A Novel Hybrid Retinal Blood Vessel Segmentation Algorithm for Enlarging the Measuring Range of Dual-Wavelength Retinal Oximetry

Abstract

The non-invasive measurement of hemoglobin oxygen saturation (SO₂) in retinal vessels is based on spectrophotometry and the absorption spectral characteristics of the tissue. The dual-wavelength retinal images are simultaneously captured via retinal oximetry. SO₂ is calculated by processing a series of images and by calculating the optic density ratio of two images. However, existing SO₂ research is focused on the thick vessels in the high-clarity region of retinal images. However, the thin vessels in the low-clarity region could provide significant information for the detection and diagnosis of neovascular diseases. To this end, we proposed a novel hybrid vessel segmentation algorithm. Firstly, a median filter was employed for image denoising. Secondly, high- and low-clarity region segmentation was carried out based on a clarity histogram. The vessels in the high-clarity areas were segmented after implementing a Gaussian filter, a matched filter, and morphological segmentation. Additionally, the vessels in the low-clarity areas were segmented using a guided filter, matched filtering, and dynamic threshold segmentation. Finally, the results were obtained through image merger and morphological operations. The experimental results and analysis show that the proposed method can effectively segment thick and thin vessels and can extend the measuring range of dual-wavelength retinal oximetry.

1. Introduction

The SO₂ in retinal vessels plays an important role in the study of microcirculation and metabolism in the eye [1]. Functional information on retinal oxygen saturation can be obtained using retinal image processing and analysis, which can be employed to diagnose retinopathies and to increase the efficiency and reliability of diagnoses. Retinal vessel oxygen saturation has been widely studied in various ocular diseases, such as retinitis pigmentosa [2], glaucoma [3], diabetic retinopathy [4], age-related macular degeneration [5], retinopathy of prematurity [6], and retinal vein occlusion [7].

The measurement of SO₂ in retinal vessels dates back to 1959 [8], and different techniques have been developed by several research groups since then (for a review, see [9,10,11,12,13,14,15,16,17]). Among the numerous retinal SO₂ measurement techniques, dual-wavelength retinal oximetry based on a fundus camera has been proven to be the most effective [18]. It is based on the Beer–Lambert law, that is, there are different optical properties for oxygenated hemoglobin (HbO₂) and hemoglobin (Hb) at various wavelengths. Retinal oximetry simultaneously acquires images at two different wavelengths: one sensitive to changes in the percentage of HbO₂ present in the blood and an isosbestic wavelength for HbO₂ and Hb. The retinal SO₂ values are finally measured after processing a series of images and calculating the optic density ratio of two images. Figure 1 shows two fundus images acquired simultaneously at 570 nm and 600 nm. The optical absorption of HbO₂ and Hb is similar at 570 nm, while it is quite different at 600 nm. The 600 nm image, which is sensitive to HbO₂ changes, shows lower contrast between the blood vessels and the background than the 570 nm image. The corresponding pseudo-colored fundus SO₂ map is displayed in Figure 2.

In recent decades, researchers have made great efforts in the area of dual-wavelength retinal oximetry to improve its repeatability [18,19,20,21], sensitivity [22], calibration [23,24,25,26,27,28], etc. These studies are helpful for the clinical application and promotion of retinal oximetry. For instance, in 2022, Gerhard et al. analyzed the difference in retinal SO₂ between patients with primary open-angle glaucoma (POAG) and healthy control subjects and concluded that POAG could reduce the total retinal SO₂ [29]. In the same year, Heitmar et al. studied the effect of endothelial microparticles on retinal SO₂ in diabetes and cardiovascular disease [30]. In 2023, Chen et al. researched the idiopathic epiretinal membrane based on the retinal SO₂ and vascular morphological characteristics [31].

