Curvature calculation method based on heuristic blood vessel segmentation

Abstract

The invention provides a curvature calculation method based on heuristic blood vessel segmentation, and belongs to the technical field of medical image processing, and the method comprises the steps: extracting a high-precision retinal blood vessel segmentation mask from a color fundus image through a deep learning model; a Zhang-suen algorithm is adopted to carry out skeletonization processing on the segmentation mask, and a vascular skeleton with the single-pixel width is generated; a vascular skeleton is divided into independent vascular branches based on a heuristic rule, the problems of main vascular fracture and branch adhesion are solved, and continuity and accuracy of a segmentation result are ensured; in the segmented blood vessel branches, curvature symbol constant sections are detected, the curvature parameters of all the branches are calculated, and the curvature calculation precision in a digital scene is improved. According to the method, deep learning and morphological algorithms are fused, the problem of error accumulation in a traditional method is solved, the full-automatic process from the original color fundus image to the blood vessel morphological quantization parameters is achieved, and efficient and reliable technical support is provided for clinical vasculopathy analysis.

Description

Technical Field

[0001] The present invention belongs to the technical field of medical image processing, and in particular relates to a curvature calculation method based on heuristic blood vessel segmentation. Background Art

[0002] Curvature is one of the earliest characteristics of vascular morphology to change, and refers to the degree of spatial tortuosity of blood vessels. Studies have shown that the tortuosity of retinal vessels is considered one of the earliest medical indicators of vascular diseases such as diabetic retinopathy, hypertensive retinopathy, and retinopathy of prematurity. However, manual assessment methods in clinical practice have failed to reach a consensus on a universal definition of tortuosity, and the assessment results are highly subjective, and the comparability of qualitative analysis cannot be guaranteed. In order to evaluate the changes in tortuosity over time, there is an urgent need to develop an objective, accurate, and clinically meaningful tortuosity calculation method to quantitatively assess the tortuosity of retinal vessels.

[0003] Many methods for calculating tortuosity have been widely used, including those based on the ratio of chord length to arc length, curvature, and the angle of change in vessel orientation. However, these methods all employ semi-automated processes and typically require manual vessel annotation. This manual annotation process is tedious and time-consuming, and the density and placement of annotations are susceptible to subjective factors, resulting in inaccurate fitting of vessel morphology and, consequently, the accuracy of the results.

[0004] Automated tortuosity calculation methods face two major challenges. First, current vessel segmentation methods typically rely on morphological filtering to identify vessel intersections and disconnect all connected vessels at these intersections. However, main vessels often branch out into multiple downstream vessels, which connect to the main vessel at intersections. Disconnecting all connections at intersections would result in the main vessel being segmented into discrete segments. Since tortuosity calculation is typically performed within connected vessel segments, a break in the main vessel would require separate calculations of tortuosity within each discrete segment, rather than for the entire vessel. Second, current tortuosity calculation methods are often based on virtual continuous vessel models constructed by fitting manually annotated vessel points. However, blood vessels in digital images are composed of discrete pixels, which differs significantly from continuous curve models. In particular, when using curvature-related methods, curvature in continuous curve models is typically calculated using the first and second derivatives at that point. In digital images, derivatives are calculated using differential methods, which can introduce significant errors, affecting the curvature calculation results and leading to inaccurate tortuosity calculations.

[0005] Therefore, the present invention has developed a new automated retinal vascular tortuosity calculation process, which can directly extract quantitative parameters from color fundus images, solving the challenges of main vessel breakage and curvature calculation in digital images. This method can more efficiently, accurately and stably quantify the full-scale retinal vascular morphological characteristics in fundus images. Specifically, the present invention proposes a retinal vascular slope-preserving segmentation method based on a heuristic method, which significantly improves the connectivity and integrity of vascular segmentation. This method optimizes the segmentation process of vascular segments by maintaining the continuity of the vascular slope, making the segmentation results more reasonable and coherent. In addition, the present invention proposes a method for calculating the curvature of digital images based on constant curvature segments, which more accurately reflects the true morphological characteristics of blood vessels. Summary of the Invention

[0006] To avoid mis-segmentation of major vessels during vessel tortuosity calculation and address the lack of suitable curvature calculation models in digital image scenes, this paper proposes a heuristic-based vessel segmentation technique to maintain the connectivity of major vessels. Furthermore, a method for calculating vessel tortuosity in digital images based on segments with constant curvature signs is designed, which more accurately reflects vessel tortuosity in digital images.

