An improved blood vessel segmentation algorithm on the basis of traditional Frangi filtering and the mathematical morphological method was proposed to solve the low accuracy of automatic blood vessel segmentation of fundus retinal images and high complexity of algorithms. First, a global enhanced image was generated by using the contrast-limited adaptive histogram equalization algorithm of the retinal image. An improved Frangi Hessian model was constructed by introducing the scale equivalence factor and eigenvector direction angle of the Hessian matrix into the traditional Frangi filtering algorithm to enhance blood vessels of the global enhanced image. Next, noise interferences surrounding small blood vessels were eliminated through the improved mathematical morphological method. Then, blood vessels were segmented using the Otsu threshold method. The improved algorithm was tested by the public DRIVE and STARE data sets. According to the test results, the average segmentation accuracy, sensitivity, and specificity of retinal images in DRIVE and STARE are 95.54%, 69.42%, and 98.02% and 94.92%, 70.19%, and 97.71%, respectively. The improved algorithm achieved high average segmentation accuracy and low complexity while promising segmentation sensitivity. This improved algorithm can segment retinal vessels more accurately than other algorithms.
Blood vessel segmentation of fundus retinal images can help doctors in diagnosing multiple eye diseases. Segmenting blood vessels integrally and accurately is necessary for accurate analysis of main blood vessels and branches [
Gray distribution of fundus retinal images is uneven due to influences of noises, artifacts, and illuminations, accompanied by low contrast between blood vessels and background. Moreover, arteries and veins in images cross over and superpose mutually, thereby resulting in difficulties of segmentation. The existing blood vessel segmentation methods of fundus retinal images include supervised and unsupervised learning. The former requires training according to the provided standard training set and uses the trained classifier to segment blood vessels in unknown images. The latter requires no training but segments blood vessels through thresholding the filtering response or depending on methods on the basis of certain rules.
Without artificial prior marking information, the retinal vessel segmentation method on the basis of unsupervised learning has a small workload and high working efficiency. Currently, unsupervised segmentation methods include methods on the basis of windows [
Chaudhuri et al. [
Frangi et al. [
Rodrigues and Marengoni [
In this study, a vessel segmentation method of fundus retinal images on the basis of the improved Frangi and mathematical morphology was proposed by combining vessel tracking and morphological operation. First, the fundus retinal image was preprocessed by global enhancement. Second, blood vessels were enhanced by the improved Frangi filtering method. Third, noise interferences surrounding the fine blood vessels were eliminated by the improved mathematical morphological method. Last, vessel segmentation of the retinal image was performed through the Otsu threshold segmentation method.
Fundus retinal images are in RGB format, which generally have to be transformed to single-channel images for the convenience of computer processing. Images in R, G, and B channels were compared (Figure
Images of R, G, and B channels: (a) R channel; (b) G channel; (c) B channel.
Enhancement of fundus retinal images can distinguish blood vessels from other background regions. Histogram equalization processing can enhance the contrast of each object in a specific image, in which the scope of image intensity will be extended. As fundus retinal images have low contrast and the vascular region is dark with low contrast, the global histogram equalization method fails to achieve the ideal enhancement of blood vessels (Figure
Contrast enhancement images: (a) Enhancement by histogram equalization; (b) enhancement by CLAHE.
Adaptive histogram equalization (AHE) implements histogram enhancement on each pixel by calculating the transformation function of each pixel neighbor domain. AHE is more appropriate to the local contrast of images and enhanced image edges to gain additional details. For retinal vascular images, AHE may amplify noises surrounding fine blood vessels in images while enhancing the contrast. Therefore, using contrast-limited adaptive histogram equalization (CLAHE) algorithm is essential to enhance retinal vessels because it can inhibit noise enhancement. Moreover, the CLAHE algorithm has a simple calculation and determines only one parameter of the amplitude limit. Figure
The enhancement results of Figure
Blood vessels present a linear tubular structure in fundus retinal images, and the diameter range falls within a limit. From Gaussian function and original image convolution, most structures that are smaller than scale
The original Hessian matrix of a two-dimensional image
where
Therefore, the Hessian matrix of the point
In a two-dimensional image, the Hessian matrix is a two-dimensional positive definite matrix that has two eigenvalues and corresponding eigenvectors. When blood vessels are low-dark tubular structures relative to the background, the Hessian matrix of the pixels at blood vessels has high positive eigenvalue
In retinal images, eigenvalues of the Hessian matrix represent curvature intensity of blood vessels, whereas eigenvectors represent the curvature direction of blood vessels. As
The output result under multiscale is
Figure
Multiscale vessel enhanced images: (a) Frangi filter enhancement; (b) improved Frangi filter enhancement.
