Blood vessel segmentation method and device based on shape constraint and edge indicator function improvement

Abstract

The application discloses a blood vessel segmentation method and equipment based on shape constraint and edge indicator function improvement, relates to the medical image segmentation field, and mainly comprises the following steps: introducing adaptive shape prior constraint and gradient indicator function in a local active contour model, extracting an initial contour from prior information, solving the model by using a variation method and a gradient descent flow method, and obtaining a final evolution curve and a segmentation result. The blood vessel segmentation method and equipment based on shape constraint and edge indicator function improvement can improve the segmentation precision and reduce the calculation amount of the model.

Description

Technical Field

[0001] This invention relates to the field of medical image segmentation, and more specifically, to a method and apparatus for blood vessel segmentation based on shape constraints and edge indicator functions. Background Technology

[0002] In medical research, blood vessels play an extremely important role. Accurate and rapid segmentation and extraction of blood vessels are crucial for the diagnosis and treatment of various diseases. Among the most challenging aspects, the complex and elongated structure of blood vessels, as well as the non-uniformity of pixel intensity and the blurring of blood vessel edges during imaging, present significant challenges.

[0003] Level set-based active contour models have become one of the commonly used methods in segmentation due to their unique advantages, with local active contour models based on local region information being the most representative. Since there are pixel-level grayscale differences between the blood vessel region and the background region in blood vessel images, this type of method minimizes the pixel differences within and outside the evolution curve by using energy minimization methods within a local range, thereby completing the segmentation of the blood vessel region.

[0004] Taking the Localizing Region (LR) model proposed by Lankton et al. (S. Lankton and A. Tannenbaum, Localizing Region-Based Active Contours, in IEEE Transactions on Image Processing, vol.17, no.11, pp.2029-2039, Nov.2008.) as an example, its energy functional representation is as follows:

[0005]

[0006]

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[0008]

[0009]

[0010] Here, F is a certain internal energy term, representing the rule followed by each point on the contour curve under a certain model. Classical segmentation models such as UM (Uniform Modeling) energy and MS (Mean Separation) energy can be selected. B(x,y) is a piecewise function used to mask the local region Ω and multiplied by a regularized impulse function. This ensures that only the contribution of points near the contour is considered in the model evolution. ε represents a parameter that controls the effective width. This is the internal force term of the curve, used to ensure the smoothness of the evolution curve. It is a regularized step function. By using a level set function to ensure the free topological transformation of the curve, it can be well applied to the extraction and segmentation of irregular and multi-target objects. At the same time, it has a solid and sufficient mathematical theory as support, can be well integrated with other knowledge, and has good scalability.

[0011] However, vascular images are mostly low-contrast and non-uniform, while local active contour models only consider local region information of the image. When dealing with low-contrast regions, they are prone to oversegmentation and undersegmentation, resulting in low segmentation accuracy. At the same time, the calculation needs to be performed for each local region, which makes the method computationally intensive. Furthermore, local active contour models are sensitive to the initial contour and model parameter settings, resulting in poor applicability. Summary of the Invention

[0012] The purpose of this invention is to provide a blood vessel segmentation method and device based on shape constraints and edge indicator functions, which can effectively improve segmentation accuracy while reducing the computational load of the model.

[0013] This invention provides a blood vessel segmentation method based on shape constraints and an improved edge indicator function, comprising the following steps: S1: acquiring a blood vessel image and performing noise reduction processing on the blood vessel image to obtain a blood vessel image to be segmented; S2: preprocessing the blood vessel image to be segmented using a thresholded multi-scale Frangi filter method to obtain an initial contour; S3: acquiring a local active contour model, and constructing an adaptive prior constraint term, an adaptive edge indicator function, a length regularization term, and a data fitting term for the local active contour model based on the initial contour; S4: acquiring an LR model using UM internal energy, and obtaining a fusion model based on TM-Frangi filtering based on the LR model using UM internal energy, the adaptive prior constraint term, the adaptive edge indicator function, the length regularization term, and the data fitting term of the local active contour model; S5: solving the fusion model based on TM-Frangi filtering using a variational method and a gradient descent flow method to obtain a final evolution curve; S6: obtaining the segmentation result based on the final evolution curve and the blood vessel image.

[0014] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described improved blood vessel segmentation method based on shape constraints and edge indicator functions.

