- Open Access
A framework for retinal vasculature segmentation based on matched filters
© Meng et al. 2015
Received: 14 March 2015
Accepted: 12 October 2015
Published: 24 October 2015
Automatic fundus image processing plays a significant role in computer-assisted retinopathy diagnosis. As retinal vasculature is an important anatomical structure in ophthalmic images, recently, retinal vasculature segmentation has received considerable attention from researchers. A segmentation method usually consists of three steps: preprocessing, segmentation, post-processing. Most of the existing methods emphasize on the segmentation step. In our opinion, the vessels and background can be easily separable when suitable preprocessing exists.
This paper represents a new matched filter-based vasculature segmentation method for 2-D retinal images. First of all, a raw segmentation is acquired by thresholding the images preprocessed using weighted improved circular gabor filter and multi-directional multi-scale second derivation of Gaussian. After that, the raw segmented image is fine-tuned by a set of novel elongating filters. Finally, we eliminate the speckle like regions and isolated pixels, most of which are non-vessel noises and miss-classified fovea or pathological regions.
The performance of the proposed method is examined on two popularly used benchmark databases: DRIVE and STARE. The accuracy values are 95.29 and 95.69 %, respectively, without a significant degradation of specificity and sensitivity.
The performance of the proposed method is significantly better than almost all unsupervised methods, in addition, comparable to most of the existing supervised vasculature segmentation methods.
Retinal vasculature, which is the main structure visible in a fundus image, is the only non-traumatically observed part of the human circulation system. Many retinal diseases are characterized by changes to vasculature abnormalities, e.g., vessel dilation, tortuosity and presence of new blood vessels. And many system conditions, e.g., arteriosclerosis, hypertension or diabetes , can be diagnosed by evaluating the lesions of vasculature. Thus, the measurement of various vessels features, like width, branching patterns, tortuosity and texture can throw light on [2–4] early prevention of system disease and pathologies. However, manual extraction of these features is tedious and time-consuming, especially when facing complex vessel networks and large quantities of images. One acceptable way is to automatically measure the features, which has already aroused much attention in the medical world .
One of the optimal tasks is vasculature segmentation, which is a prerequisite step before the acquisition of several above-mentioned morphological features. Moreover, as an invariant feature, retinal vasculature is frequently used in retinal image registration in order to construct a global view of the eye fundus . Besides, benchmark positions like fovea and optic disk can be located according to the tree-like topology of vasculature .Contrarily, in circumstances of detecting non-vasculature lesions, the vessels, as a kind of interference, must be excluded . Finally, it is proved that the retinal vasculature is distinctive enough to be a new kind of biometric patterns, and several works have been published [9, 10].
Accurate vasculature segmentation has immediate and far-reaching impact to the above-mentioned applications. Yet segmenting the tree-like vessels is still a challenging task: (1) image level, existence of random noise and uneven illumination distributions; (2) vessel level, variability of vessel intensity, diameter and shape ; (3) pathological level, presence of vessel and non-vessel lesions bring large abnormal regions [12, 13]. Though retinal vessel segmentation have been long researched, there is still room for improvement.
In order to deal with the various challenges exist in vessel segmentation and at the same time keep the simplicity of the models to enable efficiency, we consider preprocessing as a critical step. Proper preprocessing operations can remove noises, enhance the contrast between vasculature and background and emphasize the intensity differences between lesions and vasculature. In addition, good preprocessing operations should not bring deformations to vasculature and should clarify the capillary vessels. If the vasculature are greatly enhanced, subsequent segmentation operations will also be facilitated.
Based on the above-mentioned consideration, a new matched filter-based vasculature segmentation method is proposed. The method consists of three main stages: In the first stage, we threshold the images processed using weighted improved circular gabor filter (ICGF) and multi-directional multi-scale second derivation of Gaussian (MMSDG). This operation is conducted on the observation that vessels and background can be easily separated when suitable preprocessing operations exist. The ICGF is a retinal image enhancement method which is first demonstrated in our previous work . It can enhance the image contrast and at the same time clarify the capillary vessels. The MMSDG operation is also a novel technique to enhance vasculature structures. The images processed by MMSDG have more uniformly distributed backgrounds, which is complementary to IGCF. In the second stage, the raw segmented image is fine-tuned by a set of novel elongating filters. This operation preserves the true ridges and fills the hollow pixels of the raw segmented vasculature according to their various thicknesses, simultaneously with the noises significantly reduced. Finally, we eliminate the speckle like regions and isolated pixels, most of which are non-vessel noises and miss-classified fovea or pathological regions.
