Networks

Roberto Vega1, Elizabeth Guevara2, Luis E. Falcon1, Gildardo Sanchez-Ante1,and Humberto Sossa2

1 Tecnologico de Monterrey, Campus GuadalajaraComputer Science DepartmentAv. Gral Ramon Corona 2514,

Zapopan, Jal, Mexicori.vega@itesm.mx

2 Instituto Politecnico Nacional-CICAv. Juan de Dios Batiz S/N, Gustavo A. Madero 07738

Mexico, Distrito Federal, Mexico

Abstract. Blood vessel segmentation is the first step in the process ofautomated diagnosis of cardiovascular diseases using retinal images. Un-like previous work described in literature, which uses rule-based methodsor classical supervised learning algorithms, we applied Lattice NeuralNetworks with Dendritic Processing (LNNDP) to solve this problem.LNNDP differ from traditional neural networks in the computation per-formed by the individual neuron, showing more resemblance with bio-logical neural networks, and offering high performance on the trainingphase (99.8% precision in our case). Our methodology requires four steps:1)Preprocessing, 2)Feature computation, 3)Classification, 4)Postprocess-ing. We used the Hotelling T 2 control chart to reduce the dimensionalityof the feature vector from 7 to 5 dimensions, and measured the effective-ness of the methodology with the F1Score metric, obtaining a maximumof 0.81; compared to 0.79 of a traditional neural network.

1 Introduction

Diabetic Retinopathy, a complication of diabetes mellitus, affects up to 80%of diabetics and causes blindness even in developed countries like the US [1].Arteriosclerosis, the hardening and thickening of the walls of the arteries,contributes to the development of cardiovascular diseases; the leading cause ofdeath in people over age 45. It has an overall prevalence of circa 30% [2] and [3].Finally, hypertension, or high blood pressure, is a factor for myocardial infarc-tion, stroke, ischemia, and congestive heart failure. According to recent studies,the overall prevalence of hypertension is about 25 % of the population [4]. Thesethree diseases share at least three facts: 1) They affect a significant portion ofthe population; 2) They have to be monitored once diagnosed, and 3) All threecan be diagnosed and monitored through the observation of the retina [5].

The retina is a unique site where the blood vessels can be directly visualizednon-invasively and in vivo [6]. Nowadays, digital ophthalmoscopes are able to

take quite clear images of the retina, with the possibility of storing them ina digital format and offering the opportunity for automated image processingand analysis. Although this idea has attracted the attention of many researchgroups, the problem is still not completely solved. The images of the retinapresent important technical challenges, both in their capture as well as in theprocessing. These challenges are described by Abramoff et al. at [7].

The three most important areas of active research in retinal imaging include:development of cost-effective digital equipment to capture retinal images, de-velopment of techniques to study the function of the retina using oxymetry ornear-infrared analysis, and development of image processing and analysis algo-rithms that allow the classification of retinal images for automated diagnosis. Inmany cases, a set of features of the vascular structure of the retina can establisha probable diagnosis. Parameters such as diameter, color, curvature and opacityof blood vessels may serve as a basis for diagnosis, treatment, and monitor ofthe aforementioned diseases [8] and [9].

In this work, we focus on the application of one machine learning algorithmto extract the vascular (blood vessel) structure from retinal images, so that in afurther step, future parameters such as the ones described can be quantified. Inparticular, we report here the results of using a different configuration of neuralnetwork called Lattice Neural Network with Dendrite Processing (LNNDP).

The remainder of the paper is organized as follows: Section 2 describes cur-rent advances in retinal image processing, Section 3 introduces Lattice NeuralNetworks with Dendrite Processing, Section 4 presents our methodology, Section5 describes experiments and results and finally, Section 6 presents the conclusionsand future work.

2 Previous Work

In general, the correct interpretation of medical images is a complex task be-cause of the steps that are needed: preprocessing, segmentation, classification andrecognition. The two steps that are related with the work described in this paperare segmentation and classification. In a pioneering work, Goldbaum et al., [10]introduced an image management system called STARE (structured analysis ofthe retina). In such work the authors described, in theory, what things couldbe done for each step; however, they do not offer any results. Hoover et al. [11]presented a method to segment and extract blood vessels in retinal images byusing local and global vessel features cooperatively. They first generated a newimage that represents the strength of a matched filter response (MFR), and thena classification step done through threshold probing. Other authors have focusedon the same problem: segmenting blood vessels. For instance, the work reportedin [12] focuses only on the extraction of image ridges, which coincide approxi-mately with vessel centerlines. Those centerlines classify neighboring pixels eitheras vessel or not. The authors in [13], tried to classify arteries and veins. Theycompared two feature extraction methods and two classification methods basedon support vector machines and neural networks. As for feature extraction, one