It is well known that the measurement of SO₂ is based on processing a series of images. To enhance the image quality and improve the accuracy of SO₂, we proposed a VST + DDID algorithm to denoise the dual-wavelength retinal images and demonstrated that this provides much more accurate gray values for retinal oximetry [32]. Additionally, we proposed an image registration method based on camera calibration, which can greatly increase the calculation speed for retinal vessel SO₂ while ensuring accuracy [33]. Vessel segmentation is a significant step in the SO₂ calculation of retinal vessels. Although many retinal vessel segmentation algorithms have been proposed in the literature [34,35,36,37,38,39,40,41,42], they cannot be directly applied to spectrophotometric retinal vessel segmentation and need to be improved according to the features of the images. For example, in order to extract arteries and veins in dual-wavelength retinal images, Harihar et al. proposed an automatic identification algorithm based on the relative strength of the vessel central reflex [43]. Karlsson et al. used deep learning methods to segment arteries and veins in retinal images acquired by retinal oximetry [44]. Dou et al. also used deep learning methods to locate the optic disc and segment vessels in the retinal images; using these, they could obtain the SO₂ values and structural information of vessels, such as the diameter and length [45]. The existing SO₂ studies are focused on the thick arteries and veins of retinal images, including our previous studies. We can also observe that there are thin vessels which have not been segmented to measure SO₂ and are highlighted by white circles in Figure 2. It is a challenge for researchers to segment thin vasculatures, and there are still several limiting factors for achieving optimal performance [46]. These thin vasculatures have significant clinical information and could help doctors to detect neovascular diseases [47]. For instance, the smaller the retinal arteriolar-to-venular ratio (AVR) is, the more white matter lesions there are. Researchers have found that there is a strong correlation between vascular connectivity and eye diseases [48]. Hence, it is vital to achieve better vessel segmentation for the detection and treatment of eye diseases.

The existing retinal image segmentation techniques can be divided into supervised and unsupervised methods (for reviews, see [49,50,51,52,53,54,55,56]). Among the supervised methods, machine learning and deep learning algorithms have obtained enormous popularity. The ground truth for image segmentation in test sets relies on such supervised methods. In recent years, deep learning algorithms have been commonly applied to medical image segmentation. For instance, Li et al. proposed GDF-Net to achieve accurate retinal vessel segmentation [57]. To reduce the complexity, Iqbal et al. have improved Google Net to reduce feature overlaps [58]. Yang et al. proposed the attention-aware multi-scale fusion network (AMF-Net) to effectively track thin vessels [59]. Meanwhile, Du et al. proposed a modified U-Net segmentation approach based on the pyramid pooling method and attention mechanism [60]. Sathananthavathi et al. suggested an encoder-enhanced atrous architecture to improve the model’s ability to segment retinal blood vessels [61]. Apparently, the deep learning method has produced satisfactory results for the retinal vessel segmentation problem.

In contrast, training datasets are not required for unsupervised methods during the image segmentation process. The whole strategy is based on image processing, and the appropriate method is selected for segmentation according to the characteristics of the image [62,63,64,65,66,67]. Generally, unsupervised methods complete the task of retinal vessel segmentation without prior knowledge of the training set. Furthermore, this approach is less computationally intensive and obtains segmentation results in less time; this approach has been introduced in medical image processing and has achieved good performances. Khan et al. proposed a hybrid vessel segmentation algorithm based on a directional filter bank (DFB) and triple stick filter for thin vessels and a block-matching 3D (BM3D) filter and alpha-rooting for thick vessels [68]. In order to reduce the effect of uneven illumination of fundus images on vessel segmentation, Yan et al. proposed multi-scale retinex (MSR) and multi-scale Gaussian-matched filtering to enhance the retinal images and then adopted an OTSU algorithm for vessel segmentation [69]. Mahapatra et al. introduced a modified enhanced leader particle swarm optimization (MELPSO) algorithm to improve retinal image quality and used the adaptive weighted spatial fuzzy c-means (AWSFCM) clustering method to segment vessels [70]. Then, Mahtab et al. proposed a retinal vessel segmentation method based on a matched filter and Hessian matrix. The experimental results showed that it was comparable to the state-of-the-art algorithms [71].