The proposed method is easy to understand because there is no complicated image understanding techniques adopted. The contrast of vasculature and the background is enhanced by weighted combination of ICGF and MMSDG, which simplified the subsequent segmentation operations. In our proposed method, the raw segmentation is a binarization by a single threshold, which can be fixed by pilot study. Despite its simplicity, this method is shown to be both efficient and effective for the retina segmentation task. The publicly available STARE  and DRIVE  databases which are commonly considered as benchmark databases for vasculature segmentation are used to measure the performance of our method. From the accuracy and the area under the receiver operating characteristic (ROC) curve (AUC), we can figure out that our approach outperforms almost all the unsupervised methods and most of the supervised methods.
This section is a brief review of the existing techniques for vasculature segmentation in 2-D retinal images. The dedicate work of Fraz et al.  has presented a much more detailed survey of previous methodologies. In this paper, we divide the existing segmentation methods into two classes: unsupervised methods and supervised learning techniques.
The unsupervised methods encode the human knowledge to identify the vasculature. Among these methods, features related to the intensity and structure properties are mainly considered. This kind of methods can be further subdivided into four major types: matched filter, vessel tracking, morphological processing and model based methods.
The matched filter based methods enhance the vessel features by convolving the retinal image with 2-D templates. The templates are designed to simulate designated vessel feature patterns and the convolution results will indicate the presence and saliency of the pattern. Matched filters generally work well, however, may fail when vasculature abnormalities and lesions exist and when meet the capillaries . In the work of Chaudhuri et al. , the piece-wise linear segments are approximated by a Gaussian curve. pixels with highest responses are selected as vessels, and then post-processing is operated for final determination. Despite the Gaussian model , methods based on steerable filters  have also been proposed for its intrinsic advantages of faster computation. What’s more, this kind of filter works well on retinal image enhancement . The technique presented in  combines local vessel attributes with region-based ones extracted from vessel structures, and allows for multiple branching. The seminal work of Gang et al.  presents a retinal vasculature detection method that involves 2nd order Gaussian filters with filters and thresholds changed adaptively.
The vessel tracking techniques consist of locating the center point of blood vessel segment and estimating next location, using the spatial distribution properties of vessels. The most prominent advantage of these method is their efficiency in computation and meaningfulness. With the vessel area highlighted, thorough scanning over the whole image which is usually very computationally intensive and requires more time and space is omitted. However, the tracking method may fail when random structures or noises exist. Moreover, vessels cannot be complete when vessels fade away or any bifurcation points are missed. Chutatape et al.  designed a tracking method which uses Gaussian and Kalman filters to detect blood vessels. This method at first originates seed points around the perimeter of the optic disc (OD). Then vessels are tracked using Kalman filtering according to the selected seeds. Branches are also important structures in vessel tracking, related techniques are also employed for vessel detection. Related tracking methods are adopted in .
Methods of mathematical morphology  are also introduced to vessel analysis. In , the authors design a vessel pattern detection method which combines morphological filters and cross curvature evaluation. In their method, the vessels are defined as bright patterns which are piecewise connected and locally linear. To differentiate vasculature from analogous disturbing patterns, the cross curvature evaluation is then performed. Clean linear structures are extracted using this method, but they are not always connected to each other. Fraz et al.  extract the vessel tree by combining vessel centerline detection and morphological bit plane slicing. Mathematical morphology have proved to be a proficient methodology for vessel detection. Another method  first extracts the vessel centerline by using differential filters, and then the vessels are filled by morphological operators. Still, when a vessel centerline is not correctly detected, the retinal vessels will be missed in the final segmented results.
The supervised learning approaches learn the rules for vessel extraction utilizing a training set of manually segmented benchmark samples based on given features. The manually segmented blood segmented vessels which work as priori knowledge can guide the model training. On the other hand, careful vessel labeling and repeated training sample selection can improve the precision of segmentation. The supervised learning methods usually have superior performance than unsupervised methods, but some limitations still exist. The first limitation is that supervised method use various kind of features such as intensity, texture, etc. extracted from each pixel and its surroundings to find the vessels. The interrelationship of these features is complicate and the redundancy of these features always aggravates time and memory consumption. Another limitation is the need for labeled training data which has to be done by eye specialists or at least trained observers. For a typical retinal image, it will take an observer about 2 h on average for labeling . Moreover, the labeled training data may vary according to different observers. The third limitation is that the supervised learning method is time-consuming because of the pixel-level processing.