[0007] The present invention adopts the following technical solutions to solve the above problems:

[0008] A method for calculating curvature based on heuristic blood vessel segmentation, the method comprising the following steps:

[0009] S1: Use the AADG algorithm to perform joint segmentation of blood vessels and optic disc on the color fundus image, remove the optic disc part, and use the deep learning model to extract a high-precision retinal blood vessel segmentation mask from the color fundus image to obtain the optic disc-free blood vessel segmentation mask;

[0010] S2: Using the Zhang-Suen refinement algorithm to extract the vascular skeleton structure from the segmentation mask obtained in step S1, to obtain a vascular skeleton map;

[0011] S3: Design a blood vessel segmentation method based on a heuristic method to segment the blood vessel skeleton image in S2, and divide the blood vessel skeleton into independent blood vessel branches, specifically including the following steps:

[0012] S301: identifying blood vessel intersections through morphological operations and detecting intersections using specific structural elements;

[0013] S302: Select a starting point from the eight adjacent points of the intersection to determine the starting point of the independent branch;

[0014] S303: Starting from the starting point, searching for blood vessel branches step by step until an intersection or a blood vessel end is encountered, and determining the branch end point;

[0015] S304: Calculating the slope of the branch according to the starting and ending positions of the blood vessel branch;

[0016] S305: Based on the slopes of the branches, the vascular branches with similar directions are considered as main vessels, the connectivity of the main vessels is maintained, and other branches are disconnected;

[0017] S4: Design a curvature calculation method based on the curvature sign constant segment, and use the calculation method to calculate the curvature of each vascular branch after segmentation in S3.

[0018] Furthermore, in S302, each adjacent point of the intersection may correspond to the starting point of an independent branch, but four adjacent foreground points generally belong to the same independent branch, and a non-four adjacent point of the intersection is generally selected as the starting point of the independent branch.

[0019] Furthermore, in S3, the heuristic method refers to selecting the next path point based on the adjacent conditions and traversal conditions of the adjacent points. Generally, a point in an independent branch path has only two adjacent points, and only the untraversed point needs to be selected as the next path point. For a path point with three adjacent points, the next path point cannot be correctly selected by access judgment alone, so the restriction of the adjacency relationship is introduced. If there is an intersection between the two untraversed adjacent points, the point is directly selected to reduce redundant judgments and quickly find the nearest intersection. If there is no intersection, the 4-adjacent point is selected as the next path point to maintain the integrity of the path.

[0020] Furthermore, in S4, the curvature calculation method based on the curvature constant sign segment specifically includes the following steps:

[0021] S401: selecting three points with a certain pixel spacing on the blood vessel branch, and calculating the curvature of each discrete point of the digital image using a curvature fitting method;

[0022] S402: dividing the blood vessel branches according to the segments with constant curvature signs, using a hysteresis threshold method to avoid over-segmentation caused by curvature close to zero value;

[0023] S403: Calculate the total curvature based on the number of segments and the curvature of each segment.

[0024] Furthermore, in S401, the curve fitting method refers to calculating the curvature of a pixel point (x2, y2) on a blood vessel branch. We select two points (x1, y1) and (x3, y3) at intervals of a certain number of pixels in the front and back directions of the branch. Assuming that these three points can determine a quadratic curve, its parametric equation is:

[0025]

[0026] Where t is the parameter of the curve, which means the point on the curve (x i ,y i ) and (x2,y2), the calculation formula is:

[0027]

[0028] Using the known position information of the three points (x1, y1) (x2, y2) (x3, y3), we can solve the unknown coefficients (a1, a2, a3, b1, b2, b3) in the parametric equation to obtain the parametric equation of the curve. The first and second derivatives of the curve can be calculated using the following formulas:

[0029]

[0030] Substituting the calculated derivative (x′, x″, y′, y″) into the curvature formula, we can obtain the curvature formula related to the parameter t:

[0031]

[0032] Substituting t=0 into the above formula, we can obtain the curvature of the curve at (x2, y2), and use this value as the curvature estimate of the discrete point.