Theoretically speaking, the aforementioned vessel segmentation algorithms based on supervised or unsupervised methods can be used for the dual-wavelength retinal image segmentation. However, they have several limiting factors for our retinal oximetry. Firstly, in the supervised methods, the prior knowledge of vessel segmentation is obtained directly from the manual segmentation by ophthalmologists. The extracted feature vector is used to train a classifier for the automatic classification of vascular and non-vascular pixels. However, the ground truth by ophthalmologists is difficult to acquire for dual-wavelength retinal oximetry. Furthermore, the training is time-consuming and computationally expensive to satisfactorily complete the task with a new set of images [72]. This cannot meet the demand for high efficiency in SO₂ measurements. Secondly, unsupervised methods usually use the feature of blood vessels to determine whether the pixel is a blood vessel and can directly segment vessels without prior knowledge. Compared to the supervised methods, they are computationally cheap and can obtain results in a short time. However, it is challenging when the vessel’ diameter is small. In fact, thin vessels can also provide doctors with useful information in the detection of neovascular diseases [46]. This is still a challenge for researchers and is worth further study. Hence, retinal vessel segmentation methods which have been previously proposed cannot solve the aforementioned problem.

In this study, we proposed a novel vessel segmentation algorithm for dual-wavelength retinal images. Firstly, a median filter is employed to eliminate isolated points. Secondly, the high- and low-clarity region segmentation is achieved based on feature histograms. The vessels in the high-clarity areas are segmented using Gaussian filter, matched filter, and morphological segmentation. Additionally, the vessels in the low-clarity areas are segmented by a guided filter, matched filtering, and dynamic threshold segmentation. Finally, the results are obtained by image fusion and morphological operations. The experimental results and related comparative analysis show that the proposed algorithm could produce a more precise segmentation of vessels, especially in the low-clarity region. The following SO₂ analysis indicated that the proposed method could measure the SO₂ of thin vessels which can provide more valuable information for doctors in the detection and treatment of eye diseases.

The rest of the paper is organized as follows. Section 2 describes dual-wavelength retinal oximetry. Section 3 introduces the proposed vessel segmentation algorithm. Section 4 presents the vessel segmentation results and algorithm evaluation from two aspects, including a comparison of segmentation algorithms and the effect on the calculation of SO₂. Finally, Section 5 and Section 6 present the discussion and conclusions, respectively.

2. Dual-Wavelength Retinal Oximetry

Dual-wavelength retinal oximetry systems consist of two parts. One is the retinal image acquisition system and the other is the retinal SO₂ calculation software system. The former includes a commercial fundus camera, lenses (L1 and L2/L3), a beam splitter, two interference filters, and CCD cameras. The retinal image output from the fundus camera is collimated by a lens (L1) and divided into two light paths by a spectroscopic prism. Finally, the images are simultaneously reimaged on each CCD camera at the wavelengths of 570 nm and 600 nm by interference filters and objective lenses (L2 and L3), respectively. The light path of the dual-wavelength retinal image acquisition system is shown in Figure 3a. The images collected by the CCDs are sent to a computer and are post-processed by the SO₂ calculation software system. The SO₂ values in the retinal vessels are finally measured after processing a series of images and calculating the optic density ratio of two images. Figure 3b is a diagram of dual-wavelength retinal oximetry.

Because the calculation of SO₂ is based on retinal image processing, the vessel segmentation result may dramatically affect the measurement range of SO₂, especially the thin vessels in the low-clarity region which can provide doctors with valuable information for the detection of neovascular diseases. Hence, a novel hybrid segmentation algorithm was developed for dual-wavelength retinal images.

3. The Proposed Retinal Vessel Segmentation Algorithm

This section briefly details the proposed efficient blood vessel segmentation algorithm; the algorithm block diagram is shown in Figure 4. The algorithm makes full use of the characteristics of the dual-wavelength retinal images, such as uneven brightness and a great difference in clarity for different regions. It includes three steps: image pre-processing, main segmentation processing, and post-processing. In image pre-processing, classical median filtering is used to denoise the isolated noise in the image. Then, the high- and low-clarity regions are segmented based on a clarity histogram. In the main segmentation processing, the vessels in the high-clarity areas are segmented by a Gaussian filter, matched filter, and morphological segmentation. Additionally, the vessels in the low-clarity areas are segmented by a guided filter, matched filtering, and dynamic threshold segmentation. In post-processing, to realize the effective extraction of retinal blood vessels, the results are achieved by image merger and morphological operations.

