A Fast Multiresolution Approach Useful

for Retinal Image Segmentation

Dario Lo Castro

, Domenico Tegolo

1,2

and Cesare Valenti

Department of Mathematics and Computer Science, University of Palermo, via Archiraﬁ 34, Palermo, Italy

CHAB-Mediterranean Center for Human Health Advanced Biotechnologies, University of Palermo, Palermo, Italy

Keywords:

Elliptical Gaussian ﬁlters, Directional Map, Retinal Vessel, Fundus Oculi.

Abstract:

Retinal diseases such as retinopathy of prematurity (ROP), diabetic and hypertensive retinopathy present sev-

eral deformities of fundus oculi which can be analyzed both during screening and monitoring such as the

increase of tortuosity, lesions of tissues, exudates and hemorrhages. In particular, one of the ﬁrst morpholog-

ical changes of vessel structures is the increase of tortuosity. The aim of this work is the enhancement and

the detection of the principal characteristics in retinal image by exploiting a non-supervised and automated

methodology. With respect to the well-known image analysis through Gabor or Gaussian ﬁlters, our approach

uses a ﬁlter bank that resembles the “`a trous” wavelet algorithm. In this contribution we show a particular

approach to speed-up the computing time. This methodology rotates the kernels and it is a fast enough to

extract information useful to assess vessel tortuosity and to segment (not considered explicitly in this paper)

retinal images. Furthermore, we compare on the public databases DRIVE and DIARETDB0 our output im-

ages against the SCIRD-TS algorithm, which is considered as one of the most effective supervised methods

for the detection of retinal thin structures.

1 INTRODUCTION

In the last two decades the retinal diseases research

obtained great results in fundus oculi image analy-

sis. Retinal image analysis ensures a non-invasive ex-

amination that shows many characteristics of micro-

circulation, due to a useful screening tool like video-

capillaroscopy (Bellavia et al., 2014a). Recently,

some scientiﬁc contributions highlight the correla-

tion between coronary heart disease and coronary mi-

crovascular dysfunctions (McClintic et al., 2010). In-

formation about fundus oculi features, from various

methodologies, are valid and effective resources for

the physician. Optic disk, macula, retinal vessels,

hemorrhages, exudates, micro-aneurysm and tortuos-

ity are quite important features and give information

on eye health, more in general on cardiovascular cir-

culation of the patient. Image processing automated

techniques for blood vessels segmentation were de-

veloped in (Salazar-Gonzalez et al., 2014; Gupta

et al., 2016; Lukac and Subasic, 2017). By exploiting

Gabor ﬁlters, methodologies for measurement, track-

ing, detection and segmentation of the width of ma-

jor temporal arcades were described in (Oloumi et al.,

2015). In (Zhang and Zhao, 2016) we can ﬁnd an

approach that uses compactness, uniformity and lo-

cal density to locate the optic disk. That methodol-

ogy exploits bidimensional Gabor ﬁlters with a ro-

tation angle at step of 15

◦

. There are also meth-

ods based on tubular shape and geometrical models

to highlight curvilinear structures (Annunziata et al.,

2016; Soares et al., 2006). Instead, global and local

directional models are used in (Wu et al., 2016) to

identify the optic disk location by its brightness and

parabolic shape. With respect to the detection of ex-

udates an interesting approach was deﬁned by Gian-

cardo et al. (Giancardo et al., 2012) which introduces

a method for diagnosis of diabetic retinopathy by us-

ing a set of features based on color, wavelet decom-

position and segmentation of lesions. A promising

approach based on keypoints (Bellavia et al., 2014b)

was described in (Zhanga et al., 2015). In (Youssif

et al., 2008) Youssif et al. present a method to detect

the optic disk by the degree between vessel map and

vessel’s direction matched ﬁlter. Moreover, a circular

brightness object was found by Lu and Lim in (Lu

and Lim, 2011) in order to deﬁne a unique circu-

lar brightness structure of the optic disk. All these

methods adopted a model to identify the right struc-

tures. A hand-crafted ridge detector, named SCIRD,

was described in (Annunziata and Trucco, 2016), in-

variant to rotations, resizing and curvatures. This ap-

Lo Castro D., Tegolo D. and Valenti C.