[0033] Furthermore, in S402, a smaller threshold is selected, and its positive and negative values ​​are taken as the hysteresis thresholds for segmentation. When traversing along the vascular skeleton, when the curvature sequentially crosses two thresholds with different signs (i.e., one positive value and one negative value), the midpoint of the two intersections is used as the segmentation point. If the curvature sequentially crosses two thresholds with the same sign, it means that the sign of the curvature has not changed, or it only fluctuates around zero. In this case, no segmentation is performed, thereby avoiding over-segmentation caused by curvature fluctuations around zero. The segmentation result is:

[0034] B={S1,S2,S3,…,S n}

[0035] Among them S i The segment with constant curvature sign is composed of several ordered pixels, which are sorted according to the direction of the branch:

[0036]

[0037] in Represents the pixels in the segment.

[0038] Furthermore, in S403, the formula for calculating the total curvature of the curvature is:

[0039]

[0040] Where n is the number of segments, Lc B is the total length of the vascular branches, Indicates segment S i The arc length, Indicates segment S i The chord length is calculated using the following formula:

[0041]

[0042]

[0043]

[0044] where d(·) represents the distance between two points.

[0045] Furthermore, in S403, the curvature is used to calculate the total curvature, and the tortuosity of each segment is evaluated by calculating the ratio of the arc length to the chord length, and the tortuosity of all segments is summed up, thereby comprehensively considering the contribution of each segment. Since the more segments there are, the greater the overall curvature, and in order to ensure that smooth semicircular or parabolic vascular branches (i.e., when there is only one segment) have zero curvature, the constraint condition is introduced. During the calculation, in order to ensure the comparability of vascular branches of different lengths, the results were normalized and divided by the length of the vascular branch. Through the above constraints, this formula comprehensively considers the influence of the number of segments with constant curvature sign, the degree of curvature of each segment, and the length of the branch.

[0046] Furthermore, in S1, the AADG algorithm is a domain-generalized segmentation framework that uses domain-generalized automatic enhancement technology based on the segmentation network, and can effectively adapt to different image data domains without relying on specific imaging conditions.

[0047] Furthermore, in S2, the Zhang-Suen thinning algorithm is mainly used to refine the outline of objects in the binary image into a skeleton of a single pixel width. By iteratively processing the image, the boundary of the object is gradually refined, and finally a vascular skeleton with a topological structure is obtained. The vascular skeleton is a simplified structure extracted from the vascular network through image processing technology, usually manifested as a refined vascular centerline. It compresses the complex vascular morphology into a line of a single pixel width, which can effectively retain the topological structure, branching relationship and connectivity of the blood vessels, while removing the width information of the blood vessels.

[0048] Advantages of the present invention:

[0049] 1. This invention realizes a fully automated process from original color fundus images to vascular tortuosity parameters by integrating the domain generalization segmentation framework (AADG algorithm), morphological skeleton extraction and heuristic segmentation technology, providing highly reliable quantitative data support for clinical diagnosis.

[0050] 2. The present invention proposes a retinal vascular slope-preserving segmentation method based on a heuristic approach, which solves the problem of prone breakage of main vessels in the traditional vascular segmentation process, improves the continuity and integrity of independent vascular branches, and effectively supports the accuracy of subsequent curvature calculations.

[0051] The present invention proposes a method for calculating the curvature of blood vessels in digital images based on a constant curvature sign segment, which solves the problem of missing curvature calculation model in digital image scenes and improves the accuracy of curvature calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the specific embodiments of the present invention, the following will briefly introduce the drawings required for use in the description of the specific embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0053] Figure 1 This is an overall flow chart of the method for calculating curvature based on heuristic blood vessel segmentation according to the present invention;

[0054] Figure 2 The effect diagram for quantification of vascular morphological parameters;

[0055] Figure 3 Schematic diagram of the morphological filtering structure element used in the present invention;

[0056] Figure 4 Selecting an example diagram for the starting point of an independent branch involved in the present invention;

[0057] Figure 5 This is an example diagram of the independent branch endpoint search process involved in the present invention;

[0058] Figure 6 This is a schematic diagram of curvature fitting calculation involved in the present invention;

[0059] Figure 7 This is a schematic diagram of the segment division of the hysteresis threshold method involved in the present invention;

[0060] Figure 8 This is an example diagram of the RET-TORT verification dataset involved in the present invention;

[0061] Figure 9 A comparison diagram of the effects of the heuristic segmentation method and the traditional brute force segmentation method involved in the present invention;

[0062] Figure 10 This is an example diagram of the interference of microstructures of blood vessels involved in the present invention;