3.1. Image Pre-Processing

Before blood vessel segmentation for the different regions, the algorithm must first filter the isolated noise in the image to reduce its influence on the clarity calculation. Then, the image is traversed in blocks to calculate the clarity values, block by block. Finally, feature histogram analysis is carried out on the clarity results to determine the segmentation threshold, which is then used to realize the segmentation of high-definition regions and low-definition regions.

3.1.1. Median Filter

Due to the particularity of the human eye, it is inevitable for optical imaging to have local bright spots which are similar to salt and pepper noise. Meanwhile, the retinal image has high brightness around the optic disc and a relatively dark background away from the optic disc. The local bright points, which can cause fluctuations in the local gray value of the image, should be effectively eliminated. Image denoising is helpful for the stability of the subsequent calculation of clarity values.

According to the characteristics of noise, this study adopted a common non-linear median filter, which replaces the pixels to be processed by the median of each pixel value in the neighborhood of the pixels to be processed, eliminating the isolated noise in the original image [73]. In this algorithm, the median filter was realized by a two-dimensional square matrix sliding template parameter.

3.1.2. High- and Low-Clarity Region Extraction

Region extraction is divided into three steps: mask extraction of the fundus image, clarity value calculation, and region segmentation based on a clarity histogram.

• Mask extraction of the fundus image

Because the fundus target only occupies a part of the image sensor area, the pixels in the non-target area are mostly dark currents, thermal noise, etc., whose gray value is small. In order to effectively extract the fundus object from the dark background, the whole image should be binarized, and the threshold is set to 20; the corresponding result is shown in Figure 4. Because of the presence of blood vessels, the binary image will have serrated edges and even holes. Considering that the gray values of some blood vessels are similar to the background, the binarization results need to be eroded, dilated, and filled to ensure the validity of the mask image.

2.

Clarity value calculation based on block

Theoretically speaking, the gray-scale values of pixels outside the mask are zero. However, because the image sensor has dark currents and thermal noise, there will be a relatively small gray-scale value when the image is acquired. Therefore, to avoid errors in clarity calculations, the gray-scale values of pixels outside the mask are set to 0 before calculating the clarity. Then, the clarity value is calculated block by block, using a block size of 32 × 32. The clarity value is represented by the variance of the image block. The clarity value is calculated for each image block. The clarity $C_{ff}$ is represented as:

$$C_{ff}=\frac{1}{MN}{{\displaystyle \sum _{x=0}^{M-1}{\displaystyle \sum _{y=0}^{N-1}[\mathrm{f}(\mathrm{x},\mathrm{y})-\overline{f}]}}}^2$$

(1)

where $\mathrm{f}(\mathrm{x},\mathrm{y})$ is the image block, and M and N are both set as 32. $\overline{f}$ is the mean of $\mathrm{f}(\mathrm{x},\mathrm{y})$.

3.

Region segmentation based on clarity histogram

The clarity value is rounded and the feature histogram is obtained based on statistics. Through a histogram analysis, it mainly includes the background area, no blood vessel area, blood vessels with fuzzy background area, and blood vessels with clear background area. Taking the inflexion on the left side of the main peak of the histogram as the baseline and taking the near point on the right side as the threshold, a blood vessel with a clear background area can be effectively segmented from the other regions. The high-clarity region segmentation is colored green and the low-clarity region segmentation is colored yellow as shown in Figure 4.

3.2. Vessel Segmentation in the High-Clarity Region

This section consists of three steps: Gaussian filtering, matched filtering, and morphological segmentation.

