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Retinal blood vessel segmentation in high resolution fundus

photographs using automated feature parameter estimation

Jos´e Ignacio Orlandoa,b,c, Marcos Fracchiac, Valeria del R´ıocand Mariana del Fresnob,c,d

aConsejo Nacional de Investigaciones Cient´ıﬁcas y T´ecnicas (CONICET), Argentina;

bPladema Institute, Gral. Pinto 399, 7000 Tandil, Argentina;

cFacultad de Ciencias Exactas, UNCPBA, Pinto 399, 7000 Tandil, Argentina;

dComisi´on de Investigaciones Cient´ıﬁcas de la Provincia de Buenos Aires (CIC-PBA),

Buenos Aires, Argentina;

ABSTRACT

Several ophthalmological and systemic diseases are manifested through pathological changes in the properties and

the distribution of the retinal blood vessels. The characterization of such alterations requires the segmentation

of the vasculature, which is a tedious and time-consuming task that is infeasible to be performed manually.

Numerous attempts have been made to propose automated methods for segmenting the retinal vasculature from

fundus photographs, although their application in real clinical scenarios is usually limited by their ability to deal

with images taken at diﬀerent resolutions. This is likely due to the large number of parameters that have to

be properly calibrated according to each image scale. In this paper we propose to apply a novel strategy for

automated feature parameter estimation, combined with a vessel segmentation method based on fully connected

conditional random ﬁelds. The estimation model is learned by linear regression from structural properties of

the images and known optimal conﬁgurations, that were previously obtained for low resolution data sets. Our

experiments in high resolution images show that this approach is able to estimate appropriate conﬁgurations that

are suitable for performing the segmentation task without requiring to re-engineer parameters. Furthermore,

our combined approach reported state of the art performance on the benchmark data set HRF, as measured in

terms of the F1-score and the Matthews correlation coeﬃcient.

Keywords: Retinal vessel segmentation, Fundus imaging, Parameter estimation

1. INTRODUCTION

Fundus photographs are a cost eﬀective, non-invasive medical imaging modality that is widely used by ophthal-

mologists for manually inspecting the retina.1It is currently the most used imaging technique for screening

several ophthalmic diseases such as diabetic retinopathy2and glaucoma,3which are among the leading causes

of avoidable blindness in the world.4Current systems for automated fundus image analysis usually require to

segment the vasculature ﬁrst,5as blood vessels aid in numerous applications. In particular, vessel segmentations

are used for characterizing pathological changes associated with ophthalmic and systemic diseases,1for localizing

other anatomical parts of the retina,6for detecting abnormalities such as red lesions,7, 8 and as landmarks for

multimodal image registration.9

Automated blood vessel segmentation is a challenging task that has been widely explored in the literature.1

In general, it is tackled by means of supervised or unsupervised methods. Unsupervised methods are based on

pixel level features such as Gabor ﬁlters,10 line detectors11 or morphological operation,12 among others.13 These

features are designed to characterize vascular pixels, and afterwards they are thresholded to retrieve a binary

representation of the vasculature.13 Supervised methods are built on top of these strategies, and are based ﬁrst

on training a classiﬁer from annotated data and then, on categorizing image pixels using such a model.10, 14, 15

Althought most of the current methods are able to achieve high performance on standard low resolution data

sets such as DRIVE16 and STARE,17 they usually fail when images are taken at higher resolutions. This is likely

Further author information: (Send correspondence to J.I.O.)

J.I.O.: E-mail: jiorlando@conicet.gov.ar, Telephone: +54 249 4439690

(a) (b) (c)

Figure 1: Retinal blood vessel segmentation in high resolution fundus images. (a) Fundus photograph. (b)

Segmentation obtained using our method with parameters adapted using a scaling factor. (c) Segmentation

obtained using our method with parameters estimated using linear regression.

because the existing features are highly parametrized and require an intensive calibration process to improve

their original performance. However, it is extremely time consuming to tune these parameters using standard

searching approaches such as grid search.18 Furthermore, this process have to be repeated for every new data

set with a diﬀerent resolution.

One alternative to overcome this issue is to downscale the images to approximately ﬁt the same resolution than

those used for tuning parameters.3Nevertheless, this approach reduce the ability of the features to characterize

thin structures, which is relevant in clinical applications.1Other strategies are based on modeling resolution

changes and adjusting the feature parameters accordingly. In our previous work,19 we proposed to apply a scaling

factor, proportional to the change in the ﬁeld of view (FOV) width, to automatically rescale those parameters.

