segmentation of blood vessel structures in retinal …segmentation of blood vessel structures in...

Segmentation of blood vessel structuresin retinal fundus images

with Logarithmic Gabor filters

Sebastian Gross, Monika Klein, Dorian Schneider

Institute of Imaging & Computer Vision, RWTH Aachen University, 52056 Aachen,Germany

Internal Medicine III, University Hospital Aachen, 52057 Aachen, Germany

[email protected]

Abstract. The analysis of blood vessel structures in the retinal fundusimages is important for the diagnosis of many diseases. Vessel segmenta-tion can assist in the detection of pathological changes which are possibleindicators for arteriosclerosis, retinopathy, micro aneurysms and maculardegeneration.In this article, two approaches to blood vessel segmentation are pre-sented. Both of them are based on the evaluation of phase symmetryinformation using complex logarithmic Gabor wavelets. In the first ap-proach, a phase symmetry filter is combined with the front propagationalgorithm fast marching, the second method uses a hysteresis threshold-ing step.The approaches have shown excellent results for the vessel segmentationon colon polyps. Although they were adapted to structures in retinal fun-dus imaging, neither eye specific knowledge nor supervised classificationmethods are used.For high comparability with previous publications in the field, the al-gorithms are evaluated on the two publicly available image databasesDRIVE and STARE. The hysteresis thresholding approach which per-forms slightly superior achieves an average accuracy of 94.92% (sensitiv-ity: 71.22%, specificity: 98.41%) for the DRIVE and 95, 65% (sensitivity:71.87%, specificity: 98.34%) for the STARE database.

1 Introduction

In modern medicine, the analysis of retinal fundus images is of particular im-portance to various medical diagnoses [1]. Pathological changes in retinal bloodvessel systems can be an indication for several eye diseases like retinopathy, mi-cro aneurysms, and macular degeneration. In addition, the risk for cardiovasculardiseases like hypertension, arteriosclerosis, and stroke [2] can be estimated withminimal effort, since the observation of the ocular fundus is the easiest way toexamine finest blood vessels, where the first signs of vascular damage becomevisible.

2 S. Gross, M. Klein, D. Schneider

The segmentation of retinal blood vessels can be helpful either to remove thevessels from the image to detect hemorrhages or for the examination of the vesseltree itself. Features like cross sections of arteries and veins, contrast, curvature,and concentration of the vessels as well as the size of areas with insufficient bloodvessel support can be used to evaluate the condition of the blood circulation.Furthermore, segmentation can assist in localizing the optic nerve or ease theregistration.

In this paper, two approaches to automatic vessel segmentation are presentedand compared to previously published methods. They have, in similar versions,shown excellent results for the segmentation of vessels [3–5] Although they havebeen adapted to retinal fundus images, neither eye specific knowledge nor asupervised classification methods were used.

The text is structured into multiple sections. Section 2 gives an overview ofprevious work in this area. In sections 3 and 4, our methods for blood vessel seg-mentation are described and the used image databases and evaluation methodsare highlighted. In section 5, results are presented and section 6 gives a shortconclusion and discussion on the topic.

2 Overview of related work

A common approach to blood vessel segmentation is the analysis of ridge infor-mation [6–10], where the eigenvectors of the Hessian matrix are used to determinethe direction of highest orientation. Matched filters are frequently used [8–12] aswell. To reduce computational efforts, a lot of publications propose the Hessianmatrix to discover the assumed vessel direction and subsequent localization withmatched filters [8–10]. Further approaches are feature extraction and classifica-tion [13] (for example based on local binary patterns or morphological opera-tions), line detection [14], line segment detection [6] with subsequent segmentclassification based on forward feature selection [15], Gabor wavelets [16,17], orthresholding [7,18]. Numerous publications apply supervised classification meth-ods, in which, based on defined features, each pixel is classified into one of thetwo possible classes (blood vessel or background).

3 Algorithms for blood vessel segmentation

We propose to apply an approach developed for blood vessel segmentation oncolon polyps [3–5] to fundus images. A graphical overview of the approach isgiven in Fig. 1.

3.1 Pre-processing

As the green image channel provides the highest contrast between blood vesselsand background, it is chosen for the segmentation [14,16].

To minimize background variations, background equalization and contrastenhancement on the green color channel are performed with an 11 × 11 tophat

Retinal blood vessel segmentation with logarithmic Gabor Filters 3

Fig. 1. Schematic process chain of the algorithms


filter [19] as presented in [3]. A structure element is selected and rank order filteroperations [20] are performed with this structure element. First, the element isaligned horizontally and the maximum of the underlying pixels is stored at thecenter pixel’s position in a new image.