3.2.1. Gaussian Filtering

The high-clarity regions have high contrast and a matched filter can be used to segment vessels. It is well known that vessels have directionality, and the gray value distribution of cross-sections of the blood vessel is approximately Gaussian distribution. There exists white noise in the vessel and its surrounding background; this should be denoised by a Gaussian filter, which is helpful for subsequent matching filtering. A two-dimensional Gaussian kernel is represented as [74]:

$$g(\mathrm{x},\mathrm{y})=\frac{1}{2\pi {\sigma }^2}\exp (\frac{x^2+y^2}{2{\sigma }^2})$$

(2)

where ${\sigma }^2$ is the variance of the Gaussian filter. The weights in the matrix of the Gaussian filter g(x, y) are normalized and are constrained in a range of 0 to 1, and the sum of the weights is equal to 1. G(x, y) is determined as:

$$G(\mathrm{x},\mathrm{y})=\mathrm{g}(\mathrm{x},\mathrm{y})*{\mathrm{I}}_{Hc}(\mathrm{x},\mathrm{y})$$

(3)

where ${\mathrm{I}}_{Hc}(\mathrm{x},\mathrm{y})$ is the image in the high-clarity region, and $G(\mathrm{x},\mathrm{y})$ is a Gaussian filtering representation of ${\mathrm{I}}_{Hc}(\mathrm{x},\mathrm{y})$. In this algorithm, according to the diameter distribution of a blood vessel, the matrix size of $g(\mathrm{x},\mathrm{y})$ is set as 7 × 7, and $\sigma$ is set as 1.5.

3.2.2. Matched Filter

The gray distribution of a cross-section of a blood vessel is a normal distribution [75]. In accordance with the matched filtering theory, a Gaussian filter whose transfer function is consistent with the distribution of blood vessels is selected to obtain the output of maximum signal-to-noise ratio (SNR) and to realize enhancement of blood vessels. It is necessary to design a matched filter and make the structure of the filter match the blood vessel. Hence, we need to focus on the scale and direction of the filter.

The matched filter kernel is defined as follows [75]:

$$\mathrm{K}(x,y)=-\exp (\frac{-x^2}{2{\sigma }^2})\begin{array}{cc}& \left|y\right|\le \frac{L}{2}\end{array}$$

(4)

where $L$ is the length of the segment for which the vessel is assumed to have a fixed direction. Here, the direction of the vessel is supposed to be aligned along the y-axis. A detailed introduction to matched filter was described in [75].

The width of vessels corresponds to scale $\sigma$ of the Gauss function. In order to achieve a better matching effect and enhance the large and small vessels in the high-clarity region, four filters with different scale $\sigma$ values (6, 12, 18, and 24) are selected as the matched filters.

The direction of the matched filter must be perpendicular to the direction of the blood vessels, and the direction of blood vessels in the fundus is a random stretch. Therefore, a filter with 36 different directions is constructed in the algorithm, and each pixel is filtered in the 36 directions, and the one with the largest response is selected as the final response output. Finally, because blood vessels are linear, they can be approximated as segmented linear targets, that is, the direction of the segmented blood vessels is the same within a certain range of length. According to the vascular target analysis, $L$ is set as 9. This can not only guarantee the validity of piecewise linearity but also improve the efficiency.

3.2.3. Morphological Segmentation

Using the gray-scale image after matched filtering, the morphological synthesis operation is carried out. The corresponding equation can be seen in Equation (5). Let I denote a gray-scale 2D image and S the structuring element. To enhance the high-clarity region, the image is processed by a top-hat and bottom-hat transformation, which is marked as ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, respectively. The final segmentation result $\mathrm{T}$ can be represented as shown in Equation (5).

$$\begin{array}{l}{\mathrm{T}}_1=\mathrm{Tophat}\left(\mathrm{I}\right)=\mathrm{I}-(\mathrm{I}\circ \mathrm{S})\\ {\mathrm{T}}_2=\mathrm{Bothat}\left(\mathrm{I}\right)=(\mathrm{I}•\mathrm{S})-\mathrm{I}\\ {\mathrm{T}=\mathrm{I}+\mathrm{T}}_1{-\mathrm{T}}_2\end{array}$$

(5)

where $(\circ )$ denotes the opening operator and $(•)$ denotes the closing operator. Meanwhile, to enhance the vascular target effectively, the vessels in the high-clarity region should be obtained by direct binarization. The segmentation result for the high-clarity region is shown in Figure 5b.