[0063] Figure 11 This figure shows the implementation results of the curvature calculation method based on heuristic blood vessel segmentation involved in the present invention. DETAILED DESCRIPTION

[0064] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0065] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0066] like Figure 1 、 Figure 2 As shown, the present invention discloses a method for calculating curvature based on heuristic vessel segmentation, the main steps of which are as follows:

[0067] S1: Use the AADG algorithm to perform joint segmentation of blood vessels and optic disc on the color fundus image, remove the optic disc part, and use the deep learning model to extract a high-precision retinal blood vessel segmentation mask from the color fundus image to obtain the optic disc-free blood vessel segmentation mask;

[0068] S2: Using the Zhang-Suen refinement algorithm to extract the vascular skeleton structure from the segmentation mask obtained in step S1, to obtain a vascular skeleton map;

[0069] S3: Design a blood vessel segmentation method based on a heuristic method to segment the blood vessel skeleton image in S2, and divide the blood vessel skeleton into independent blood vessel branches;

[0070] S4: Design a curvature calculation method based on the curvature sign constant segment, and use the calculation method to calculate the curvature of each vascular branch after segmentation in S3.

[0071] Example 1

[0072] As a preferred embodiment of the present invention, this calculation method specifically includes the following steps:

[0073] S1: Use the AADG algorithm to jointly segment the blood vessels and optic disc of the color fundus image, remove the optic disc part, and use the deep learning model to extract a high-precision retinal blood vessel segmentation mask from the color fundus image to obtain the optic disc-free blood vessel segmentation mask.

[0074] It should be noted that the AADG algorithm is a domain-generalized segmentation framework that uses domain-generalized automatic enhancement technology based on the segmentation network. It can effectively adapt to different image data domains without relying on specific imaging conditions.

[0075] S2: Using the Zhang-Suen refinement algorithm, the segmentation mask obtained in step S1 is subjected to vascular skeleton structure extraction to obtain a vascular skeleton map.

[0076] The Zhang-Suen thinning algorithm is a skeleton extraction algorithm commonly used in image processing. It is mainly used to thin the outline of objects in binary images into a skeleton with a single pixel width. The algorithm iteratively processes the image, gradually thinning the boundaries of the object, and ultimately obtaining a skeleton with a topological structure.

[0077] like Figure 2 As shown, the vascular skeleton involved is a simplified structure extracted from the vascular network through image processing technology, usually manifested as a refined vascular centerline. It compresses the complex vascular morphology into a line with a single pixel width, which can effectively preserve the topological structure, branching relationship and connectivity of the blood vessels, while removing the width information of the blood vessels. Compared with the vascular segmentation mask, the vascular skeleton can more clearly present the tortuosity of the blood vessels.

[0078] S3: Design a blood vessel segmentation method based on a heuristic method to segment the blood vessel skeleton image in S2, and divide the blood vessel skeleton into independent blood vessel branches, specifically including the following steps:

[0079] S301: Identify blood vessel intersections through morphological operations and detect intersections using specific structural elements.

[0080] like Figure 3 As shown, in a digital image, an intersection generally has a morphological feature that can divide the foreground points in its neighborhood into at least three independent branches. Therefore, this embodiment designs a structural element to identify the intersection.

[0081] S302: Select a starting point from the eight adjacent points of the intersection to determine the starting point of the independent branch.

[0082] Since the intersection is the meeting point of independent branches, the adjacent foreground points can be used as the starting points of independent branches. Figure 4As shown in , four-adjacent foreground points generally belong to the same independent branch. We generally choose the non-four-adjacent points of the intersection as the starting point of the independent branch.

[0083] S303: Starting from the starting point, searching for blood vessel branches step by step until an intersection or a blood vessel end is encountered, and determining the end point of the branch.

[0084] The heuristic method proceeds as follows: starting from the starting point, the algorithm searches for unvisited foreground points within the 8-way neighborhood of the current point as the next path point, until an intersection or the end of a blood vessel is found, thus completing the traversal of the independent branch. The last pixel of the path is the end point of the branch.