Albeit this approach is able to improve results on high resolution data sets, the resulting segmentations suﬀer

from issues such as false negatives due to arteries central reﬂex (Figure 1), and are less accurate than the obtained

on low resolution images. Vostatek et al.20 have recently proposed a diﬀerent strategy for predicting parameters,

based on using linear regression. Such an approach is focused on correlating these values with the angular

resolution of the images. A line is ﬁtted to these points by minimizing the mean squared error, and its slope and

intercept are subsequently used to automatically predict the parameters suitable for a new given resolution.

In this study we propose to take advantage of this recently published strategy by integrating it with our

blood vessel segmentation method based on learning a fully connected conditional random ﬁeld model.15, 19

In particular, we improve the original estimation strategy proposed by Vostatek et al.20 by analyzing other

structural parameters of the images that are also easily measurable. Moreover, we apply this estimator in

combination with our supervised method, which incorporates shape priors within the learning process to better

capture the interaction between vascular pixels.15, 19 Our hypothesis is that integrating this parameter estimator

with our segmentation approach will result in better performance than merely using simple pixel classiﬁers such

as Gaussian Mixture Models (GMMs).10, 20 We have evaluated this adaptive model on a benchmark data set

of high resolution fundus images, HRF,18 which is widely used in the literature for evaluating segmentation

methods. Our results empirically shows that this hybrid approach signiﬁcantly improve the original performance

of the method, outperforming other existing strategies evaluated following a similar protocol.

The remainder of this paper is organized as follows. Section 2 explains our method, including details about

the selected features, our segmentation approach and the parameter estimation strategy. Section 3 describes the

data sets used in our experiments and the quantitative metrics applied for evaluation, while Section 4 presents

the obtained results. Finally, Section 5 concludes the paper.

2. METHODS

A schematic representation of our method is depicted in Figure 2. Given diﬀerent training sets of low resolution

fundus images and their manual annotations, a grid search approach is followed to ﬁnd the optimal conﬁguration

of feature parameters for each of their resolutions (Section 2.1.1). Subsequently, structural parameters such as

Figure 2: Schematic representation of our strategy for segmenting retinal vessels in high resolution images with

automated parameter estimation.

the approximate diameter of the optic disc and the FOV, the calibre of the largest vessel and the ratio between

the FOV diameter and the angle of aperture are measured from a subset of image examples. These values and

the optimal parameters are afterwards used to ﬁt an estimation line using linear regression. To learn the vessel

segmentation model from other high resolution images, the structural parameters are taken from a subset of

these other images, and they are used afterwards to automatically adjust the parameters of the selected features

to this new resolution (Section 2.2). Finally, the features are extracted and used for training our supervised

segmentation approach (Section 2.1.2), which is applied in test time to segment the vasculature on new images

with unknown annotations.

2.1 Vessel segmentation approach

2.1.1 Feature extraction

As a proof of concept, we have retrieved a set of three diﬀerent features that are widely applied in the literature

for characterizing pixels belonging to blood vessels: the vessel enhancement technique based on mathematical

morphology by reconstruction proposed by Zana and Klein,12 the 2D Gabor wavelet by Soares et al.,10 and

the multiscale line detectors by Nguyen et al.11 Nevertheless, this approach can be extended to other features

diﬀerent from those used in this paper. We will brieﬂy describe them in the sequel to analyze their relevant

parameters. The interested reader could refer to their original references and/or to a recently published review13

for further information. Table 1 summarizes the parameters of these features.

The green color band is the one that exhibits the highest contrast between the retinal vasculature and the

remaining anatomical parts of the fundus.13, 21, 22 Hence, all the features are extracted from the inverted version

of this speciﬁc channel. Furthermore, a larger angle of aperture is simulated as proposed by Soares et al.10 to

reduce potential artifacts in the borders of the FOV.

The feature based on morphological operations by reconstruction was originally introduced by Zana and

Klein12 for enhancing curvilinear structures on retinal angiographies and remote sensing imagery. It relies on a

series of morphological operations performed at diﬀerent angles, using a linear structuring element of length l.

By means of the application of openings, top-hats, a Laplacian of Gaussian, an additional opening, a closing and

a last opening, linear connected elements whose curvature varies smoothly along a crest line are retrieved. We

have used our own implementation of the feature, which has been made publicly available.19 The design of its

main parameter, l, was empirically observed to be extremely relevant to achieve a proper vessel enhancement.