method is based on the vessel profile, while the other is based on a region of inter-est around the vessel pixel found on the center line. Given a hand-segmentationof vessels, their approach correctly classifies 95.32 % vessel pixels. There is noinformation on how much time this process takes. Other approaches have usedcolor to perform the segmentation, such as in [14] and in [15]. Maruthusivaraniet al. compared two different segmentation methods for blood vessel extraction:a local entropy based thresholding, and a morphological operation [16]. Theauthors of [17] also compared three methods (moment invariants [18], morpho-logical image processing, and hybrid filtering). The work of Fraz et al. reportsthe application of linear discriminant analysis [5]. Probing methods have alsobeen proposed, allowing the segmentation in pieces [11]. In [19] a graph-basedapproach was used to connect the pixels.

3 Lattice Neural Networks

The analysis of retinal images is a classification problem in which a given bloodvessel is labeled as blood vessel or non blood vessel. One possible way of solvingclassification problems is through the use of artificial neural networks (ANN).This approach seems attractive because an ANN can be used to estimate onlythe behavior of a function from observations, rather than obtaining the modelequation itself. Thus, if the ANN is fed with images in which blood vesselsare hand labeled, then the network may discover the inherent properties of theimages, allowing the proper classification of new images.

Some researchers have argued that traditional ANN models bear little re-semblance with the biological neural networks [20] and [21]; thereby driving thedesign of new generations of neural networks: Lattice Neural Networks (LNN),Morphological Neural Networks [22] and Spiking Neural Networks, among others.New findings in neurocomputing propose that the primary autonomous compu-tational unit in brain capable of realizing logical operations are the dendrtites.Therefore, Ritter et al. proposed a new paradigm of LNN that considers compu-tation in the dendritic structure as well as in the body of the neuron. In a singlelayer feedforward neural network has been observed that there are no conver-gence problems and the speed of learning exceeds traditional back propagationmethods [21]. Morphological neural networks (MNN) derive their name from thestudy of morphological transformations. Two such operations are dilation anderosion which are used to perform shape analysis [23] and [24].

In a traditional ANN the activation function is given by a linear combinationof the weights and the input vector, adding also a term called “bias”. In contrast,in a LNN the activation function is given by computing logical operations ANDand OR, as well as the sum.

In order to train the LNNDP, we used a modified version the model pro-posed by Ritter and Schmalz [25]. This model proposes a set of n input neuronsN1, . . . , Nn, where n is the number of features in the input vector, and m outputneurons M1, . . . ,Mm, where m is the number of classes in which the data isclassified. Fig. 1 shows a representation of the LNNDP.

In this model, the weight of the axonal branch of neuron Ni terminating onthe k− th dendrite Dk of Mj is denoted by ωlijk, where the superscript l ∈ {0, 1}distinguishes between excitatory (l = 1, marked as a black dot on Fig. 1), andinhibitory (l = 0, marked as an open dot on Fig. 1) input to the dendrite. Thecomputation of the k-th dendrite Dk of Mj is given by:

τ jk(x) = pjk∧

i∈I(k)

∧l∈L(i)

(−1)1−l(xi + ωlijk) (1)

where x = (x1, . . . , xn) denotes the input value of the neurons N1, . . . Nn, I(k) ⊆{1, . . . , n} corresponds to the set of all input neurons with terminal fibers thatsynapse on the k-th dendrite Dk of Mj , L(i) ⊆ {0, 1} corresponds to the set ofterminal fibers Ni that synapse on the k-th dendrite Dk of Mj , and pjk ∈ {−1, 1}denotes inhibitory or excitatory response of the k-th dendrite Dk of Mj to thereceived input. The total output of the neuron Mj is given by the equation:

τ j(x) = pj

Kj∨k=1

τ jk(x) (2)

where Kj represents the total number of dendrites in the neuron Mj , τjk(x) is the

output of the dendrite k of neuron Mj ; pj = 1 to denote that the particular inputis accepted; and pj = 0 to denote that the particular input is rejected. Finally,according to [25] the input vector x is assigned to the class whose neuron resultsin the biggest value:

y =

m∨j=1

τ j(x) (3)

where m is the number of classes, and τ j(x) is the output of the neuron Mj .