[0085] like Figure 5 As shown in the example in , in general, Figure 5 As shown in (a), the points in the independent branch path have only two adjacent points, so we only need to select the untraversed point as the next path point; Figure 5 As shown in (b), some path points may have three adjacent points. This is a normal phenomenon of image pixelation and does not meet the characteristics of intersection points. For such points, it is impossible to correctly select the next path point by only judging by access. Therefore, we introduce the restriction of the adjacency relationship. If there is an intersection between two adjacent points that have not been traversed, the point is directly selected to reduce redundant judgments and quickly find the nearest intersection. If there is no intersection, the 4-adjacent point is selected as the next path point to maintain the integrity of the path.

[0086] S304: Calculate the slope of the branch according to the starting point and end point of the blood vessel branch.

[0087] S305: Based on the slope of the branch, the vascular branches with similar directions are considered as main vessels, the connectivity of the main vessels is maintained, and other branches are disconnected.

[0088] In digital images, we use the slopes of different independent branches to represent the direction of the branch. Similar slope values ​​and signs indicate similar directions. When segmenting blood vessels at bifurcation points, we consider the two independent branches with the most similar slopes to be the main blood vessels, and the remaining branches to be subordinate blood vessels branching off from the main blood vessel at the bifurcation point. Therefore, we choose to maintain the connectivity of the two independent branches belonging to the main blood vessel and disconnect the other branches to complete the blood vessel segmentation at the bifurcation point.

[0089] S4: Design a curvature calculation method based on the curvature sign constant segment, and use the calculation method to calculate the curvature of each vascular branch after segmentation in S3.

[0090] S401: Select three points with a certain pixel spacing on the blood vessel branch, and use the curvature fitting method to calculate the curvature of each discrete point of the digital image.

[0091] like Figure 6 As shown, this embodiment uses a curve fitting method to calculate the curvature of discrete points. To calculate the curvature of a pixel point on a blood vessel branch (denoted as (x2, y2)), we select two points (x1, y1) and (x3, y3) at intervals of a certain number of pixels in the front and back directions of the branch. Assuming that these three points can determine a quadratic curve, its parametric equation can be expressed as:

[0092]

[0093] Where t is the parameter of the curve, which means the point on the curve (x i ,y i ) and (x2,y2), the calculation formula is:

[0094]

[0095] Using the known position information of the three points (x1, y1) (x2, y2) (x3, y3), we can solve the unknown coefficients (a1, a2, a3, b1, b2, b3) in the parametric equation to obtain the parametric equation of the curve. Then, we can calculate the first and second derivatives of the curve using the following formula:

[0096]

[0097] Substituting the calculated derivative (x′, x″, y′, y″) into the curvature formula, we can obtain the curvature formula related to the parameter t:

[0098]

[0099] Substituting t=0 into the above formula, we can obtain the curvature of the curve at (x2, y2), and use this value as the curvature estimate of the discrete point.

[0100] S402: Divide the blood vessel branches according to the curvature sign constant segment, and use a hysteresis threshold method to avoid over-segmentation caused by curvature close to zero value.

[0101] like Figure 7As shown in the figure, the hysteresis threshold method aims to avoid the occurrence of small segments with tortuosity close to zero caused by directly using the intersection of the curvature curve and the zero value as the segmentation point. These small segments will cause the final curvature calculation result to be too small. The implementation method of this method is to select a smaller threshold and take its positive and negative values ​​as the hysteresis threshold for segmentation; when traversing along the direction of the vascular skeleton, when the curvature successively crosses two thresholds with different signs (i.e., one is positive and the other is negative), the midpoint of the two intersections is used as the segmentation point. If the curvature successively crosses two thresholds with the same sign, it means that the sign of the curvature has not changed, or it only fluctuates around zero. In this case, we do not segment, thereby avoiding excessive segmentation caused by curvature fluctuations around zero. The segmentation result is:

[0102] B={S1,S2,S3,…,S n}

[0103] Among them S i The segment with constant curvature sign is composed of several ordered pixels, which are sorted according to the direction of the branch:

[0104]

[0105] in Represents the pixels in the segment.

[0106] S403: Calculate the total curvature based on the number of segments and the curvature of each segment.

[0107] The formula for curvature based on the constant sign of the curvature section is:

[0108]

[0109] Where n is the number of segments, Lc B is the total length of the vascular branches, Indicates segment S i The arc length, Indicates segment S i The chord length is calculated using the following formula:

[0110]

[0111]

[0112]

[0113] where d(·) represents the distance between two points.