A Fast Multiresolution Approach Useful for Retinal Image Segmentation.

DOI: 10.5220/0006579203400345

In Proceedings of the 7th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2018), pages 340-345

ISBN: 978-989-758-276-9

proach uses an appearance and context model, includ-

ing multi-range learned ﬁlters, to extract a tubular-

ity measure, obtained by convolving the image with

second-order directional derivatives similar to a Ga-

bor ﬁlter bank (Soares et al., 2006). In this way, that

approach faces the problem of point-like and irregular

structures. The drawback of that methodology is the

ﬁne-tuning of various parameters. SCIRD-TS, before

of choosing the ﬁnal values, requires to test various

parameters, therefore spending so much training and

computing time. In literature there are non-automated

methods that needed a manual tuning, or an initial

training step which is deeply subjected to the val-

ues of parameters proposed by the trainer. However,

those methods should be considered non-supervised

and non-automated as they require a long computing

and processing time, because the a priori choosing of

the input values.

Vice versa, our method, instead of the well-known

Gabor ﬁlter approaches, uses an elliptical Gaussian

ﬁlter bank in a way that resembles the “`a trous”

wavelet algorithm (Shensa, 1992), pre-calculated ﬁl-

ters and without no particular tuning of parameters.

Therefore it results faster with respect to the tradi-

tional methods that require a priori settings of the

input parameters. For this reason, we consider our

methodology as a non-supervised approach. Fur-

thermore, we introduced a color directional map

to assess better visually the retinal vessels tortuos-

ity (Aghamohamadian-Sharbaf et al., 2016). In this

contribution we carryed out a comparison against the

output images obtained from SCIRD-TS by Annun-

ziata et al (Annunziata and Trucco, 2016) on im-

ages with different resolutions and size from the well-

known public databases DRIVE (Staal et al., 2004)

and DIARETDB0 (Kauppi et al., 2012).

2 PROPOSED METHODOLOGY

In order to put in evidence both linear and curvilin-

ear structures of retinal vessels (see ﬁgure 2) we pre-

ferred to use elliptical Gaussian ﬁlters with respect to

the standard Gabor ﬁlters (Biran et al., 2016; Carn-

imeo et al., 2016; Fraz et al., 2017; Geetharamani and

Balasubramanian, 2016; Kuri, 2015). In this way the

vessel proﬁle is matchable with the kernel one (see

ﬁgure 1 and ﬁgure 2). To compute the ﬁlters bank we

implemented the following function:

G(x, y, σ

, σ

, µ

) =

−

(x−µ

)

2σ

−

(y−µ

)

2σ

2πσ

(1)

where µ

=0 and µ

=0 so that the center of the func-

tion coincides with the center of the kernel κ and

where σ

= 0.8 and σ

= 1.6, determined experimen-

tally, modulate the frequency along the main axis.

Furthermore, we have that x, y∈{−2, −1, 0, 1, 2}.

⊗κ

Figure 1: The sequence of convolutions with κ

, κ

and κ

(which have the size 5×5, 9×9 and 13×13) is equivalent

to single convolutions on the same image with kernels with

size 5×5, 13×13 and 25×25. The overall shape of the

elliptical Gaussian function is maintained.

Our methodology exploits the “`a trous” ap-

proach (Shensa, 1992) (in French it means “with

holes” due to the zero elements) to increase the pro-

cessing velocity and to decrease the computing time

(indeed the algorithm considers the same number of

non-zero elements for every kernel). As in ﬁgure 1,

starting from the 5× 5 kernel κ, we added zero (i.e the

holes) in order to enlarge κ, thus obtaining a bigger

kernel κ

(nx, ny)=κ(x, y) (2)

where index n rules only the size of kernel, keeping

the same number of non-zero elements unchanged.