It was previously reported that the value of lis correlated with the caliber of the major vessel in the image.

The 2D Gabor wavelets are known by their intrinsic ability to capture oriented features, which become

relevant for characterizing pixels belonging to the retinal vessels.10 We have used the public implementation

provided by Soares et al.10 for extracting this feature. The main parameter of the method is the set of scales a,

which is associated with the multiple calibres of the vessels in the image.

Finally, we also evaluated the application of line detectors, as proposed by Nguyen et al.11 This approach

is based on analyzing the response of the image to a line of length l∈ {1, ..., W }rotated at diﬀerent angles.

Wcorresponds to the largest length of the analyzed segments, and is a signiﬁcant parameter of the method.

As considering values of ltoo similar to each other in high resolution images would signiﬁcantly increase the

size of the feature vector with redundant information, we have restricted the number of potential scales to eight

equidistant lvalues, spanning from 1 to W.

2.1.2 Fully connected CRF model for retinal vessel segmentation

The blood vessel segmentation task is tackled by means of a recently published method based on learning a Fully

Connected Conditional Random Field (FC-CRF) model using a Structured Output Support Vector Machine

(SOSVM). Such an approach has demonstrated to be eﬀective enough for extracting the retinal vasculature,15, 19

and has been also applied in the context of other tasks such as automated glaucoma screening3or red lesion

detection.8The interested reader could refer to the original reference for further details.

Formally, our purpose is to assign a labeling y={yi}to every pixel iin the image I, with yi∈ L ={−1,1},

corresponding -1 to a non-vascular pixel and 1 to a vessel pixel. An estimated segmentation y∗can be obtained

by solving:

y∗= arg min

y∈L E(y|I) (1)

where E(y|I) is a Gibbs energy deﬁned over the cliques of Gfor a given labeling yfor I. This energy is given by:

E(y|I) = X

i

ψu(yi,xi) + X

(i,j)∈CG

ψp(yi, yj,fi,fj) (2)

where xiand fiare the unary and pairwise features, respectively. Unary potentials ψudeﬁne a log-likelihood

over y, and are obtained using a classiﬁer.23 On the contrary, pairwise potentials ψpdeﬁne a similar distribution

but over the interactions between pairs of pixels, as given by CG. This set is deﬁned by the graph connectivity

rule: in our fully connected deﬁnition, all the pixels interact with each other.

Unary potentials are obtained as follows:

ψu(yi,xi) = −hwuyi,xii − wβyiβ(3)

where βis a bias constant, and wuyiand wβyiare weight vectors for the features and the bias term, respectively,

associated to the label yi. The unary vector xiis given by an arbitrary combination of features extracted from

the image (in this work, line detectors and 2D Gabor wavelets).

Pairwise potentials are restricted to be a linear combination of Gaussian kernels by the eﬃcient inference

approach by Kr¨ahenb¨uhl and Koltun,23 which is applied to minimize E(y|I). The pairwise energy is given by:

ψp(yi, yj,fi,fj) = µ(yi, yj)

M

X

m=1

wp(m)k(m)f(m)

i, f (m)

j(4)

where each k(m)is a ﬁxed function over an arbitrary feature f(m)(in this work, the response to the vessel

enhancement method by Zana and Klein), wp(m)is a linear combination weight, and µ(yi, yj) is a label com-

patibility function. The Gaussian kernels are used to quantify the similarity of f(m)between neighboring pixels,

Table 1: Parameters to estimate.

Method Reference Identiﬁed

parameters

Mathematical morphology Zana and Klein, 200112 l

2D Gabor Wavelets Soares et al., 200610 a

Line detectors Nguyen et al., 201311 W

Fully connected CRF Orlando et al., 201415 and 201719 θp

while the compatibility function µpenalizes similar pixels assigned to diﬀerent labels, and is given by the Potts

model µ(yi, yj)=[yi6=yj].19 The pairwise kernels have the following form:

k(m)f(m)

i, f (m)

j= exp

−|pi−pj|2

2θ2

p

−|f(m)

i−f(m)

j|2

2θ2

(m)

(5)

with piand pjbeing the coordinate vectors of pixels iand j. Including the positions in the pairwise term allows

to increase the eﬀect of close pixel interactions over distant ones. The parameters θpand θ(m)are used to control

the degree of relevance of each kernel in the expression. Hence, if θpincreases, much longer interactions are taken

into account. On the other hand, if θpdecreases, only local neighborhoods aﬀect the result. Likewise, increasing

or decreasing θ(m)will tolerate higher or lower diﬀerences on the pairwise feature. As in our previous work, θ(m)

is ﬁxed automatically as the median of a random sample of pairwise distances.19 On the contrary, θpmust be

properly adjusted as it strongly depends on the resolution of the images. We have evaluated if this parameter

can be automatically determined by our estimation strategy, as described in Section 2.2.