3.3. Vessel Segmentation in the Low-Clarity Region

The low-clarity region has low contrast. If a Gaussian filter is employed to denoise the low-clarity regions, the vessels would be blurred. It is necessary to use an edge-preserving filter to keep information of the blood vessel while eliminating the noise. Therefore, guided filtering is first used to enhance the vessels in the low-clarity regions. Then, a matching filter is employed to extract the blood vessel, similar to the processing method in the high-definition region. Finally, dynamic threshold segmentation is employed to extract blood vessels.

3.3.1. Guided Filtering

It is necessary to keep the information of the blood vessels while eliminating the noise, so the algorithm adopts guided filtering for the low-clarity region. The guided filtering is mathematically represented as [76]:

$$\left\{\begin{array}{c}a=\left(f_{mean}\left(\mathrm{I}*\mathrm{p}\right)-f_{mean}\left(\mathrm{I}\right)\ast f_{mean}\left(\mathrm{p}\right)\right)/\left(f_{mean}\left(\mathrm{I}*\mathrm{I}\right)-f_{mean}\left(\mathrm{I}\right)\ast f_{mean}\left(\mathrm{I}\right)+\epsilon \right)\\ b=f_{mean}\left(\mathrm{p}\right)-a\ast f_{mean}\left(\mathrm{I}\right)\\ q=f_{mean}\left(a\right)\ast I+f_{mean}\left(b\right)\end{array}\right.$$

(6)

where $\mathrm{p}$ is the input image and $f_{mean}$ is the mean filter. The guided filter is a local linear model between the guided image $\mathrm{I}$ and the output image $q$. In the local region of the image, parameters $a$ and $b$ are constant coefficients. $\epsilon$ is a minimal positive number for avoiding a denominator of 0. The derivative of a local linear model is obtained. $\partial q=f_{mean}\left(a\right)\ast \partial \mathrm{I}$. The edge information in the output image only comes from the guided image I, allowing the guided filter to preserve the edge details.

3.3.2. Dynamic Threshold Segmentation

The results of the guided filter are also processed by a matched filter to enhance the blood vessel. The parameter scale $\sigma$ is set as 1.5, 3, 4.5, and 6. The number of directions is 36 and the segment length is 9.

The dynamic threshold segmentation algorithm is employed to segment the image after matched filtering. It can be described as follows:

$$\left\{\begin{array}{ccc}\mathrm{I}\left(x,y\right)=255,& if& \mathrm{I}\left(x,y\right)-f_{mean}\left({\mathrm{I}}_{7\times 7}\left(x,y\right)\right)\ge \mathrm{T}\\ \mathrm{I}\left(x,y\right)=0,& if& \mathrm{I}\left(x,y\right)-f_{mean}\left({\mathrm{I}}_{7\times 7}\left(x,y\right)\right)<\mathrm{T}\end{array}\right.$$

(7)

The threshold segmentation of the image is realized by comparing the difference between the gray value of any pixel and the threshold value of the pixels in a given neighborhood, in which T is the threshold value and $f_{mean}$ is the mean filter of the neighborhood image block. The segmentation result for the low-clarity region is shown in Figure 5c.

3.4. Post-Processing

Because some small elements and noise are produced in the previous steps, a post-processing step should be carried out to remove them. This step mainly includes morphological processing, such as erosion and dilation. Then, a final binary image is produced for later evaluation. The final result of the vessel segmentation process is shown in Figure 5d.

4. Analysis of the Results and Comparisons

4.1. Comparison of Dual-Wavelength Retinal Image Segmentation Results

In an earlier study, we used a multi-scale Hessian filter to realize retinal vessel segmentation [77]. To evaluate the effectiveness of our proposed algorithm and compare the differences between the proposed vessel segmentation algorithm and the original algorithm, we used the same dataset of dual-wavelength retinal images from Ref. [33]. The dataset includes 50 pairs of retinal images centered on the optic disc of five healthy volunteers aged between 25 and 30, including their right eyes and left eyes. Although SO₂ calculations depend on the 570 nm image and 600 nm image, we only need to segment the 570 nm image and use registration parameters to obtain the corresponding vessel location in the 600 nm image [33]. The vessel segmentation results for Figure 1a based on the different algorithms are shown in Figure 6.