In the work of Niemeijer et al. , for each pixel a feature vector which is extracted using multi-scale Gaussian and its derivatives is defined. Then the K-nearest neighbor (kNN) algorithm is employed to estimate whether a pixel is belong to vessels. Staal et al.  exploits the intrinsic property of vessel by using ridge profiles. In their method, 27 features are selected using a sequential forward selection method and a kNN algorithm is applied. In , features for each pixel are calculated by employing a multi-scale analysis using a Gabor wavelet transform. A Gaussian mixture model classifier is used to determine wether a pixel is a vessel pixel or not. Ricci and perfetti  apply a bunch of line operators to extract features, and then Support Vector Machine (SVM) is employed for classification. Lupascu et al.  introduce a supervised method which is named feature based Adaboost classifier (FABC) for vasculature segmentation. In their work, a 41-D feature vector extracted using different filters for each pixel has been defined. Neural Network has also been used in retinal vasculature segmentation [37, 38]. The methodology presented by Marin et al.  employs a 7-D feature vector consisted of moment invariant based and gray-level features. A multi-layer feed forward neural network is utilized for training and classification. The combination of the radial projection and the semi-supervised self-training method using SVM is employed by You et al.  for vessel segmentation. Moreover, in order to further improve performances, methods based on ensemble learning were employed to the segmentation of retinal vessel by Fraz et al. [40, 41].
Enhancing the vessel structures and normalize the background distribution using weighted ICGF and MMSDG;
Coarsely segmenting the vasculature by assessing the proportion of vessels in the image;
Filtering the coarsely segmented region in eight different directions using a bank of filters (generated by rotating the vertical line using bilinear interpolation), then result image of different directions are intersected;
Removing the speckle-like regions and non-vessel pixels.
Each step of the proposed method is further illustrated in the following parts.
The green channel of the original color retinal image is selected in the proposed method, since the blood vessels in this channel have the highest contrast against the background. The blue channel tends to be empty and the red channel tends to be saturated. In addition, the retinal images always suffer from low contrast problems and random noise which can seriously affect the performance of segmentation algorithms. In our method, the retinal image is preprocessed using weighted ICGF and MMSDG.
Improved circular gabor filter
Multi-directional multi-scale second derivation of Gaussian (MMSDG)
Blood vessels can be considered as dark elongated or line structures which are of different diameters and orientations on a brighter background. To make the vessels more salient and separable in terms of intensity, a preprocessing method based on enhanced vessels over different directions and scales is proposed. As vessels are of different diameters, different scales are used to calculate the various responses and then the maximum response at each pixel is kept.
Rotating the base filters into five different orientations using bilinear interpolation, thus filters of 0°, 30°, 60°, 90°, 120°, 150° are generated.
Filtering the retinal image by convolving it with the generated filters, then, for each pixel, picking the maximum intensity value.
Normalizing each image by dividing the sum of templates for each scale, respectively. Then, averaging the images from different scales.
Normalizing the image into 0–255, and enhancing the image by histogram equalization.
Weighted ICGF and MMSDG
To obtain clean and accurate segmentation, another essential operation is post-processing. The image post-processing stage includes two basic procedures: denoising and speckle-like region removal. These two operations are implemented by measuring the region properties in an image. It is based on the observation that noises are always isolated regions and are discontinuous to each other. It consists of three steps: (1) determine the connected component; (2) compute the area of each component and acquire the length of major and minor axis of the ellipse that has the same normalized central moments as each connected component; (3) remove objects of small areas and speckle like components. The regionprops Matlab command  is adopted to implement the operation. When applied to the retinal images with speckle noises and vessels, it creates one structure for each component. Components that are too small in area are considered as noises and are eliminated from the image. And components that have equal major and minor axis length are most probably miss-segmented fovea or pathological regions. The effects of area threshold and ratio of major axis length divided by minor axis length are analyzed in the experiment section.
The proposed method has been tested on the DRIVE and STARE databases which are publicly available and popularly used in vasculature segmentation evaluation. Both databases are aimed to convenient performance comparisons with existing segmentation methods and are considered as gold standard databases.
All experiments for the proposed segmentation method are carried out with the following parameter settings, which were found with statistical analysis or pilot study.