The weights for both the unary and the pairwise potentials are learned using a SOSVM, as we have formerly

proposed.15 Further details about this supervised learning approach can be found in the reference.

2.2 Automated adjustment of feature parameters

Table 1 lists all the parameters to estimate: the length lof the structuring elements used by the Zana and Klein

method, the scales aused to compute the 2D Gabor wavelets, the W0,Wand step values for the line detectors,

and the amplitude θpof the fully connected CRF.

As previously mentioned, we used our version of the parameter estimation strategy proposed by Vostatek

et al.20 The original approach consists on ﬁrst using low resolution images and their corresponding manual

annotations to optimize each parameter by grid search, evaluating each conﬁguration considering a performance

measurement Q. Afterwards, a linear regression model must be learned from pairs of data points consisting

on the optimal parameter value and its angular resolution. Our version of this approach introduces several

modiﬁcations to the original pipeline. Vostatek et al. proposed to use the area under the ROC curve20 as Q,

to guide the optimization process. However, it has been previously demonstrated that this metric is aﬀected by

the degree of imbalance in the data.24 Instead, we propose to use the area under the precision/recall curve to

quantify the quality of the feature parameters, which is more appropriate to this type of problems.24, 25 The

nature of the θpparameter forces us to use a diﬀerent optimization approach, as the FC-CRF have to be trained

for a certain θpvalue and then evaluated in terms of a binary segmentation metric. We performed this task

as follows: given a value of θp, we trained the FC-CRF on the training set and evaluated its contribution to

improving the average F1-score (Section 3.2) in the validation set. This process was repeated for all the θpvalues,

and the parameter that reported the highest F1-score was taken as optimal.

Once the optimal parameters are found, diﬀerent structural measurements are manually taken from 2 ran-

domly sampled images of each subset in the set used for optimizing parameters. The average for each image pair

is taken as a representative estimator of the other images in the subset. In particular, we have considered:

•Largest vessel calibre (in pixels): measured as the average length of 3 proﬁles manually drawn at

diﬀerent locations of the largest vessel.

Table 2: Data sets used in our experiments.

Data set

FOV

(angle of

aperture)

Resolution Training

set Test set

DRIVE 45◦565 ×584 20 images Not used

STARE 35◦605 ×700 10 images Not used

ARIA 50◦768 ×576 55 images Not used

CHASEDB1 30◦999 ×960 8 images Not used

HRF 60◦3504 ×2336 15 images 30 images

•Horizontal diameter of the optic disc (in pixels): by measuring the length of a line horizontally drawn

from the left to the right edge of the optic disc.

•Width of the FOV (in pixels): obtained automatically from the FOV binary masks.

•Angular resolution: taken as the ratio between the width of the FOV and the angle of aperture of the

fundus camera.20

To analyze which of these structural measurements are more suitable for estimating each parameter, diﬀerent

lines are ﬁtted to this data, and the coeﬃcient of determination R2of each linear regression model is used as

an indicator of the overall model quality.26 The structural measurement that resulted in the highest R2value

is taken as the optimal metric for a given model. Subsequently, this measure is manually taken from any new

image, and the feature parameters are ﬁxed according to the estimation provided by its corresponding model.

Finally, F-tests were also performed to evaluate whether a linear regression model is suitable to perform the

parameter estimation or not.26

3. EXPERIMENTAL SETUP

3.1 Materials

As previously indicated in Section 2, our approach requires to be trained in two diﬀerent ways. First, low

resolution data sets are used to optimize feature parameters and to compute the corresponding estimators. Once

these models are learned, a second training set, with approximately the same resolution than the test set, is

needed to ﬁnally learn the fully connected CRF model.