Starting from the 5×5 kernel, κ

≡κ, we have 25 non-

zero elements, regardless to the size of the kernel of

the ﬁlters bank. Unlike the original “`a trous” algo-

rithm, we set the distance between a kernel and its

next bigger one does not grow up like a power of 2,

because so we had kernels matchable with the width

of retinal vessels in a more precise way.

Starting from a ﬁlters bank composed by 5×5 κ

9×9 κ

and 13×13 κ

kernels (see top row of ﬁg-

ure 1), by convolving every ﬁlter with the previous

one, we obtained elliptical kernels (see bottom row

ﬁgure 1)with 5×5, 13×13 and 25×25 sizes, respec-

tively. This approach makes constant the computing

time and achieves good results with respect to those

with more time complexity. Furthermore, we wanted

to make our approach invariant to rotations, thus to

obtain and to extract theinformation about retinal ves-

sels tortuosity. Unlike (Annunziata et al., 2016; An-

nunziata and Trucco, 2016; Zhang and Zhao, 2016)

which use an angle θ at step of 15

◦

to overtake the

time complexity problem due to convolutions, we ro-

tated the kernels with a step of 2

◦

, with an angle

θ = [0

◦

, 178

◦

]. In such a way we ensured a ﬁne val-

uation of the vessel orientation. Furthermore, we did

not analyze the results through neural networks and

we did not apply any sub-sampling (Paranjape et al.,

2015; Rizvi et al., 2016; Wang et al., 2017). At the

end, we had a more general κ

and only three itera-

tions and convolutions with the input (for every n and

θ). Different directions and sizes of the kernels high-

light in turn the various curvilinear structures of input

image (see ﬁgure 3).

Figure 2: A zoomed detail of 24×24 pixels (gray levels

interpolated and emphasized for better display purposes).

The small central reﬂex, usually present along the vessel,

can be matched by 5×5 elliptical Gaussian kernel.

Our approach, starting from the smallest 5×5 ker-

nel convolved with the input image, for every rotation

angle, subtract from the input image all highlighted

structures. This process is repeated with bigger ker-

nels in order to bigger always retinal structures. It

must be noted how the smallest details are detected

by κ

kernels even if normally they are considered

noise, whereas wider vessels are enhanced by κ

. For

the DRIVE and DIARETDB0 databases it is not nec-

essary to use kernels bigger than κ

to match the ves-

sel width. This approach, considering θ= [0

◦

, 178

◦

locates vessels orientation, because the deﬁnitive di-

rection corresponds to the maximum correlation value

in that pixel, for the whole set of convolutions. By

exploiting this information, we obtain a directional

map of colors inspired by the HSV palette (see ﬁg-

ure 4 and ﬁgure 5). To avoid any problem due the fact

that even zones that do not present any vessel show

a preferential color/direction, we exclude the back-

ground by multiplying the map by the maximum cor-

relation value itself. The resulting direction is coher-

ent with respect to the image; this approach is sim-

ple but stable and it does not require any interven-

tion to reduce possible ﬂuctuations (e.g. a median ﬁl-

ter in post-processing (Guastella and Valenti, 2016)).

We believe that the information about vessels orien-

tations extracted from the directional map can be a

useful tool for a possible segmentation step (Escorcia-

Gutierrez et al., 2016; Hamad et al., 2014; Keivani

and Pourghassem, 2015; Mookiah et al., 2015; Ro-

taru et al., 2015; Waheed et al., 2015) together with

the vessels brightness. We also believe that the direc-

tional map can be used to assess globally and locally

retinal vessels tortuosity (Khansari et al., 2017).