4 Methodology

4.1 Image Acquisition

To evaluate the proposed methodology, we used the publicly available databaseSTARE [11]. This database contains 400 retinal images with several patholo-gies, including various types of diabetic retinopathy, vein occlusion, and arteryocclusion. In 20 of the 400 images, the blood vessels are hand labeled by twoindependent experts. These 20 images were used, selecting the labeling of thefirst expert as ground truth. The retinal fundus slides used were originally cap-tured with a TopCon TRV-50 fundus camera at 35 field of view. The slides weredigitalized to produce 605 x 700 color images, 24 bits per pixel. Half of the im-ages are of patient retinas with no pathology, and the other half of the imagesare of retinas containing pathologies that obscure or confuse the blood vesselappearance, making the vessels harder to identify [11]. An example of each kindof image, as well as its hand labeled segmentation, is shown in Fig. 2.

Fig. 1: Representation of a lattice neural network with dendritic computing.

Fig. 2: Left: Normal fundus image and its segmentation, Right: Pathology fundusimage and its segmentation.

4.2 Preprocessing and Feature Extraction

In a dendritic model, a set of n input neurons N1, . . . , Nn accepts as an inputa vector x = (x1, . . . , xn) ∈ Rn [24]. Marin, et al. proposed a neural networkscheme for pixel classification and computed a 7-D vector composed of gray-levels and moment invariants for pixel representation [18]. In this work, we used asimilar methodology to obtain a 7-D feature vector. The procedure is summarizedas follows:

Since color fundus images often show important lighting variations, poorcontrast and noise, a preprocessing step is needed. The steps involved in thisstage are: 1) Vessel central light reflex removal, 2)Background homogenization,and 3)Vessel enhancement.

– Vessel central light reflex removal: The green layer of the image was isolatedfrom the images because it shows the highest contrast between blood vesselsand background [12]. Then, a morphological opening was implemented onthe green layer in order to remove the light streak included in some vessels.

The structuring element used in the operation was an eight-connectivity,three-pixel diameter disc. The resultant image is labeled as Iγ .

– Background homogenization: In order to remove background lighting vari-ations, a shade-corrected image is obtained from a background estimate.First, a 3× 3 mean filter is applied over Iγ , followed by a convolution with aGaussian kernel of 9× 9, using a mean µ = 0, and variance σ2 = 1.8. Then,a background image (Ib) is obtained applying a 25 × 25 median filter. Toobtain the shade corrected image, the background image is subtracted fromthe image after the morphological opening:

D(x, y) = Iγ(x, y)− Ib(x, y) (4)

Then the image was linearly transformed to cover all possible ranges of gray-levels [0, 255]. This new image is called ISC . The transform implements theequation [26]:

Nx,y =Nmax −NminOmax −Omin

× (Ox,y −Omin) +Nmin (5)

where, Nmax, Nmin, Omax and Omin are the desired maximum and minimumgray level values of the new, and old histograms respectively; and Ox,y is thevalue of the pixel to be changed. Finally, to reduce the influence of intensityvariations along the image, a homogenized image IH is obtained displacingtoward the middle of the histogram the pixel intensities of the images. Thisis accomplished by applying the transformation function:

gOutput =

0 if g < 0255 if g > 255g otherwise

(6)

where

g = gInput + 128− gInputMax (7)

where gInput and gOutput are the gray-level values of the input and outputimages. gInputMax represents the mode of the pixel-value intensities in ISC .

– Vessel Enhancement: This step is performed by estimating the complementimage of IH , I

cH , and then applying a morphological Top-Hat transformation

using as a structuring element a disc of eight pixels in radius. The vesselenhanced image, IV E is then defined as:

IV E = IcH − γ(IcH) (8)

where γ is the morphological opening operation.

Once the preprocessing stage is finished, the resultant images IH , IV E areused to extract a 7 feature vector for each pixel in the image. The effect of eachstep in the preprocessing stage is shown in Fig. 3.

The features are divided in two groups:

(a) (b) (c) (d)

(e) (f) (g) (h)

Fig. 3: (a) Green layer of the image. (b) Image after morphological opening. (c)Image after gaussian filter. (d)Image after applying a median filter. (e) Differenceof (b) and (d). (f) Normalization of (e). (g) Homogenized image. (h) Image aftertop-hat transformation.

– Gray level features: based on the gray-level intensity if the pixel of interest,and a statistical analysis of its surroundings. For these features, we use IH .

– Moment invariants-based features: features based on moment invariants forsmall regions formed by a window centered at the pixel of interest. For thesefeatures, we use IV E .