To train our parameter estimators, we used the training sets of DRIVE16 and CHASEDB1,27 and two

additional sets sampled from STARE17 and ARIA.28, 29 Afterwards, the data set HRF18 was applied for validating

the complete pipeline. Table 2 summarizes the main characteristics of each database.

DRIVE16 comprises 40 color fundus photographs (7 with pathologies), obtained from a diabetic retinopathy

screening program in Netherlands. The set was originally divided into a training and a test set, each of them

containing 20 images. However, we only used the training set in our experiments. STARE17 contains 20 fundus

images (10 of them with pathologies) commonly used to evaluate vessel segmentation algorithms. As the set

is not divided into a training and a test set, we used the ﬁrst 10 images to train the linear regression models.

ARIA28, 29 is made up of three diﬀerent groups of fundus images, 23 taken from patients with age related macular

degeneration, 59 of patients with diabetes and 61 of healthy subjects. We built a training set from ARIA by

extracting the ﬁrst 8, 23 and 24 images from each subset, respectively. Finally, CHASEDB127 contains 28 fundus

images of children, centered on the optic disc. This set is divided into a training and a test set, each of them

containing 20 and 8 fundus photographs, respectively. We used these last 8 images for training our parameter

estimator.

HRF18 was used to validate our segmentation approach. It comprises 45 images, 15 of healthy subjects, 15

of patients with diabetic retinopathy and 15 of glaucomatous persons. As this data set was used for evaluating

the full segmentation approach, we divided it as in19 into a training and a test set. The training set is made up

of the ﬁrst 5 images of each subset, while the remaining 30 images were used for test. Moreover, the training

set was randomly split into a training* and a validation set, with the ﬁrst one (10 images) used for learning the

CRF model and the second one (5 images) for validating the regularization parameter C.

3.2 Evaluation metrics

Several metrics are used in the literature for evaluating blood vessel segmentation algorithms. In general, most

of them are expressed in terms of sensitivity (Se, also known as recall, Re), speciﬁcity (Sp) and precision (P r ),

which are obtained as follows:

Se =Re =T P

T P +F N (6)

Sp =T N

T N +F P (7)

P r =T P

T P +F P (8)

Sensitivity quantiﬁes the ability of the segmentation method to identify the vasculature, while precision measures

how well the method is able to diﬀerentiate it with respect to other structures of the fundus. Similarly, speciﬁcity

determines the capability of the method to properly distinguish the non-vascular structures.

As previously mentioned in Section 2.2, a metric Qis needed to guide the feature optimization procedure. All

our experiments were performed using the area under the precision/recall curve to quantify feature’s performance.

We choose this evaluation metric as it is appropriate to characterize features in inbalanced problems where the

proportion of positive samples is smaller than the proportion of negative ones.24, 25

To estimate the ability of our method to segment the vessels, we used Se,Sp and P r . Moreover, we included

other global metrics such as the Matthews Correlation Coeﬃcient, the F1-score and the G-mean, which are also

robust under class inbalance.19

The Matthews Correlation Coeﬃcient (MCC)22 compares manual and automated segmentations, and is given

by the equation:

MCC =T P/N −S×P

pP×S×(1 −S)×(1 −P)(9)

where N=T P +T N +F P +F N is the total number of pixels in the image, S= (T P +F N )/N and

P= (T P +F P )/N. It takes values between -1 and +1, where +1 indicates a perfect prediction, 0 is a random

prediction and -1 a segmentation that is exactly the opposite than the true one.

The F1-score19 is deﬁned as the harmonic mean of the P r and Re:

F1-score = 2×P r ×Re

P r +Re .(10)

Its maximum value, 1, corresponds to a perfect segmentation, while its minimum value, 0, corresponds to a

completely wrong detection. This metric is equivalent to the Dice coeﬃcient, which is also widely used for

evaluating segmentation methods.