3 DATABASE AND

EXPERIMENTAL RESULTS

We used our approach on the retinal images of two

standard and well-known public databases: the Dia-

betic Retinopathy Database and Evaluation Protocol

(DIARETDB0) (Kauppi et al., 2012) and the Digital

Retinal Images for Vessel Extraction (DRIVE) (Staal

et al., 2004). Both databases present retinal images

with both pathologies and no pathologies, with dif-

ferent resolutions. DIARETDB0 consists of 130 reti-

nal images, 110 contain various symptoms of diabetic

retinopathy and 20 without any diseases; all of 130

were labeled by four experts to locate the presence of

hemorrhages, exudates and micro aneurysms. DRIVE

consists of 40 retinal images, 7 contain symptoms

mild early diabetic retinopathy and 33 do not show

any sign of diseases; all of 40 images were labeled

by two experts and divided into test and training sets,

containing 20 images each. DIARETDB0 has images

of 1500×1152 pixels, whereas DRIVE has images

of 768×584 pixels. Despite this, the bank of ﬁlters

, κ

and κ

were used to process both databases,

matching the dimensions of fundus oculi structures

in any case. To compare the results of our approach

with SCIRD-TS (Annunziata and Trucco, 2016) we

used the FSIM (Zhang et al., 2011) and Dice (Abirami

et al., 2015) measures. In order to put in evidence the

differences between these measures (FSIM evaluates

the overall aspect of the images, whereas Dice per-

forms a pixel-wise analysis) to evaluate the robustness

of the proposed method we introduced Gaussian noise

Figure 3: Graphic representation of convolutions with κ

, κ

and κ

together, which corresponds to a 25×25 kernel.In general

the bigger the kernel, the wider the detected components.Rotating the kernel allows to identify the orientation of the vessels

(highlighted by the arrows in the case of horizontal and vertical targets).

Figure 4: Qualitative comparison between the results obtained on the DRIVE input image (ﬁgure 2) by the algorithm described

in (Annunziata and Trucco, 2016) (a) and our methodology (b).We produce also a direction map (c) whose hue indicates the

orientation assigned to each pixel while the luminosity is extracted by the result itself (c).

Figure 5: Qualitative comparison between the results obtained on a typical DIARETDB0 image by the algorithm in (Annun-

ziata and Trucco, 2016) (a) and our methodology (b,c).

up to 30%, too. The FSIM measure uses the phase

congruency to extract the characteristics and the gra-

dient magnitude to code the contrast information and

evaluates the feature similarities of the images on a lo-

cal basis, as for the human visual system. Vice versa,

the Dice measure compares pixel-by-pixelsimilarities

of the images. For the input parameters of SCIRD-

TS (freely distributed implementation available at

http://staff.computing.dundee.ac.uk/rannunziata), we

used its default values.

Average results are reported in ﬁgure 6 and in par-

ticular they show FSIM=0.88 and Dice=0.85 with re-

spect to DRIVE and FSIM=0.89 and Dice=0.83 with

respect to DIARETDB0. To verify the robustness of

our method we also introduced a Gaussian noise with

a step of 1% up to 30% in the input images (see ﬁg-

ure 6). We have to point out that our methodology

does not require any time in choosing the parameters,

as opposed to the SCIRD-TS algorithm or as opposed

to many other algorithms described in the literature.

Our method is non-supervised, while it is only sub-

ject to the smallest κ

(which depends on the width

Figure 6: Average quantitative comparison through the

FSIM and Dice measures between the output images ob-

tained by the algorithm described in (Annunziata and

Trucco, 2016) and our methodology, with respect to differ-

ent amount of Gaussian noise.

of the smallest vessels). Our algorithm was devel-

oped in MatLab language without taking care of par-

ticular optimization tricks. In a low level language,

thanks to the pre-computed bank of ﬁlters, our algo-

rithm takes few seconds to process an image on an

Intel Core i7-3770 CPU with 3.40 Ghz, 8.0 GB-RAM

and a NVIDIA GeForce GT 620; therefore it should

be useful in the case of a real time applications.

4 CONCLUSIONS AND FUTURE

WORK

Our approach, despite its simplicity, is able to put in

evidence and to enhance the retinal features and the

prevalent directions of curvilinear and linear struc-

tures. The virtues of our methodology are: being a

non-supervised approach; not having to tune parame-

ters; minor computing time to process retinal images

with respect to SCIRD-TS. We obtained good results

in comparing our outputs and the SCIRD-TS ones. In

the future work, we aim to decrease the complexity

time by optimizing the code; to get a binary represen-

tation of the vessels by segmenting our output images;

to use the color directional map to evaluate the vessels

tortuosity.

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