In the MMSDG operation, six orientations are employed as described in the image enhancement sextion, and the parameter \(\sigma\) has three values which is 1, 2 and 3. Thus three scales \(7\times 7\), \(13\times 13\) and \(19\times 19\) are used. To best compromise the global intensity distribution and local contrast, the weight parameter \(\alpha\) for ICGF and MMSDG is set to 0.33 for the STARE database and 0.43 for the DRIVE database.
The preprocessed retinal images are coarsely segmented with \(\rho MN\) pixels labeled as vessels. In the STARE and DRIVE database, \(0.081\times 565\times 584\) and \(0.065\times 605\times 700\) are labeled as pixels belonging to vessels, respectively. The value of \(\rho\) for the STARE database is smaller than value for the DRIVE database because images from the STARE database have large empty backgrounds. What’s more, with a different FOV, the vessels are not that rich as on the DRIVE database.
For the elongating filters, a threshold of \(\eta =2.23\) is selected by pilot experiments to binarize the convolution results. If \(\eta\) is too big, too much noise will be involve, and if \(\eta\) is too small, even the vessels will be eliminated.
In the post-processing stage, components with an area that contains less than 40 pixels is eliminated. Objects with ratio of major axis length divided by minor axis length that is bigger than 0.3 and major axis length less than 40 pixels are eliminated.
Four possible results for vessel detection
True positive (TP)
True negative (TN)
Vessel not detected
False positive (FP)
False negative (FN)
Different criterions for performance evaluation
TP/(TP + FN)
TN/(TN + FP) or 1 − FPF
TP/(TP + FP)
TN/(TN + FN)
(TP + TN)/FOV pixel count
Area under ROC curve
(P(A) − P(E))/(1 − P(E))
The true positive fraction (TPF), also called sensitivity, is calculated as the rate of pixels correctly classified as vessel pixels (TP) divided by the total number of vessel pixels in the gold standard segmentation. The false positive fraction (FPF) in the number of pixels incorrectly classified as vessel pixels (FP) divided by the total number of non-vessel pixels in the gold standard segmentation. The positive predictive value (PPV) is the ratio of pixels classified as vessel pixels that are correctly classified. Negative predictive value (NPV) is the ratio of pixels classified as background that are correctly classified. The accuracy (Acc) for one image is the fraction of pixels correctly classified at a special threshold. As for the area under ROC curve (AUC), we can figure out that the closer a curve approaches the top left corner, the better the performance of the system. AUC is a single measure to quantify the behavior. We also compute the kappa values (a measure for observer agreement, where the two observers are the gold standard and the proposed segmentation method) .
Performance of the proposed method
Performance results on DRIVE database images
Performance results on STARE database images
The processing time of our algorithm is less than 3 s on the DRIVE database for a single retinal image on average, and less than 3.5 s on the STARE database, running on a PC with an Intel Core2Duo CPU at 3.2 GHz and 4GB of RAM. Since this method is experimented on MATLAB, which is an integrated platform, the performance might still be improved.
Comparison with existing methods
Results comparison with existing methods on complete DRIVE database
2nd human observer
Zana et al. 
Jiang et al. 
Mendonca et al. 
Al-Diri et al. 
Lam et al. 
Miri et al. 
Fraz et al. 
You et al. 
Zhao et al. 
Niemeijer et al. 
Soares et al. 
Staal et al. 
Ricci et al. 
Lupascu et al. 
Marin et al. 
Fraz et al. 
Vega et al. 
Results comparison with existing methods on complete STARE database.
2nd human observer
Hoover et al. 
Jiang et al. 
Mendonca et al. 
Lam et al. 
Al-Diri et al. 
Lam et al. 
Fraz et al. 
You et al. 
Zhao et al. 
Staal et al. 
Soares et al. 
Ricci et al. 
Marin et al. 
Fraz et al. 
Vega et al. 
For the proportion of vessels picked in the coarse segmentation, it was observed statistically that an average of 12.7 % of retina pixels in the FOV is vessels . In the coarse segmentation, the proportion is chosen to be smaller than the average proportion because the random noises must be considered. To better compare the effects of this parameter, M and N on the STARE database are set to 584 and 565, respectively. If \(\rho\) is too big, too much noise is enrolled, and if \(\rho\) is too small, too many pixels belong to vessel will be eliminated. \(\rho\) is set to 0.081 for the DRIVE database and 0.083 for the STARE database when best accuracies are achieved,as is shown in Fig. 5b.