[0015] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the above-described improved blood vessel segmentation method based on shape constraints and edge indicator functions.

[0016] The improved blood vessel segmentation method and device based on shape constraints and edge indicator functions provided by this invention have the following beneficial effects:

[0017] 1. Proposing an edge indication function with better indication effect: Under the two conditions of satisfying the monotonically decreasing edge indication function and the function being 0 when the independent variable tends to ∞, this invention proposes an edge indication function constructed with the negative logarithmic function as the main body, which has a more prominent change effect, and achieves better indication effect. Furthermore, regional information is introduced into it to obtain an adaptive edge indication function that integrates regional information, which can adaptively adjust the weights in different regions of the image, thereby better improving the edge indication capability;

[0018] 2. Improved multi-scale Frangi filtering: This invention obtains a better enhanced blood vessel image by using thresholded multi-scale Frangi filtering (TM-Frangi filtering) and uses TM-Frangi filtering to coarsely extract blood vessel images, and uses the coarse extraction results as the initial contour and prior information for subsequent evolution.

[0019] 3. Introducing improved shape prior constraint information: Based on the traditional prior constraint terms, this invention constructs an adaptive prior weight by the difference between the local mean inside the evolution curve and the local mean inside the prior curve. This weight has a larger value when the curve deviates from the prior curve, which pushes the curve to the position of the prior shape quickly. When the curve is near the prior shape, the weight decreases, thereby improving blood vessel segmentation. Attached Figure Description

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0021] Figure 1 This is a flowchart of the improved blood vessel segmentation method based on shape constraints and edge indicator functions provided by the present invention;

[0022] Figure 2 This is a schematic diagram of the processing procedure of the improved blood vessel segmentation method based on shape constraints and edge indicator functions provided by the present invention;

[0023] Figure 3 This is a diagram of the blood vessel image and its multi-scale Frangi filtering processing results provided by the present invention;

[0024] Figure 4This is a diagram of a blood vessel image and its thresholding processing result provided by the present invention;

[0025] Figure 5 This is a statistical diagram of the area of ​​each connected region in the thresholded blood vessel image provided by the present invention;

[0026] Figure 6 This is a vascular enhancement image provided by the present invention;

[0027] Figure 7 This invention provides a priori shape curve obtained by edge extraction of a blood vessel enhancement image.

[0028] Figure 8 This is a prior curve obtained on different vascular images using the adaptive weight parameters of the prior terms provided by this invention.

[0029] Figure 9 This is a comparison diagram of different edge indicator functions and their corresponding influence functions provided by the present invention;

[0030] Figure 10 This is a comparison chart of the changes in different edge stopping functions and gradient magnitude thresholds provided by this invention;

[0031] Figure 11 This is a comparison chart showing the indicative effects of different threshold parameters provided by this invention on blood vessel images;

[0032] Figure 12 This is a comparison chart of the segmentation results of various models provided by this invention on blood vessel images;

[0033] Figure 13 This is a comparison chart of the average Dice coefficients and average VOE coefficients of each model provided by the present invention;

[0034] Figure 14 This is a comparison chart of the average computation time and average number of iterations for each model provided by this invention;

[0035] Figure 15 The segmentation results are obtained by setting the parameter ν provided by this invention to 0.01-0.06 respectively;

[0036] Figure 16 This is a structural block diagram of the computer device provided by the present invention. Detailed Implementation

[0037] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0038] Figure 1A schematic diagram of the improved blood vessel segmentation method based on shape constraints and edge indicator functions according to this embodiment is shown. The improved blood vessel segmentation method based on shape constraints and edge indicator functions in this embodiment includes the following steps:

[0039] S1: Acquire a blood vessel image, perform noise reduction processing on the blood vessel image to obtain the blood vessel image to be segmented;

[0040] Specifically, the above-mentioned noise reduction processing can be implemented by Gaussian filtering or median filtering;

[0041] S2: Based on the blood vessel image to be segmented, the initial contour is obtained by preprocessing using the thresholded multi-scale Frangi filtering method.