The variability between the proposed segmentation and the original segmentation algorithms is graphically shown in Figure 7. Figure 7a displays the segmentation based on the proposed method in green. Figure 7b displays the segmentation made by the original vessel segmentation algorithm in red. According to this color scheme, Figure 7c displays the variation obtained from the new method with respect to the original segmentation. The yellow color in Figure 7c corresponds to the overlapping segmentation results between the new and original vessel segmentation methods. The results of the variability show that the proposed algorithm can obtain much better segmentation which can be seen where the green color of the segmentation predominates.

Meanwhile, the recent method in Ref. [71] was used to segment the dual-wavelength retinal images; the corresponding code can be downloaded from https://github.com/Mahtab-Shabani/Retinal-Blood-Vessel-Segmentation-by-Active-Contour. The results for the image in Figure 1 are shown in Figure 8. On the one hand, these thin blood vessels near the macula were not effectively segmented indicated by the yellow box in Figure 8a. On the other hand, over-segmentation often occurred in some regions indicated by the red boxes in Figure 8a. This seriously affects the measurement of SO₂ in the regions indicated by the white box in Figure 8b. Hence, it can be concluded that the proposed algorithm has better segmentation results for follow-up blood oxygen calculations.

4.2. Evaluation of the Effect of the Segmentation Algorithm on the Calculation of SO₂

To evaluate the effect of the proposed algorithm on the calculation of SO₂, two pseudo-colored retinal SO₂ maps calculated by our SO₂ calculation software system are shown in Figure 9. They are representative SO₂ maps based on the proposed and original segmentation algorithms for the image in Figure 1. In healthy people, retinal arterioles are normally colored orange to red (approximately 90–100% saturation). Retinal venules are colored green to yellow-green (approximately 50–60% saturation). Colors indicate SO₂ in retinal vessels (scale on the right side of the image). According to the two SO₂ maps, we can also conclude that the measurement range of SO₂ is much larger after using the proposed algorithm to segment the dual-wavelength retinal images. These SO₂ of thin vessels in the low-clarity region indicated by the arrows can provide valuable information for doctors (Figure 9a).

Meanwhile, we used the same dataset to evaluate the effect of the segmentation algorithm on the reproducibility of the retinal oximetry. Five sets of dual-wavelength retinal images of each volunteer were tested. The optic disc and its edges are high and bright because of the retinal nerve fiber layer, and these high reflex areas will cause retinal SO₂ fluctuations and deviations from the truth value. To reduce the influence of the optic disc on the SO₂ calculation, two different radii of circles centered on the optic disc center were painted for each set of dual-wavelength retinal images. The SO₂ was calculated for the corresponding arterial and venous sections in the annular areas. The annular area for retinal SO₂ analysis is determined manually, and the SO₂ calculation software system can automatically calculate the SO₂ values for each arterial and venous section. To conveniently analyze the result, average SO₂ values for one arterial section and one venous section in the annular areas are shown in Figure 9.

Table 1. The mean and SD of the five images of the same volunteer based on the original vessel segmentation algorithm.

	Artery	Vein
Mean/%	92.54 83.46–101.38	56.63 49.94–68.15
SD/%	3.15 1.28–5.12	3.43 1.18–6.20

and

Table 2. The mean and SD of the five images of the same volunteer based on the proposed vessel segmentation algorithm.

	Artery	Vein
Mean/%	92.52 83.44–101.34	56.66 49.91–68.11
SD/%	3.13 1.26–5.14	3.45 1.19–6.15

display the mean and SD of the five repeated measurements of the same vessel section based on the original and proposed algorithms, respectively. According to Table 1 and Table 2, we obtained almost the same SO₂ values using the original and the proposed segmentation algorithms. This is because we used the same principle to measure SO₂ and only improved the vessel segmentation algorithm.

One arteriole section and one venule section near the optic disc were measured in each volunteer. To evaluate reproducibility, the mean and SD were calculated for each individual (from five images). Table 1 and Table 2 present the means and range for these individual means and SDs based on the original and proposed segmentation algorithm, respectively.