In the parameter analysis, only one parameter are changed each time. From Fig. 5, we can see that the performance changes slightly when parameter varies which implies robustness of the proposed method.
We also replaced the elongating filters with the morphological operations to show the superiority of the proposed operation over the traditional approaches. The accuracies are 0.9487 and 0.9548 on the DRIVE and STARE databases after replacing which have significant degradations compared with 0.9529 and 0.9569. The proposed method has better performances because the elongating filters treat the vasculature with various thicknesses adaptively. However, if the morphological operations are involved, all the vasculature are dilated and then eroded simultaneously, thus the spaces among bifurcations and isolated capillaries may be filled together with unnatural vasculature edges.
Discussion and conclusion
The methodology represented in this paper was designed based on the observation that the vasculature can be easily separated if appropriate preprocessing operations exist. In the proposed method, the retinal images were first enhanced by weighted ICGF and MMSDG. After the preprocessing, the vessels were enhanced with the background uniformly distributed. What’s more, the true edges of the vessels were also kept. The enhancement simplifies the subsequent segmentation. The preprocessed images were then coarsely segmented by simple thresholding and fine-tuned by multi-directional elongating filters. Finally, the isolated pixels and speckle-like regions were eliminated. The proposed method were evaluated on the STARE and DRIVE database, the results reported in Tables 5 and 6 illustrate that, the performance of our method is superior to almost all the unsupervised method and most of the supervised method.
As a framework for vasculature segmentation, the generality of the proposed method can be seen in two aspects. First, the functional components can be used in other programs: (1) the retinal images enhanced by fused ICGF and MMSDG can be used as input of other vasculature segmentation methods. Moreover, clarified vessels and normalized backgrounds can also facilitate the performances of other segmentation models. (2) The fine-tuning and post-processing operations can be used in existing methods as additional processing steps. Second, each of the functional components of the framework can be replaced: (1) the raw segmentation operation is a simple threshold binarization, if more powerful segmentation models are involved, the performances of the proposed method may be improved. (2) The post-processing method can also be further improved or replaced by more powerful methods.
Though the proposed method achieves promising results, it still suffers from common problems of retinal vasculature segmentation. We prepared to make improvements in two aspects: Dealing with pathologies and Capillary vessels preserving.
The ICGF operation has the ability to clarify the capillary vessels, but as the vessels fade away, the capillary vessels still tend to be discontinuous. Since the proposed method has been designed to be fast and provide high performances without understanding the image details, local vessel tracking was not involved. In the post-processing operation, the fragmented capillary vessels may also be eliminated. In the future, local tracking will be included to complete the vessel maps and to further improve the performance.
XM developed the proposed method and drafted the manuscript. Implementation and experiment results analysis were done by XM, ZH and XY. YY supervised the project, contributed to discussion and analysis and participated in manuscript revisions. GY participated in manuscript revisions and provided critical review that helped in improving the manuscript. All authors read and approved the final manuscript.
The work is supported by NSFC Joint Fund with Guangdong under Key Project U1201258, the National Science Foundation of China under Grant No. 61573219, the Fundamental Research Funds of Shandong University No.2014JC028 and Shandong Natural Science Funds for Distinguished Young Scholar under Grant No. JQ201316.
The authors declare that they have no competing interests.