[0114] The tortuosity of each segment is evaluated by calculating the ratio of the arc length to the chord length of each segment, and the tortuosity of all segments is summed up to comprehensively consider the contribution of each segment. Since the more segments there are, the greater the overall tortuosity, and in order to ensure that smooth semicircular or parabolic vascular branches (i.e., when there is only one segment) have zero tortuosity, we introduce the constraint To ensure comparability among vascular branches of varying lengths, we normalized the results by dividing by the branch length. This constraint allows the formula to take into account the number of segments with constant curvature sign, the degree of curvature within each segment, and the length of the branch.

[0115] Example 2

[0116] To validate the vessel segmentation method and curvature calculation method proposed in this paper, we used two retinal image datasets: DRIVE and RET-TORT.

[0117] The DRIVE dataset, widely used in the research and development of retinal vessel segmentation algorithms, originates from the Dutch diabetic retinopathy screening program and contains 40 retinal images, divided into a training set and a test set of 20 images each. Each image is accompanied by a vessel segmentation mask manually annotated by experts. We performed vessel skeleton extraction and segmentation on the segmentation masks of the 20 images in the test set and manually evaluated the accuracy of the segmentation results.

[0118] The RET-TORT dataset was created by the University of Padova and contains retinal vascular images of 30 arteries and 30 veins, manually annotated single vessel coordinate sequences, and curvature rankings performed by experts based on these annotations. The fundus images in the dataset are as follows: Figure 8 As shown in the figure, in addition to the single blood vessel used for sorting, other blood vessels are also included. If the blood vessels are directly segmented on these images and the curvature is calculated based on this, the existence of other blood vessels will obviously interfere with the calculation results. Therefore, we adopt an alternative method to directly generate a skeleton digitized image of a single blood vessel; specifically, we interpolate the marked blood vessel coordinates and take the interpolation results as integer coordinate positions to simulate the image digitization process. The skeleton image generated in this way can accurately reflect the morphology of a single blood vessel and has discrete characteristics, similar to the skeleton extracted from the fundus image through processes such as segmentation and refinement. Therefore, this method is more suitable for the application scenario of automated curvature calculation, and the digital image curvature calculation evaluation based on the skeleton image is more convincing.

[0119] Figure 9This is a comparison of the overall effects of using the brute force segmentation method and the slope-preserving segmentation method to segment the vascular skeleton. As can be seen from the figure, the brute force method will disconnect all branches at the intersection, causing the main blood vessel to break into many small branches. Our method can effectively alleviate this problem. At the intersection, only the lower-level shunt vessels are disconnected and the connectivity of the main blood vessel branches is maintained, thereby achieving more accurate and coherent blood vessel segmentation. This shows that the slope-preserving segmentation method has a significant advantage in maintaining the integrity of the vascular structure, thus providing a more reliable basis for subsequent vascular analysis and medical diagnosis.

[0120] like Figure 10 As shown in (a), the skeletonization algorithm is very sensitive to small structural changes and may produce unnecessary protrusions during the vessel thinning process, such as Figure 10 As shown in (b), these protrusions will lead to a large number of redundant intersections. Since the independent branches corresponding to these redundant intersections are usually very short, consisting of only a few pixels, and in some cases, there may even be loops within the independent branches, these segmentation errors caused by the refinement process are irrelevant to our segmentation method. Considering that these redundant intersections do not represent the real vascular structure, it is meaningless to evaluate these intersections when evaluating the accuracy of the segmentation method.

[0121] To this end, when quantitatively evaluating the vascular segmentation method, we first identified invalid intersections caused by protrusions, and then evaluated the segmentation accuracy at valid intersections, respectively counting the efficiency and segmentation accuracy of the intersections. During the segmentation verification process of 20 images in the DRIVE test set, a total of 3,339 intersections were identified, of which 82.5% were valid after excluding redundant intersections caused by refinement. Among these valid intersections, the segmentation accuracy reached 83.9%. This result proves that our method can achieve good results in different vascular network structures and proves the robustness of the method.

[0122] Because the labels in the RET-TORT dataset only provide ophthalmologists' curvature rankings without specific numerical values, we calculated the curvature of each image and ranked the images based on the calculated results. We then verified the effectiveness of our method by evaluating the correlation between the calculated ranking and the label ranking. To this end, we used the Spearman coefficient for correlation analysis; the Spearman coefficient is a nonparametric statistical method used to measure the monotonic relationship between two rankings. The closer the coefficient is to 1, the closer the calculated ranking is to the true ranking, indicating that our method is more effective.