After the fundus retinal image is enhanced by the improved Frangi filter, small branches of blood vessels are enhanced. At the same time, the noises in the background are increased. Therefore, the primary goal is to eliminate noise interferences in the background region of the image while retaining fine blood vessels as much as possible before image segmentation.
Basic operations of mathematical morphology include dilation and erosion, which are defined, respectively, as
Open operation in morphology refers to the erosion operation of the image by using the structural element
The structural element in mathematical morphology is very important to image processing. The linear structure was chosen as the structural element considering that blood vessels in fundus retinal images have tubular structures. This structural element has two parameters, namely, length and angle. Traditional mathematical morphology can only use the same linear structural elements (length and angle in the structural element are fixed) to process the entire image. Blood vessels in the fundus retinal image are in network distribution and have different diameters and directions. Therefore, traditional mathematical morphological processing fails to achieve the ideal effect (Figure
Mathematical morphology processing: (a) traditional mathematical morphology; (b) subregion magnification of (a); (c) improved mathematical morphology; (d) subregion magnification of (c).
First, the lengths of linear structural element increase from the minimum diameter (2 pixels) of blood vessels to the maximum diameter (12 pixels) for every 1 pixel. Second, the angles of the linear structural element are determined every 10° from 0° to 170° given that the direction of blood vessel sections ranges between 0° and 360° and is symmetric. In this way, open operation results of 198 templates could be gained. If the gray value of the open operation results of
Figures
Otsu algorithm is a high-efficiency and simple algorithm for image binarization. According to gray characteristics of images, the Otsu algorithm divides an image into background and foreground. Then, gray histograms of the background and foreground pixels were calculated, and their variances were compared to find the optimal threshold. This threshold refers to the threshold at the maximum variance and is used to distinguish background and foreground pixels.
For an image,
The overall average gray level of the image is
The variances of foreground and background pixels are
When the variance
In this study, the proposed algorithm was tested on the test set of public fundus retinal images by the DRIVE and STARE data sets. Qualitative and quantitative contrast analyses among segmentation results of the proposed method and manual segmentation of two experts and traditional Frangi filter processing were carried out. For comparative assessment, segmentation effects of the proposed method were compared with those of new algorithms. The traditional Frangi filtering process is also performed after the CLAHE-enhanced image, and then, improved mathematical morphology operations and Otsu algorithm are used for segmentation.
The manual segmentation results of the two experts are the most important indicators to assess the segmentation effect of fundus retinal images. Figure
The comparison of blood vessel segmentation effect of fundus retinal image. (a) Original color fundus retinal images; (b) results of manual segmentation by the first expert; (c) results of manual segmentation by the second expert; (d) results processed by traditional Frangi filter; (e) results processed by the proposed method.
The results of manual segmentation by experts, traditional Frangi filtering segmentation, and the proposed method segmentation of three fundus retinal images which were chosen randomly from the DRIVE data set are shown in Figure
1D cross sections of the middle row of marked subarea in the first image in Figure
Figure
Detailed comparison of segmentation results. (a) Segmentation results of the proposed method; (b)~(d) are the enlarged maps of the marked detail area of the results of expert manual segmentation, traditional Frangi filter processing, and the proposed method segmentation, respectively.
For the objective evaluation of the segmentation effect of blood vessels, accuracy (Acc), sensitivity (Se), and specificity (Sp) are generally applied in quantitative assessment. Acc refers to the proportion of accurately classified pixels in total pixels of fundus retinal image. Se and Sp refer to the proportion of vascular and nonvascular pixels that are recognized accurately in the segmentation result, respectively. Table
The calculation formulas of blood vessel segmentation evaluation indicators in fundus retinal image.