Each of the following filters uses the preceeding filter results as input image.The next step is filtering with a vertically aligned structure element. Subse-quently, a second horizontal filter operation is performed. However, this time,the minimum value is stored at the center pixel’s position. Finally, a verticalminimum filter operation completes the tophat filter operation.

The tophat filter results are used to scale the original image. To this is end,each pixel is divided by the value of the corresponding pixel from the tophatfilter results.

The result is then subtracted from the original green channel. Additionally,a small median filter of size 3 × 3 is applied to the image for noise reduction.The image borders are padded by periodic repetition to allow filter operationson the whole image [16].

3.2 Soft vessel segmentation

Examining the cross-section of the vessel, the gray level is increasing symmetri-cally towards the vessel’s centerline. For the detection and analysis of symmetricand asymmetric structures, Peter Kovesi presented an algorithm, which eval-uates the local symmetry information in gray-level images based on complexlogarithmic Gabor functions [21,22] as suggested by Field [23].

An advantage compared to other algorithms is the independency of contrastvariations. Furthermore, no segmentation of the objects prior to the symmetryanalysis is necessary. Kovesi’s algorithm uses logarithmic Gabor wavelets to eval-uate the local phase symmetry, which corresponds to mirror symmetry in thespatial domain.

Gabor wavelets are described by complex sine functions multiplied with aGaussian in the spatial domain

gω0(x) =

ω20

σ2e

−ω20x2

2σ2 ejω0x (1)

where x is the input image’s gray value and σ is the Gaussian standard deviation.In the spectral domain, they are represented by a Gaussian with the sine

wave’s frequency w0 as central point.

G(ω) = e−σ2

2ω20 e(ω−ω0)

2

(2)

As Gabor wavelets are limited in the spatial as well as the spectral domainand provide an optimal compromise between spatial and frequency resolution,they are well suited as local band pass filters. By adaptation of the wavelet scalen, structures of different sizes can be found. For the detection of small structures,a low scale n is used, which provides high resolution in the spatial domain. For


larger structures, a higher scale n is applied. This provides a small bandwidthin the frequency domain, which is essential for noise suppression.

Scaling factors n = n0 ·c ·m for Kovesi’s implementation are described by theminimum wavelet size n0 = 3, a constant factor c = 2.1 and m ∈ {1 . . .mscales}with mscales = 3 being the number wavelet scales (detail images: n0 = 2 andmscales = 4). The parameters are determined empirically. To this end, severaltests have been performed and results were evaluated by experienced observers.

For image processing, however, and especially for the detection of sharperstructures, an optimal resolution in the spatial domain with larger bandwidthin the frequency domain is often preferable. A solution is the use of logarithmicGabor wavelets, which have a Gaussian frequency response over a logarithmicinstead of a linear frequency scale. The transfer function on a logarithmic scaleis given by

G(ω) = e(−log( ωω0)2)/(2(log( σω0

))2). (3)

as recommended by Field [23], where ω0 is the center frequency. κ is used tokeep κ/ω0 constant while ω0 changes due to scaling of the filter (denoted by n).

Compared to normal Gabor wavelets, a larger bandwidth is possible whilestill maintaining a zero mean.

In order to apply logarithmic Gabor wavelets in different directions, the filteris combined with directional filters in six different directions (resolution 30◦). Inaddition, they are multiplied with a large circular high pass filter. This allowsusing a rectangular filter without the problem of varying maximum frequenciesin different directions. In each direction, filters with multiple scales are applied.All filter results are added up to gain the final filter response.

Like Gabor wavelets, logarithmic Gabor wavelets consist of a symmetric realand an asymmetric imaginary part [24]. Therefore, by convolution with the greenchannel image, the real part responds to symmetric frequencies, whereas theimaginary part detects asymmetric structures in the image. The preprocessedimages as well as the real and imaginary part of the log Gabor filter responseare shown in Fig. ??.

Real and imaginary part of the filter response with scale n are calculated byconvolution of the symmetric and asymmetric Gabor filter pair with the inputimage’s green channel intensities and represented by en(x) and on(x).

An =√en(x)2 + on(x)2 (4)

describes the magnitude. Kovesi proposes

sym(x) =

∑n b|en(x)| − |on(x)| − T c∑

nAn(x) + ε(5)

to be calculated by subtracting the absolute values of en(x) and on(x) for eachscale, adding the results together, and normalizing the sum to the magnitudeAn.

Furthermore, a noise component T is subtracted to suppress symmetry re-sponses caused by noise. T is estimated by the mean squared filter response at


the smallest scale. Since An is of non-negative value, a component ε > 0 is addedto prevent division by zero. Applying this approach, however, the detected bloodvessel responses appear much too thin in the results.