[0123] On this basis, we also calculated the p-value to further verify the significance of the correlation. The p-value is used to measure whether the observed correlation may be due to random factors. If the p-value is less than the set significance level (usually 0.05), it means that the correlation between the calculated result and the label ranking is significant, supporting the effectiveness of our method in the ranking task. Conversely, a larger p-value indicates that the correlation is not significant, and further analysis of the data or method is required. The Spearman correlation coefficient and its corresponding p-value results when sorting the curvature of arteries and veins based on the skeleton image digitized by a single vascular coordinate sequence in the RET-TORT dataset using different methods are shown in the following table:

[0124]

[0125] In contrast, the proposed curvature calculation method achieved a Spearman correlation coefficient of 0.73 for arteries, an improvement of approximately 10% compared to other methods. Our method also performed well for veins. This experimental result fully demonstrates the effectiveness of our proposed curvature calculation method in digital image scenarios.

[0126] In order to evaluate the effectiveness of our overall process of automatic curvature measurement, we performed image segmentation, skeleton extraction, vessel segmentation, and curvature calculation on the color fundus image in sequence to obtain the final curvature numerical result. Figure 11 The fundus images, skeleton images, and curvature of two fundus images with significantly different curvatures are displayed. Both the original image and the vascular skeleton clearly show that the upper image has a higher curvature than the lower image. The curvature results are consistent with the image performance, indicating that the overall process is applicable to the overall curvature measurement of fundus images.

[0127] The present invention has been described in detail above through the embodiments, but the contents are only preferred embodiments of the present invention and cannot be considered to limit the scope of implementation of the present invention. All equal changes and improvements made within the scope of application of the present invention should still fall within the scope of the patent coverage of the present invention.

Claims

1. A method for calculating curvature based on heuristic vessel segmentation, characterized by: The method comprises the following steps: S1: Use the AADG algorithm to perform joint segmentation of blood vessels and optic disc on the color fundus image, remove the optic disc part, and use the deep learning model to extract a high-precision retinal blood vessel segmentation mask from the color fundus image to obtain the optic disc-free blood vessel segmentation mask; S2: Using the Zhang-Suen refinement algorithm to extract the vascular skeleton structure from the segmentation mask obtained in step S1, to obtain a vascular skeleton map; S3: Design a blood vessel segmentation method based on a heuristic method to segment the blood vessel skeleton image in S2, and divide the blood vessel skeleton into independent blood vessel branches, specifically including the following steps: S301: identifying blood vessel intersections through morphological operations and detecting intersections using specific structural elements; S302: Select a starting point from the eight adjacent points of the intersection to determine the starting point of the independent branch; S303: Starting from the starting point, searching for blood vessel branches step by step until an intersection or a blood vessel end is encountered, and determining the branch end point; S304: Calculating the slope of the branch according to the starting and ending positions of the blood vessel branch; S305: Based on the slopes of the branches, the vascular branches with similar directions are considered as main vessels, the connectivity of the main vessels is maintained, and other branches are disconnected; S4: Design a curvature calculation method based on the curvature sign constant segment, and use the calculation method to calculate the curvature of each vascular branch after segmentation in S3.

2. The method for calculating curvature based on heuristic vessel segmentation according to claim 1, characterized in that: In S302, each adjacent point of the intersection may correspond to the starting point of an independent branch, but four adjacent foreground points generally belong to the same independent branch, and a non-four adjacent point of the intersection is generally selected as the starting point of the independent branch.

3. The method for calculating curvature based on heuristic vessel segmentation according to claim 2, characterized in that: In S3, the heuristic method refers to selecting the next path point based on the adjacent conditions and traversal conditions of the adjacent points. Generally, a point in an independent branch path has only two adjacent points, and only the untraversed point needs to be selected as the next path point. For a path point with three adjacent points, the next path point cannot be correctly selected by access judgment alone, so the restriction of the adjacency relationship is introduced. If there is an intersection between the two untraversed adjacent points, the point is directly selected to reduce redundant judgments and quickly find the nearest intersection. If there is no intersection, the 4-adjacent point is selected as the next path point to maintain the integrity of the path.