Finally, the G-mean has a similar behavior than the F1-score, although it is obtained as the geometric mean

of the Se and Sp:

G-mean = pSe ×Sp (11)

4. RESULTS

4.1 Parameter estimation

Table 4 presents the R2values obtained using each structural measurement for ﬁtting the parameter estimation

models. For the Soares et al. feature we computed three diﬀerent estimators, one for each of the three scales

a={a1, a2, a3}. These values grow almost linearly with the image resolution, so the resulting model has a high

R2value. On the contrary, predicting θpusing linear regression appeared to be unfeasible, as the obtained R2

Table 3: R2values obtained for each combination of feature parameter and structural measurements. p-values

of the F-tests performed for each learned model are also included.

hhhhhhhhhhhhhh

h

Measurement

Parameter l a1a2a3Wθp

Vessel calibre 0.941

p≈6.1×10−30.953

p≈4.4×10−30.985

p≈7.5×10−40.974

p≈1.8×10−30.976

p≈1.6×10−30.003

p≈0.936

Optic disc diameter 0.990

p≈4.5×10−40.945

p≈5.6×10−30.953

p≈4.4×10−30.914

p≈1.1×10−20.985

p≈7.6×10−40.000

p≈0.977

FOV diameter 0.971

p≈2.2×10−30.813

p≈3.6×10−20.818

p≈3.5×10−20.734

p≈6.4×10−20.898

p≈1.4×10−20.016

p≈0.838

Angular resolution 0.973

p≈1.9×10−30.947

p≈5.2×10−30.935

p≈7.2×10−30.914

p≈1.1×10−20.982

p≈1.1×10−30.000

p≈0.996

values are close to 0. This means that the simplest possible model, which is the average of the samples used for

learning the line, performs much better than the estimated model.

When analyzing each structural measurement separately, it is possible to see that the diameter of the optic

disc allows to obtain the best estimations of Wand l, while the calibre of the largest vessel is the best predictor

for a. This results are complementary to those reported by Vostatek et al., who only analyzed the number of

pixels in the ground truth labeling and the angular resolution. The p-values reported by the F-tests performed

for each learned model also support the idea that using lines to estimate feature parameters is valuable, although

not for θp.

Figure 3 illustrates the best parameter estimators for each feature and for θp. Optimal values obtained by

adjusting each parameter on the HRF training set are also included for comparison purposes, although they were

not used to ﬁt the model. It is possible to see that l,aand Wgrows linearly with their corresponding structural

measurement, which justify the usage of linear regression for ﬁtting their values. On the contrary, the optimal θp

values of the low resolution data sets do not change linearly, a setting that explains why they cannot be properly

approximated with linear regression.

4.2 Segmentation results

Segmentation results using our approach with automated feature parameter estimation are given in Table 4.

As mentioned in Section 4.1, estimating θpusing a linear regression model is not feasible due to its non-linear

behavior with respect to the selected structural measurements. Hence, θpwas ﬁxed to the optimal value obtained

according to the validation set sampled from the HRF training set. We also included other works in the literature

that used the same evaluation protocol and/or training and test splits. Vostatek et al.20 reported the performance

obtained by evaluating the supervised method by Soares et al.10 on HRF. Such an approach is based on learning

a Gaussian Mixture Model classiﬁer from the responses to the 2D Gabor wavelets. Vostatek et al. trained this

method using a random sample of 15 images taken from HRF. It is unfeasible to perform an exact comparison

as we have no certainty that the images used for testing are exactly the same than those used to evaluate our

model. However, we also included these results to provide a general idea of the contribution of the fully connected

CRF model with respect to using the original classiﬁer. A series of Wilcoxon signed-ranks hypothesis tests were

performed to compare the results obtained by our method with respect to our previous approach19 and to those

obtained by Odstrˇcil´ık et al.18

As seen in Table 4, our approach consistently perform better than our previous proposal based on scaling

parameters using a compensation factor. The improvements obtained by adapting the feature parameters with

our strategy and the selection of an optimal θpvalue, as measured by all the considered quality metrics, are also

statistically signiﬁcant. In particular, this strategy is able to achieve consistently higher F1-score (p < 9.2×10−7),

G-mean (p < 9.2×10−7) and MCC (p < 9.2×10−7) values, which corresponds to a general improvement in the

quality of the results. When decomposing these metrics in terms of their individual measurements, it is possible

to see that the Se is signiﬁcantly improved (p < 9.2×10−7) by the estimation of the features, a setting that

is related with a better ability to detect thin structures (Figure 4) and to overcome the issues of the original

approach to deal with the bright central reﬂex in arteries (Figure 5). Moreover, larger Sp (p < 0.0044) and P r

(p < 6×10−6) values indicate a reduction in the number of false positive detections.

(a) Zana and Klein feature (b) Soares et al. feature

(c) Nguyen et al. feature (d) θpparameter

Figure 3: Best parameter estimators for each feature parameter. Optimal values on HRF are included only for

comparison purposes, but were not used to ﬁt the linear regression model.