An investigation shows that the responses to the asymmetric filter ofteneliminate the small vessels completely. Furthermore, this can completely preventthe detection of small vessels. Both filter results for overview and detail imagescan be seen in Fig. 2.

Blood vessels, however, are in general well contrasted symmetrical structuresin retinal fundus images. Sofka postulates that blood vessel structures are piece-wise symmetric and single edges do not occur [9, 10]. Therefore, we propose toignore the imaginary part and use

sym(x) =

∑n b|en(x)| − T c∑

nAn(x) + ε(6)

as modified approach.The results of the phase symmetry filter contain the segmentation as well as

an orientation matrix containing the direction of the highest filter response foreach pixel. In a further step, each pixel above a heuristically selected thresholdwhich is connected to at least seven such pixels is segmented. Additionally, theorientation output of the symmetry filter is used to remove all pixels, which arenot connected to a minimum number of pixels with the same orientation.

3.3 Binary classification

For binary classification (binary segmentation), two different strategies are com-pared: the front-propagation algorithm fast marching [25] and a method using ahysteresis thresholding step.

In the first case, the phase symmetry filter is tuned to locate as many vesselsas possible. This may lead to a reduced accuracy in the detection of the extentof bigger vessels. However, as the filter results sym(x) as presented in Eqn. 5are skeletonized and used as seed points for the subsequent fast marching step,the full extent of the vessels is detected in the second step. Such seeds for frontpropagation algorithms form starting regions. These starting regions are thenextended into the direction of lowest cost until a heuristically stop threshold isreached.

f(x) =1

1 + e−10x(7)

The cost matrix, which is only used in the fast marching step, is created byapplying

f(x) =1

1 + e−10x(8)

as a scaling function to the green color channel intensity values x. The resultsshow enhanced contrast between blood vessels and background and, therefore,are ideal to calculate marching step costs for each possible fast marching step.

For the second approach, the phase symmetry filter is applied twice withdifferent parameters in order to find thick as well as very thin blood vessels. For


Fig. 2. Left column: full size image, right column: detail image. Top row: green channelimage, second row: median and tophat filtered image, third row: absolute value of thereal part en(x), bottom row: absolute value of imaginary part on(x).


the recognition of large vessels, many different high scales are chosen whereas forsmall vessels, smaller and fewer different scales are used. The resulting segmen-tations are combined by hysteresis tresholding to receive the final segmentation.The outcomes of the phase symmetry filters and the final segmentations for bothalgorithms are shown in Fig. 3.

Fig. 3. Top: fast marching approach: left: phase symmetry output, center: thinnedimage, right: final segmentation, hysteresis approach: left and center: phase symmetryoutput for different parameter settings, right: final segmentation.

4 Material

The performance of the segmentation algorithms is evaluated on two publiclyavailable databases of retinal fundus images, which have been published for thepurpose of comparing approaches on vessel segmentation with identical data.

The DRIVE database was published in 2004 by Niemeijer [26] and consistsof a test and a training set both containing 20 images. For each image, the fieldof view (FOV) is specified by a mask.

The STARE database was presented by Hoover [12] in 2000 and contains20 images, 10 of which are pathological. As no predefined FOV is available, itis determined by thresholding prior to the segmentation. Furthermore, STAREdoes not contain a separate training set. If not mentioned otherwise, parametersfor STARE were determined using the DRIVE training set.


For both databases manual segmentations developed by trained observers areused as gold standard for the evaluation of the segmentation. For the STAREdatabase and the test set of the DRIVE database a second manual segmenta-tion was included by the authors to evaluate inter-observer differences. Intra-observer results are listed in Tab. 1 for reasons of comparison as well.

The two algorithms presented in this paper are applied to the DRIVEdatabase [26]. The superior approach is also tested on the STARE [12] databaseas it offers additional challenges because it contains pathological images.

The segmentations are compared to the first manual segmentations used asgold standard. To obtain the highest comparability, the evaluation criteria usedin previous publications [6–12] are adopted.

5 Results

For both algorithms, two parameters T1 and T2 may be chosen: in case of thefast marching approach the segmentation threshold for the phase symmetry filterand the stop threshold for the fast marching algorithm, in case of the hysteresisapproach the thresholds for the two phase symmetry filters. By modifying T1and T2, a compromise between correctly classified blood vessel pixels and falselyselected background pixels has to be found. The results of these modificationsmade during extensive testing can be seen in the curves in Fig. 4.