According to Table 2, the SO₂ values in the arterioles and venules near the optic disc were 92.52 ± 3.13% and 56.66 ± 3.45%, respectively. To obtain the SO₂ values of the thin vessels in the low-clarity region, we mainly measured the vessels in the area further from the optic disc, which are indicated by the arrows in Figure 9a. Using the same measurement method used to obtain the results in Table 2, the SO₂ values in the arterioles and venules further from the optic disc were 92.49 ± 3.52% and 58.12 ± 2.58%, respectively. Hence, we can conclude that venous SO₂ is higher in the smaller vessels than in the larger vessels. Arterial SO₂ remained relatively constant with vessel width. This is consistent with the conclusions of studies [78,79], whose research focus was the relationship between SO₂ and the length and width of the vessel. These SO₂ values can provide doctors with important information for the detection and treatment of eye diseases.

4.3. Evaluation of Time Complexity

Under the same hardware conditions (CPU: Intel(R) Core(TM) i7-4510U, frequency: 2.0 GHZ, memory: 16G), the proposed segmentation method took 4 min after testing. This is mainly because matched filtering is time-consuming since its time complexity is O(n^2). The time complexity of the other steps is O(n). Hence, the time complexity of the proposed algorithm is O(n^2). This is not convenient for clinical applications of retinal oximetry. Hence, there is still room for improvement in the efficiency of the algorithm.

5. Discussion

In this paper, we have proposed a novel hybrid method for segmenting vessels, in order to efficiently segment dual-wavelength retinal images and enlarge the measurement range of SO₂ in retinal vessels. As far as we know, this is the first study to improve the image segmentation result in retinal oximetry using image characteristic analysis and a specific unsupervised segmentation algorithm. The experiments with dual-wavelength retinal images demonstrated the effectiveness and accuracy of the proposed algorithm in improving the SO₂ measurement range and confirmed the reliability of calculating SO₂.

It is worth noting that our work is focused on the effect of the segmentation algorithm on the SO₂ calculation and measurement range for the retinal oximetry. There are no corresponding manual segmentation results by experts for the dual-wavelength retinal images. Currently, we cannot provide quantitative metrics to show how well the method performs overall. Ongoing work is required to further improve the proposed algorithm to make it generalizable to other datasets, such as DRIVE, STARE, and CHASE_DB. Then, the corresponding evaluation indicators could be obtained, such as ROC curves, accuracy, sensitivity, and specificity. In addition, although the proposed segmentation algorithm can provide more SO₂ information, it is time-consuming and is not convenient for clinical applications. Thus, there is still room for improvement in the efficiency of the algorithm.

Our work was carried out under the assumption that only the segmentation result affects the calculation and measurement range of SO₂. However, SO₂ calculations can be affected by fundus pigmentation, calibration, etc. It is worth further improving SO₂ calculation reliability. In addition, this study has obtained some preliminary results on the differences and reasons for retinal SO₂ in the different measurement regions, which need further study and exploration. Meanwhile, we need a more comprehensive background description of the data for healthy and unhealthy retinal images, to conduct more detailed and multi-parameter analyses under different conditions. For example, the relationship between unhealthy retinal image and SO₂ in thin vessels is not known. There is ongoing work in collaboration with the Chengdu University of Traditional Chinese Medicine and Ineye Hospital of the Chengdu University of TCM to collect unhealthy dual-wavelength retinal images from patients with various conditions, such as diabetic retinopathy, glaucoma, age-related macular degeneration, retinopathy of prematurity, and retinal vein occlusion.

6. Conclusions

According to the analysis in Section 1 and Section 2, in the calculation of SO₂ based on retinal image processing, the vessel segmentation result may dramatically affect the measurement range of SO₂. In particular, the thin vessels in the low-clarity region can provide doctors with valuable information for the detection of neovascular diseases. Hence, we proposed a novel hybrid segmentation algorithm for dual-wavelength retinal images. It can segment the tiny vessels and be helpful to enlarge the measurement range for retinal oximetry. Finally, we evaluated the effect of the segmentation algorithm on the reproducibility of the retinal oximetry results and running time. The proposed method is time-consuming and should be optimized for subsequent adoption into clinical applications.