4. The method for calculating curvature based on heuristic vessel segmentation according to claim 1, characterized in that: In S4, the curvature calculation method based on the constant curvature sign section specifically includes the following steps: S401: selecting three points with a certain pixel spacing on the blood vessel branch, and calculating the curvature of each discrete point of the digital image using a curvature fitting method; S402: dividing the blood vessel branches according to the segments with constant curvature signs, using a hysteresis threshold method to avoid over-segmentation caused by curvature close to zero value; S403: Calculate the total curvature based on the number of segments and the curvature of each segment.

5. The method for calculating curvature based on heuristic vessel segmentation according to claim 4, characterized in that: In S401, the curve fitting method refers to calculating the curvature of a pixel point (x2, y2) on a blood vessel branch. We select two points (x1, y1) and (x3, y3) at intervals of a certain number of pixels in the front and back directions of the branch. Assuming that these three points can determine a quadratic curve, its parametric equation is: Where t is the parameter of the curve, which means the point on the curve (x i ,y i ) and (x2,y2), the calculation formula is: Using the known position information of the three points (x1, y1) (x2, y2) (x3, y3), we can solve the unknown coefficients (a1, a2, a3, b1, b2, b3) in the parametric equation to obtain the parametric equation of the curve. The first and second derivatives of the curve can be calculated using the following formulas: Substituting the calculated derivative (x′, x″, y′, y″) into the curvature formula, we can obtain the curvature formula related to the parameter t: Substituting t=0 into the above formula, we can obtain the curvature of the curve at (x2, y2), and use this value as the curvature estimate of the discrete point.

6. The method for calculating curvature based on heuristic vessel segmentation according to claim 4, characterized in that: In S402, a smaller threshold is selected, and its positive and negative values ​​are taken as the hysteresis thresholds for segmentation. When traversing along the vascular skeleton, when the curvature sequentially crosses two thresholds with different signs (i.e., one positive value and one negative value), the midpoint of the two intersections is used as the segmentation point. If the curvature sequentially crosses two thresholds with the same sign, it means that the sign of the curvature has not changed, or it only fluctuates around zero. In this case, we do not segment, thereby avoiding over-segmentation caused by curvature fluctuations around zero. The segmentation result is: <h2 style=";text-align:left;direction:ltr">B = {S1,S2,S3,…,S<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr">} Among them S i The segment with constant curvature sign is composed of several ordered pixels, which are sorted according to the direction of the branch: in Represents the pixels in the segment.

7. The method for calculating curvature based on heuristic vessel segmentation according to claim 4, characterized in that: In S403, the formula for calculating the total curvature is: Where n is the number of segments, Lc B is the total length of the vascular branches, Indicates segment S i The arc length, Indicates segment S i The chord length is calculated using the following formula: where d(·) represents the distance between two points.

8. The method for calculating curvature based on heuristic vessel segmentation according to claim 7, characterized in that: In S403, the curvature is used to calculate the total curvature. The tortuosity of each segment is evaluated by calculating the ratio of the arc length to the chord length, and the tortuosity of all segments is summed up to comprehensively consider the contribution of each segment. Since the more segments there are, the greater the overall curvature. At the same time, in order to ensure that smooth semicircular or parabolic vascular branches (i.e., when there is only one segment) have zero curvature, the constraint condition is introduced. During the calculation, in order to ensure the comparability of vascular branches of different lengths, the results were normalized and divided by the length of the vascular branch. Through the above constraints, this formula comprehensively considers the influence of the number of segments with constant curvature sign, the degree of curvature of each segment, and the length of the branch.

9. The method for calculating curvature based on heuristic vessel segmentation according to any one of claims 1 to 8, characterized in that: In S1, the AADG algorithm is a domain-generalized segmentation framework that uses domain-generalized automatic enhancement technology based on the segmentation network. It can effectively adapt to different image data domains without relying on specific imaging conditions.

10. The method for calculating curvature based on heuristic vessel segmentation according to claim 1, characterized in that: In S2, the Zhang-Suen thinning algorithm is mainly used to refine the outline of objects in the binary image into a skeleton with a single pixel width. By iteratively processing the image, the boundary of the object is gradually refined, and finally a vascular skeleton with a topological structure is obtained. The vascular skeleton is a simplified structure extracted from the vascular network through image processing technology, usually manifested as a refined vascular centerline. It compresses the complex vascular morphology into a line with a single pixel width, which can effectively preserve the topological structure, branching relationship and connectivity of the blood vessels, while removing the width information of the blood vessels.

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