For the evaluation on the DRIVE database, parameters T1 and T2 are ad-justed for the 20 images from the test data set and are subsequently used ontest data set containing 20 images as well. The resulting average accuracy forthe fast marching approach is 94.74% (sens = 73.07%, spec = 97.99%), for thehysteresis approach 94.92% (sens = 71.22%, spec = 98.41%). In table 1, the re-sults of former publications are listed alongside our new results. Fig. 4 shows theresults of the hysteresis approach used on the DRIVE database test set for vary-ing parameters T1 and T2. The average accuracy and the False Positive Rate areshown as function of the True Positive Rate. The highest value for the maximumaverage accuracy of 94.95% is obtained for T1 = 0.18 and T2 = 0.62.

The hysteresis thresholding approach shows the superior classification perfor-mance for the DRIVE database and a higher sensitivity. Furthermore, observersacknowledged a better representation of smaller blood vessels in the hystere-sis thresholding results. Therefore, this approach is used in additional tests onthe STARE database [12] to evaluate the difference between normal and patho-logical images. The maximum average accuracy for healthy images is 95.81%(sens = 74.74%, spec = 98.35%). For pathological images, it decreases to 95.50%(sens = 69.16%, spec = 98.28%). The best result for the overall average accuracywas 95.65% (sens = 71.87%, spec = 98.34%).

6 Conclusion and outlook

The paper evaluates phase symmetry filtering as introduced by Kovesi [21,22] forthe segmentation of vascular patterns on retinal images. The main component


Author DRIVE STARE

MAA Sens Spec MAA Sens Spec

PS+FM 0.9474 0.7307 0.9799 - - -

PS+Hysteresis 0.9492 0.7122 0.9841 0.9565 0.7187 0.9834

Budai [7] 0.9490 0.7509 0.9680 0.9380 0.6510 0.9750

Wu [8] - 0.9023 0.9518 - - -

Soares [16] 0.9466 - - 0.9480 - -

Staal [6] 0.9441 0.7194 0.9773 0.9516 - -

Ricci [14] 0.9595 - - 0.9646 - -

Mendoca [27] 0.9463 0.7315 0.9781 0.9479 0.7123 0.9758

Niemeijer [26] 0.9416 0.6898 0.9696 - - -

Fadzil [28] 0.9316 0.9084 0.9335 - - -

Rezatofighi [13] 0.9462 0.7358 0.9767 - - -

Garg [29] 0.9361 - - - - -

Al-Diri [30] - 0.7282 0.9551 - 0.7521 0.9681

Alonso-Montes [31] 0.9180 - - - - -

MacGillivray [32] 0.9400 - - - - -

Farzin [33] 0.9370 - - 0.9480 - -

Fraz [34] 0.9352 - - 0.9384 - -

Hoover [12] - - - 0.9275 - -

Lam [35] - - - 0.9474 - -

intra-observer [13,26] 0.9473 0.7761 0.9725 0.9349 0.8951 0.9572

only background [26] 0.8727 0.0000 1.0000 0.8958 0.0000 1.0000

Table 1. Comparision of maximal average accuracy (MAA), sensitivity (sens), andspecificity (spec) taken from different publications for DRIVE [26] and STARE [12].


Fig. 4. Change of average accuracy and False Positive Rate (FPR) as a function of theTrue Positive Rate (TPR) for varying parameters T1 and T2.

of Kovesi’s approach are the Gabor wavelets which have already been used forthe task in, e.g., [16,17].

As shown in the evaluation the method is, in general, well suitable for thesegmentation of retinal blood vessels. It outperforms many previously publishedalgorithms which were developed especially for the purpose of retinal blood vesselsegmentation. The results for the STARE database, which improved over thosefor the DRIVE database, indicate that the algorithmdoes not particularly sufferfrom the pathological changes in the images. The improvement is in line with thepresented results for other algorithms, however, it is high (δMAA = 0.7%) andon a high level of (MAA = 95.65%) in comparison to other published results.

For further improvement, special knowledge about the structure of the retinalfundus could be used. For example, the blood vessels are always descendingfrom the papilla and proceeding outwards without erratic changes in the vesselscross section. Furthermore, arteries and veins can be distinguished from colorand structure and never cross with other vessels of the same type. The post-processing can additionally be expanded by localizing and removing artefactscaused by noise or tubular structures and segmented by the phase symmetryfilter from the final segmentation.

7 Acknowledgments

[removed for blind review] The authors would like to thank the late Prof. Dr.-Ing.Til Aach, Institute of Imaging & Computer Vision, RWTH Aachen Universityfor his continuous support and generous advice. We would also like to acknowl-edge the funding of this work by the German Federal Ministry of Education


and Research (support code 01EZ1006B) and the German Federal and StateExcellence Initiative.

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segmentation of blood vessel structures in retinal …segmentation of blood vessel structures in...

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