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- Kanski JJ. Retinal vascular disease, in clinical ophthalmology. London, UK: Elsevier Health Sciences; 2007.Google Scholar
- Heneghan C, Flynn J, OKeefe M, Cahill M. Characterization of changes in blood vessel width and tortuosity in retinopathy of prematurity using image analysis. Medical Image Anal. 2002;6(4):407–29.View ArticleGoogle Scholar
- Grisan E, Ruggeri A. A divide et impera strategy for automatic classification of retinal vessels into arteries and veins. In: Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2003. vol. 1, p. 890–3.Google Scholar
- Foracchia M, Grisan E, Ruggeri A. Extraction and quantitative description of vessel features in hypertensive retinopathy fundus images. In: 2nd International Workshop on Computer Assisted Fundus Image Analysis: June 2001. 2001.Google Scholar
- Sussman EJ, Tsiaras WG, Soper KA. Diagnosis of diabetic eye disease. Jama. 1982;247(23):3231–4.View ArticleGoogle Scholar
- Zana F, Klein J-C. A multimodal registration algorithm of eye fundus images using vessels detection and hough transform. IEEE Trans Med Imag. 1999;18(5):419–28.View ArticleGoogle Scholar
- Li H, Chutatape O. Automated feature extraction in color retinal images by a model based approach. IEEE Trans Biomed Eng. 2004;51(2):246–54.View ArticleGoogle Scholar
- Niemeijer M, van Ginneken B, Staal J, Suttorp-Schulten MS, Abràmoff MD. Automatic detection of red lesions in digital color fundus photographs. IEEE Trans Med Imag. 2005;24(5):584–92.View ArticleGoogle Scholar
- Mariño C, Penedo MG, Penas M, Carreira MJ, Gonzalez F. Personal authentication using digital retinal images. Pat Anal Appl. 2006;9(1):21–33.View ArticleGoogle Scholar
- Köse C, İki C. A personal identification system using retinal vasculature in retinal fundus images. Exp Syst Appl. 2011;38(11):13670–81.Google Scholar
- Ricci E, Perfetti R. Retinal blood vessel segmentation using line operators and support vector classification. IEEE Trans Med Imag. 2007;26(10):1357–65.View ArticleGoogle Scholar
- Lam BS, Gao Y, Liew A-C. General retinal vessel segmentation using regularization-based multiconcavity modeling. Medical Imaging, IEEE Transactions on. 2010;29(7):1369–81.View ArticleGoogle Scholar
- Al-Diri B, Hunter A, Steel D. An active contour model for segmenting and measuring retinal vessels. IEEE Trans Med Imag. 2009;28(9):1488–97.View ArticleGoogle Scholar
- Meng X, Yin Y, Yang G, Xi X. Retinal identification based on an improved circular gabor filter and scale invariant feature transform. Sensors. 2013;13(7):9248–66.View ArticleGoogle Scholar
- Hoover A, Kouznetsova V, Goldbaum M. Locating blood vessels in retinal images by piecewise threshold probing of a matched filter response. IEEE Trans Med Imag. 2000;19(3):203–10.View ArticleGoogle Scholar
- DRIVE Database. http://www.isi.uu.nl/Research/Databases/DRIVE
- Fraz MM, Remagnino P, Hoppe A, Uyyanonvara B, Rudnicka AR, Owen CG, Barman SA. Blood vessel segmentation methodologies in retinal images-a survey. Comp Methods Programs Biomed. 2012;108(1):407–33.View ArticleGoogle Scholar
- Jiang X, Mojon D. Adaptive local thresholding by verification-based multithreshold probing with application to vessel detection in retinal images. IEEE Trans Pat Anal Mach Intel. 2003;25(1):131–7.View ArticleGoogle Scholar
- Chaudhuri S, Chatterjee S, Katz N, Nelson M, Goldbaum M. Detection of blood vessels in retinal images using two-dimensional matched filters. IEEE Trans Med Imag. 1989;8(3):263–9.View ArticleGoogle Scholar
- Li H, Hsu W, Lee ML, Wang H. A piecewise gaussian model for profiling and differentiating retinal vessels. In: Proceedings. 2003 International Conference On Image Processing, 2003. ICIP 2003, IEEE. 2003. vol. 1, p. 1069.Google Scholar
- Freeman WT, Adelson EH. The design and use of steerable filters. IEEE Trans Pat Anal Mach Intel. 1991;13(9):891–906.View ArticleGoogle Scholar
- Kochner B, Schuhmann D, Michaelis M, Mann G, Englmeier KH. Course tracking and contour extraction of retinal vessels from color fundus photographs: Most efficient use of steerable filters for model-based image analysis. In: International Society for Optics and Photonics Medical Imaging’98. 1998. p. 755–61.Google Scholar
- Gang L, Chutatape O, Krishnan SM. Detection and measurement of retinal vessels in fundus images using amplitude modified second-order gaussian filter. IEEE Trans Biomed Eng. 2002;49(2):168–72.View ArticleGoogle Scholar