[0042] Specifically, step S2 of the improved blood vessel segmentation method based on shape constraints and edge indicator functions includes the following steps: S21: Based on the blood vessel image to be segmented, a multi-scale Frangi filter enhancement image is obtained using the multi-scale Frangi filter method; S22: According to a preset segmentation threshold, the multi-scale Frangi filter enhancement image is subjected to threshold segmentation and binarization to obtain a threshold processing result; S23: The threshold processing result is labeled using an eight-neighbor connection method to obtain a labeled image; connected regions in the labeled image whose area is less than a preset area threshold are filtered out to obtain a blood vessel enhancement image; S24: Edge extraction is performed on the blood vessel enhancement image to obtain an initial contour, which is used as a priori shape curve;

[0043] S3: Obtain the local activity contour model, and construct the adaptive prior constraint term, adaptive edge indicator function, length regularization term and data fitting term of the local activity contour model based on the initial contour.

[0044] Specifically, step S3 of the above-mentioned improved blood vessel segmentation method based on shape constraints and edge indicator functions includes the following steps: S31: Obtain a local active contour model, and construct an adaptive prior constraint term for the local active contour model based on the initial contour, as shown in the formula:

[0045]

[0046]

[0047]

[0048]

[0049] in, For adaptive prior constraints, The level set function corresponding to the evolution curve. Let Ω be the level set function corresponding to the prior shape curve, and Ω be the image domain. y For the local image domain, H ε (·) is the regularized step function. This indicates the shape formed by the evolution curves. Let represent the prior shape formed by the evolution curve, η be the adaptive weight parameter of the prior term, exp[] be the natural exponent, m be the length of the image, n be the width of the image, and s be the length of the image. ij Let t be the element in the i-th row and j-th column of the local gray-level mean matrix calculated under the current evolution curve. ij Let S be the element in the i-th row and j-th column of the local gray-level mean matrix calculated under the prior curve, S be the local gray-level mean matrix calculated under the current evolution curve, T be the local gray-level mean matrix calculated under the prior curve, B(x,y) be the piecewise function, and I be the blood vessel gray-level image.

[0050] S32: An adaptive edge indicator function for constructing a local activity contour model, as shown in the formula:

[0051]

[0052]

[0053]

[0054] Where g is an adaptive edge indicator function based on a logarithmic function, ω is an adjustment parameter used to adjust the indication range of the indicator function, C is the normalized smooth image gradient matrix, L is the gradient magnitude threshold, and c ij Let be the element in the i-th row and j-th column of matrix C, and let κ be the local minimum. For the gradient operator, G σ Let I be the Gaussian kernel function, I be the grayscale image of the blood vessel, max(.) be the maximum value function, |.| be the absolute value, θ be a constant controlling the noise sensitivity, c1 be the mean grayscale value of the curve inside the grayscale image of the blood vessel, c2 be the mean grayscale value of the curve outside the grayscale image of the blood vessel, and ζ be a constant controlling the convergence speed of the curve.

[0055] S33: Length regularization term for constructing the local activity profile model;

[0056] S34: Data fitting terms for constructing the local activity contour model, as shown in the formula:

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] in, For data fitting terms, Let Ω be the regularized impulse function, and Ω be the image domain. y Let B(x,y) be a piecewise function in the local image domain, and F be the internal energy term. UM For the internal energy term using UM (Uniform Modeling) energy, H ε (.) represents the regularized step function, I is the grayscale image of the blood vessel, s1 is the local grayscale mean of the curve inside the blood vessel grayscale image, and s2 is the local grayscale mean of the curve outside the blood vessel grayscale image. ε is the regularized impulse function, and ε is a parameter that controls the effective width of the regularized impulse function;

[0063] Specifically, step S33 of the above-mentioned improved blood vessel segmentation method based on shape constraints and edge indicator functions includes: constructing a length regularization term for the local active contour model, as shown in the formula:

[0064]

[0065]

[0066] in, For length regularization terms, Let Ω be the level set function, and Ω be the image domain. For gradient operators, H is a step function. ε (.) is the regularized step function, and ε is the control function. The parameter for effective width;

[0067] S4: Obtain the LR model using UM internal energy. Based on the adaptive prior constraint term, adaptive edge indicator function, length regularization term and data fitting term of the LR model using UM internal energy and the local active contour model, obtain the fusion model based on TM-Frangi filtering.

[0068] Specifically, step S4 of the above-mentioned improved blood vessel segmentation method based on shape constraints and edge indicator functions includes: obtaining an LR model using UM internal energy; and obtaining a fusion model based on TM-Frangi filtering, as shown in the formula, based on the adaptive prior constraint term, adaptive edge indicator function, length regularization term, and data fitting term of the LR model using UM internal energy and the local active contour model.