Compared to other existing methods, it is worth noting that our approach achieved the highest average

F1-score (p < 4.1×10−6) and MCC (p < 1.9×10−6) values. A higher average G-mean was obtained by

the baseline method of Odstrˇcil´ık et al.18 Yet, the diﬀerence is not statistically signiﬁcant (p= 0.23). Such

an approach reported also a higher average Se value than our method, but it is not statistically signiﬁcant

(p= 0.09). Furthermore, it is important to underline that the method by Odstrˇcil´ık et al. is based on matched

ﬁlter responses that are recovered from ﬁlters calibrated for this speciﬁc data set. In our case, we used an

automated parameter estimation approach that does not require such an intensive calibration. Moreover, our

method achieve higher Sp (p < 0.006) and P r (p < 1.3×10−5) values, which correspond to a reduction in the

number of false positive detection.

5. DISCUSSION

In this paper we have presented an ensemble approach for blood vessel segmentation in high resolution images,

based on automatically estimating feature parameters. In particular, we have integrated a novel strategy for

parameter estimation using linear regression with a fully connected CRF model, which is known to achieve better

Table 4: Results obtained on HRF.

Methods Se Sp Pr F1 G-mean MCC

Odstrcilik et al., 201318 0.7772 0.9652 0.6950 0.7316 0.8657 0.7065

Vostatek et al., 2017 (Soares)20 0.7340 0.9800 - - 0.8481 -

Vostatek et al., 2017 (Sofka)20 0.5830 0.9780 - - 0.7550 -

Orlando et al., 201719 0.7201 0.9713 0.7199 0.7168 0.8361 0.6900

Our approach 0.7669 0.9725 0.7407 0.7503 0.8636 0.7267

(a) (b)

(c) (d)

Figure 4: Detection of thin vessels, as seen on results obtained on image 10 h from HRF. (a, c) Results obtained

using the ρmultiplier. (b, d) Results obtained using our approach.

results than other existing approaches. We have experimentally analyzed diﬀerent structural measurements of

the images and their potential usage as guidelines to automatically ﬁt a regression line. Our results indicated

that the optic disc diameter is suitable to estimate the parameters of the line detectors and the feature based

on morphology by reconstruction, while the calibre of the major vessel is the best structural measurement to

estimate the scales of the 2D Gabor ﬁlter. On the contrary, the experiments made to automatically adjust θp

indicated that this parameter does not scale linearly with respect to the resolution of the images (Figure 3(d)).

When analyzing the optimal θpvalues for each individual data set, we can see that the higher parameters

were assigned to STARE and ARIA, while the lower values corresponded to DRIVE and CHASEDB1. STARE

and ARIA are characterized by serious pathological cases in which large hemorrhages or exudates occur. On

the contrary, images on DRIVE and CHASEDB1 correspond mostly to healthy patients. HRF also contains

pathological images, although lesions are smaller. This might indicate that larger θpvalues are more suitable to

be used to segment images of patients with large pathologies.

When evaluating the segmentation method quantitatively, it was observed that integrating the parameter

estimation approach improved all the evaluation metrics with respect to using the original scaling factor. Fur-

thermore, the comparison to other works showed that our approach performed consistently better than other

existing approaches that were evaluated using a similar training and test split.

In conclusion, it is possible to see that the estimation strategy applied in this context allows to obtain better

(a) (b)

(c) (d)

(e) (f)

Figure 5: Improved segmentation of arteries with bright central reﬂex, as seen on image 12 h from HRF. (a, c,

e) Results obtained using the ρmultiplier. (b, d, f) Results obtained using our approach.

results in terms of overall quality measurements, with a consistent improvement in the detection of the thinner

vessels and a more appropriate behavior under the presence of bright central reﬂex. This approach can be

exploited not only for adjusting the parameters of hand crafted features but also to calibrate deep learning based

methods, for instance, which are usually trained using patches whose size depends on the image resolution.30

Segmentation masks and further implementation details are provided in https://github.com/ignaciorlando/

high-resolution-vessel-segmentation.

Acknowledgments

This work is partially funded by a NVIDIA Hardware Grant and ANPCyT PICT 2014-1730, PICT 2016-0116

and PICT start-up 2015-0006. J.I.O. is funded by a doctoral scholarship granted by CONICET. We would also

like to thank Odstrˇcil´ık et al. for providing us with their segmentations.

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