In the following equations, which define the features, Sw(x,y) represents the set

of points in a window of w × w, centered at the pixel (x, y). The five gray levelfeatures can be expressed as:

f1(x, y) = IH(x, y)−min(s,t)∈S9x,y{IH(s, t)} (9)

f2(x, y) = max(s,t)∈S9x,y{IH(s, t)− IH(x, y)} (10)

f3(x, y) = IH(x, y)−mean(s,t)∈S9x,y{IH(s, t)} (11)

f4(x, y) = variance(s,t)∈S9x,y{IH(s, t)} (12)

f5(x, y) = IH(x, y) (13)

The moment invariant features proposed were the logarithm of the first andsecond moments of Hu in a window of 17× 17 centered at the pixel of interest,which are defined as:

f6(x, y) = log(η20 + η02) (14)

f7(x, y) = log((η20 + η02)2 + 4η211) (15)

where

ηpq =µpq

(µ00)(p+q2 +1)

; p+ q ≥ 2 (16)

µpq =∑x

∑y

(x− x)p(y − y)qf(x, y);x, y ∈ S17x,y (17)

x =m10

m00; y =

m01

m00(18)

mij =∑x

∑y

xiyjf(x, y);x, y ∈ S17x,y (19)

4.3 Classification

The seven features were calculated for each pixel in the 20 images. Then, wetook a reference image and extracted 30,000 random pixels (half hand-labeledas blood vessels, and half as non-blood vessels) to train the neural network.

According to Ritter and Schmalz in [21], there are two different approachesto learning in LNNDP: training based on elimination, and training based onmerging. In this work, we used the training based on merging, which is based inthe creation of small hyperboxes of n dimensions around individual patterns, orsmall groups of patterns belonging to the same class.

Training is completed after merging all the hyperboxes for all patterns of thesame class. Because this approach is used, the values of p in equations 16, and17 are set to 1. Sossa and Guevara proposed an efficient method for the trainingof LNNDP [25]. The process is summarized as follow:

Given p classes of patterns Ca, a = 1, 2, p, each with n attributes:

1. Create an hypercube HCn, that includes all the patterns in the set.2. Verify if all the hypercubes enclose patterns of just one class. If that is

the case, label the hypercube with the name of the corresponding class andproceed to step 4, else proceed to step 3.

3. For all the hypercubes that have patterns of more than one class, divide thehypercube into 2n smaller hypercubes. Check if the condition stated on step2 is satisfied.

4. Based on the coordinates on each axis, calculate the weights for each hypercube that encloses patterns belonging to Ca.

In this method, each hypercube is represented by a dendrite Dk, and each class ofpatterns is represented by an output neuron Mj . Since the number of hyperboxesfor each class may vary, each class may have different number of dendrites. Eachinput neuron Ni will connect to an output neuron Mj through a dendrite Dk

at two different points: one excitatory (l = 1), and one inhibitory (l = 0). Theweight ωlijk associated with each connection will be the borders of the hypercuberepresented by Dk over the axis i. The lowest value of the border will be assignedto −ω1

ijk, while the highest value will be assigned to −ω0ijk. Figure 4 shows an

example of how weights would be assigned to a hypercube n = 2.

Fig. 4: Example of weight definition of an hypercube of n = 2.

4.4 Postprocessing

In order to improve the results, we implemented a postprocessing stage. As it willbe shown in the following section, the images predicted by the neural networkcontain “salt and pepper” noise, and small regions misclassified as blood vessels.The first step consists in applying a median filter using a mask of 5 × 5. Thisfilter eliminates most of the isolated points labeled as blood vessels, although itcan also add some points that were not in the original prediction. In order toeliminate these new points, we made the conjunction of the original and filteredimages. Finally, we classified as non-vessel the regions whose area was below 25pixels. In this case, the area of a region is the number of pixels connected.

5 Experiments and Results

In a first experiment, using the proposed methodology, we achieved an accuracyof 99.02% in the training phase. 4844 dendrites were in the neuron that classifiesthe pixels as blood vessels, and 4786 dendrites in the one that classifies themas non blood vessels. The weights obtained in the training phase were used tomake the segmentation of the 20 images on the dataset.

In a second experiment, we made a control chart in order to eliminate outliersin the training set that could diminish the performance of the neural network.The most familiar multivariate control procedure is the Hotelling T 2 controlchart for monitoring the mean vector of the process [27], so we used this proce-dure as a first choice. After implementing this control chart, we expected to labelabout 1% as outliers; however, about 6.6% of the samples fell in this category.A more profound analysis of this behavior made us realize that the features f4and f6 were the cause of so many outliers. After removing these features, thepercentage diminished to 2.4%. We removed the outliers from the new 5 dimen-sional feature set and we ran the experiment again. This experiment created6966 dendrites for the first class and 6611 for the second class, and it achievedan accuracy of 99.8% in the training phase.

Finally, we ran a third experiment training the network with 3 images insteadof just one. In this last experiment we used the 5 dimensional feature vector.