Evaluation indicators | Calculation formulas |
---|---|
Accuracy (Acc) | |
Sensitivity (Se) | |
Specificity (Sp) |
In Table
Figure
Comparisons of evaluation indicators between traditional Frangi filter and the proposed method.
For a better assessment, the proposed method was compared with other relatively new algorithms in terms of accuracy, sensitivity, and specificity. Performance comparison of the proposed method with some of the existing methods on both the DRIVE and STARE data sets was also conducted, as shown in Tables
Performance comparison of blood vessel segmentation methods with the DRIVE data set.
Methods | Evaluation indicators | ||
---|---|---|---|
Acc | Se | Sp | |
Chaudhuri et al. [ | 0.8773 | 0.3357 | 0.9794 |
Li et al. [ | 0.9343 | 0.7154 | 0.9716 |
Barkana et al. [ | 0.9502 | 0.7224 | 0.9840 |
Hassanien et al. [ | 0.9388 | 0.7210 | 0.9710 |
Rezaee et al. [ | 0.9463 | 0.7189 | 0.9793 |
Zhao et al. [ | 0.9477 | 0.7354 | 0.9789 |
Fu et al. [ | 0.9470 | 0.7294 | — |
Guo et al. [ | 0.9613 | 0.9859 | 0.7046 |
Budak et al. [ | 0.9685 | 0.7439 | 0.9900 |
Guo et al. [ | 0.9075 | 0.8990 | 0.9283 |
The proposed method | 0.9554 | 0.6942 | 0.9802 |
Performance comparison of blood vessel segmentation methods with the STARE data set.
Methods | Evaluation indicators | ||
---|---|---|---|
Acc | Se | Sp | |
Li et al. [ | 0.9407 | 0.7192 | 0.9692 |
Barkana et al. [ | 0.9553 | 0.7014 | 0.9846 |
Hassanien et al. [ | 0.9468 | 0.6490 | 0.9820 |
Rezaee et al. [ | 0.9521 | 0.7202 | 0.9741 |
Zhao et al. [ | 0.9509 | 0.7187 | 0.9767 |
Fu et al. [ | 0.9545 | 0.7140 | — |
Guo et al. [ | 0.9539 | 0.9861 | 0.5628 |
Budak et al. [ | 0.9735 | 0.8196 | 0.9871 |
The proposed method | 0.9492 | 0.7019 | 0.9771 |
From the performance comparison of the methods in Tables
Fu et al. [
Vessel segmentation of fine blood vessels for fundus retinal images is difficult. Compared with other classical methods, the proposed method achieves higher accuracy because it can segment fine blood vessels well while protecting the integrity of the trunk after segmentation. Using the improved Frangi Hessian model in enhancing blood vessels not only extracts vascular feature maps under multiscale but also enhances fine branches of blood vessels effectively. In addition, the proposed method eliminates noise interferences surrounding fine blood vessels through the improved mathematical morphological operation. Hence, the proposed method highlights fine blood vessels, thus enabling accurate segmentation.
A blood vessel segmentation algorithm of fundus retinal images on the basis of the improved Frangi and mathematical morphology is proposed in this study. The proposed method uses the improved Frangi Hessian model to enhance blood vessels, thereby achieving the extraction of blood vessel feature maps under multiscale conditions and enhancing small blood vessels. Moreover, an improved mathematical morphological operation is used to eliminate noise interferences surrounding the fine blood vessels, considering the diameter and direction of blood vessels. Hence, fine blood vessels can be recognized as blood vessel pixels accurately in the final Otsu segmentation. The proposed method is tested by the public DRIVE and STARE data sets. According to the test results, the average segmentation accuracy, sensitivity, and specificity of retinal images in DRIVE and STARE are 95.54%, 69.42%, and 98.02% and 94.92%, 70.19%, and 97.71%, respectively. Moreover, the proposed method can maintain relatively high segmentation accuracy under the premise of ensuring segmentation sensitivity and shows good overall performances. However, the optic disk may interfere, thus influencing the segmentation effect. Hence, future studies may focus on eliminating such influences on the segmentation effect.
In this study, the proposed algorithm was tested on the test set of public fundus retinal images by the DRIVE database.
The authors declare that they have no conflicts of interest.
This work was financially supported by the Project of Science and Technology of Shaanxi (No. 2020GY-029).