- Chutatape O, Zheng L, Krishnan S. Retinal blood vessel detection and tracking by matched gaussian and kalman filters. In: Proceedings of the 20th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1998. vol. 6, p. 3144–9.Google Scholar
- Quek FK, Kirbas C. Vessel extraction in medical images by wave-propagation and traceback. IEEE Trans Med Imag. 2001;20(2):117–31.View ArticleGoogle Scholar
- Miri MS, Mahloojifar A. Retinal image analysis using curvelet transform and multistructure elements morphology by reconstruction. IEEE Trans Biomed Eng. 2011;58(5):1183–92.View ArticleGoogle Scholar
- Zana F, Klein J-C. Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation. IEEE Trans Image Process. 2001;10(7):1010–9.MATHView ArticleGoogle Scholar
- Fraz MM, Barman S, Remagnino P, Hoppe A, Basit A, Uyyanonvara B, Rudnicka AR, Owen CG. An approach to localize the retinal blood vessels using bit planes and centerline detection. Comp Methods Programs Biomed. 2012;108(2):600–16.View ArticleGoogle Scholar
- Mendonca AM, Campilho A. Segmentation of retinal blood vessels by combining the detection of centerlines and morphological reconstruction. IEEE Trans Med Imag. 2006;25(9):1200–13.View ArticleGoogle Scholar
- Lam BS, Yan H. A novel vessel segmentation algorithm for pathological retina images based on the divergence of vector fields. IEEE Trans Med Imag. 2008;27(2):237–46.View ArticleGoogle Scholar
- Sum K, Cheung PY. Vessel extraction under non-uniform illumination: a level set approach. IEEE Trans Biomed Eng. 2008;55(1):358–60.View ArticleGoogle Scholar
- Zhao YQ, Wang XH, Wang XF, Shih FY. Retinal vessels segmentation based on level set and region growing. Pat Recogn. 2014;47(7):2437–46.View ArticleGoogle Scholar
- Staal J, Abràmoff MD, Niemeijer M, Viergever MA, van Ginneken B. Ridge-based vessel segmentation in color images of the retina. IEEE Trans Med Imag. 2004;23(4):501–9.View ArticleGoogle Scholar
- Niemeijer M, Staal J, van Ginneken B, Loog M, Abramoff MD. Comparative study of retinal vessel segmentation methods on a new publicly available database. In: International Society for Optics and Photonics Medical Imaging 2004. p. 648–56.Google Scholar
- Soares JV, Leandro JJ, Cesar RM, Jelinek HF, Cree MJ. Retinal vessel segmentation using the 2-d gabor wavelet and supervised classification. IEEE Trans Med Imag. 2006;25(9):1214–22.View ArticleGoogle Scholar
- Lupascu CA, Tegolo D, Trucco E. Fabc: retinal vessel segmentation using adaboost. IEEE Trans Inform Technol Biomed. 2010;14(5):1267–74.View ArticleGoogle Scholar
- Marín D, Aquino A, Gegúndez-Arias ME, Bravo JM. A new supervised method for blood vessel segmentation in retinal images by using gray-level and moment invariants-based features. IEEE Trans Med Imag. 2011;30(1):146–58.View ArticleGoogle Scholar
- Vega R, Sanchez-Ante G, Falcon-Morales LE, Sossa H, Guevara E. Retinal vessel extraction using lattice neural networks with dendritic processing. Comp Biol Med. 2015;58:20–30.View ArticleGoogle Scholar
- You X, Peng Q, Yuan Y, Cheung Y-M, Lei J. Segmentation of retinal blood vessels using the radial projection and semi-supervised approach. Pat Recogn. 2011;44(10):2314–24.View ArticleGoogle Scholar
- Fraz MM, Remagnino P, Hoppe A, Uyyanonvara B, Rudnicka AR, Owen CG, Barman SA. Ensemble classification system applied for retinal vessel segmentation on child images containing various vessel profiles. In: Image Analysis and Recognition, Springer. 2012. p. 380–9.Google Scholar
- Fraz MM, Remagnino P, Hoppe A, Uyyanonvara B, Rudnicka AR, Owen CG, Barman SA. An ensemble classification-based approach applied to retinal blood vessel segmentation. IEEE Trans Biomed Eng. 2012;59(9):2538–48.View ArticleGoogle Scholar
- Zhang J, Tan T, Ma L. Invariant texture segmentation via circular gabor filters. In: Proceedings 16th international conference on pattern recognition, 2002. vol. 2, p. 901–4.Google Scholar
- Chang T, Kuo C-C. Texture analysis and classification with tree-structured wavelet transform. IEEE Trans Image Process. 1993;2(4):429–41.View ArticleGoogle Scholar
- Lindeberg T. Scale-space theory in computer vision. Springer. 1993.Google Scholar
- T.M.W inc.: MathWorks. Image Processing Toolbox Use Guide. The Math Works Inc. 1997.Google Scholar