Although could be expected that a lattice neural network achieved 100%accuracy in the training set, this was not the case because some pixels withthe same feature vector were classified sometimes as blood vessels, and someother times as non vessels. This behavior could have been caused by noise in theimages, in the data, or human error in the hand labeling process. Usually, the stopcriterion for a LNNDP is that all of the patterns must be correctly classified; if,however, the same pattern belongs to different classes, the stop will never occur.In order to avoid convergence problems caused by inconsistencies in the data,we had to re-label the pixels whose feature vector belonged to different classes.The re-classification criterion was to assign all the pixels with the same featurevector to the most frequent class present in this feature vector. For example, ifnine identical pixels were labeled as class 0, and one pixel as class 1, then all thepixels were re-labeled as class 0.

In order to evaluate the predicted images, we used a metric called F1Score,which is defined as:

F1Score =(2 ∗ truePositives)

(2 ∗ truePositives+ falseNegatives+ falsePositives)

Table 1 lists the results of the different experiments implemented over the20 images of the dataset before postprocessing (bp), and the results after post-processing (ap) in the experiment 2; the experiment which had the best results.Figure 5 shows an example of the prediction made by the neural network in eachexperiment. The proposed neural network with dendritic processing is also com-pared with a multilayer perceptron with 9 dendrites in the hidden layer (NN9),and our implementation of the methodology proposed by Martın et al. [18],which consists of a neural network with 3 hidden layers, each containing 15 hid-den units. The results of our implementation of the methodology proposed byMarin et al. showed a lower performance than the results reported by them. Thisdifference could be caused by the selection of the training set: they chose thetraining set manually, while we chose it randomly.

(a) (b) (c) (d) (e)

Fig. 5: (a) Exp. 1 bp. (b) Exp. 2 bp. (c) Exp. 3 bp. (d) Exp. 1 ap. (e) Hand-labeledimage.

Table 1: Results of the experiments show a better performance applying aLNNDP using a 5 dimensional feature vector.

Exp. 1 bp Exp. 2 bp Exp. 3 bp NN9 Exp. 2 ap Marın et. al

Average F1Score 0.5490 0.5539 0.4183 0.5587 0.6616 0.6565Min F1Score 0.4149 0.3805 0.2803 0.2579 0.4232 0.4287Max F1Score 0.6586 0.6722 0.5123 0.7351 0.8123 0.7916

6 Conclusions

The use of a LNNDP could solve the problem presented, showing a better per-formance (about 2% in the best case) when compared with the use of multilayerperceptron, and presenting a very high performance (99.8%) on the trainingset. Unfortunately, we could not compare our results against many other worksavailable in literature because their algorithms used accuracy as metric, whilewe used F1Score. The problem with accuracy is that between 92% and 95%of the pixels in the images are non blood vessels, so an algorithm that alwayslabel a pixel as non blood vessel will have 92% - 95% of accuracy, giving a falseidea of good performance. The metric F1Score gives a more realistic evaluationby calculating the relationship between true positives, false negatives, and falsepositives. In this way, an algorithm that always label the pixels as non bloodvessels will have a grade of 0, and an algorithm that labels all the pixels correctlywill have a grade of 1.

We ran three experiments to evaluate the performance of three differenttraining sets. The best result was obtained with the training set obtained by asingle image, and characterized by a feature vector of 5 dimensions. Contraryto intuition, adding more images to the training set reduced the performanceof the LNNDP. This was due to the high variety of the images in the database.Besides,we implemented six different methodologies to remove noise and falsepositives; however, most of them also removed fine details of the images. Wepresented the one that obtained better results. Finally, the Hotelling T 2 controlchart allowed us to reduce the dimensionality of the training set from 7 dimen-sions to 5 dimensions. The statistical analysis of data prior to using machinelearning algorithms is often missing in the literature review that we made, butit proved to be very usefull in our implementation. In this way, our methodologynot only performed better that traditional neural networks, but also included amissing step in previous works.

Besides the aforementioned characteristics, we want to point out that aLNNDP creates as many dendrites as needed in an automatic way, making un-necessary to specify a configuration prior to the training phase. If we also addthat the performance of the training phase is usually 100%, we can concludethat LNNDP is a powerful tool for solving classification problems.

Acknowledgments

The authors thank Tecnologico de Monterrey, Campus Guadalajara, IPN-CICunder project SIP 2013-1182, and CONACYT under project 155014 for theeconomical support to carry out this research. We also acknowledge professorMarco de Luna for his insight about statistical analysis, and all the reviewersfor their valuable comments that helped us to improve this work.

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