[0069]

[0070]

[0071]

[0072] in, This is a fusion model based on TM-Frangi filtering, where ν is the weight parameter of the local term and g is the adaptive edge indicator function. Here is the regularized impulse function. For local data fitting, For adaptive prior constraints, Here, Ω represents the length regularization term, Ω represents the local image domain, B(x,y) is the piecewise function, and H... ε (.) represents the regularized step function, I is the grayscale image of the blood vessel, s1 is the local grayscale mean of the curve inside the blood vessel grayscale image, and s2 is the local grayscale mean of the curve outside the blood vessel grayscale image. For gradient operators;

[0073] S5: Using variational method and gradient descent flow method, solve the fusion model based on TM-Frangi filter to obtain the final evolution curve;

[0074] Specifically, step S5 of the above-mentioned improved blood vessel segmentation method based on shape constraints and edge indicator functions includes: S51: Based on the fusion model based on TM-Frangi filtering, the gradient descent flow equation is obtained using the variational method, and the fusion model based on TM-Frangi filtering is numerically calculated using the finite difference upwind form to obtain the discretized iterative formula of the gradient descent flow equation; S52: Based on the discretized iterative formula of the gradient descent flow equation, the evolution curve of each iteration is obtained; when the difference between the evolution curves of two adjacent iterations is greater than a preset threshold, the process returns to step S3; when the difference between the evolution curves of two adjacent iterations is not greater than the preset threshold, the final evolution curve is obtained;

[0075] Specifically, step S51 of the above-mentioned improved blood vessel segmentation method based on shape constraints and edge indicator functions includes: obtaining the gradient descent flow equation using a variational method based on the fusion model based on TM-Frangi filtering, and performing numerical calculations on the fusion model based on TM-Frangi filtering using a finite difference upwind form to obtain the discretized iterative formula of the gradient descent flow equation, as shown in the formula:

[0076]

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[0080]

[0081]

[0082]

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[0085]

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[0089] in, The level set function corresponding to the evolution curve. This is a fusion model based on TM-Frangi filtering, where g is an adaptive edge indicator function. Here, is the regularized impulse function, and div(.) is the divergence function. Here, ν is the gradient operator, μ1 is the data fitting term inside the curve, μ2 is the data fitting term outside the curve, η is the adaptive weight parameter of the prior term of the LR model, and H is the gradient operator. ε (.) represents the regularized step function. Let Ω be the level set function corresponding to the prior shape curve. y Let B(x,y) be the piecewise function, I be the grayscale image of the blood vessel, s1 be the local grayscale mean of the curve inside the grayscale image of the blood vessel, s2 be the local grayscale mean of the curve outside the grayscale image of the blood vessel, and D1 be the discrete scheme of the divergence operator combining forward and backward differences in the x-direction. This indicates backward difference, where h represents the distance between grid points. Indicates forward difference, For the nth iteration S1 is Discrete scheme combining forward difference and central difference in the x-direction. D2 represents the central difference, and is a discrete scheme combining forward and backward differences in the y-direction using the divergence operator. Indicates backward difference, Indicates forward difference, S2 is Discrete scheme combining forward difference and central difference in the y-direction. This represents the central difference, where n is the nth iteration, Δt is the iteration step size, and g i,j It is an adaptive gradient indicator function;

[0090] S6: Obtain the segmentation result based on the final evolution curve and blood vessel image.

[0091] In some embodiments, the above-described improved blood vessel segmentation method based on shape constraints and edge indicator functions can also be implemented in the following ways.

[0092] like Figure 2 This is a schematic diagram of a blood vessel segmentation method improved based on shape constraints and edge indicator functions. In this embodiment, the blood vessel segmentation method improved based on shape constraints and edge indicator functions includes the following steps:

[0093] (S1) Input image

[0094] The input image is used to read the blood vessel image for subsequent segmentation processing. When the image is noisy, Gaussian filtering or median filtering can be used to reduce noise and facilitate subsequent image processing.

[0095] (S2) Preprocess the image using TM-Frangi and obtain the initial contour from it.

[0096] S2.1 Multiscale Frangi Filter

[0097] Depend on Figure 3 It can be seen that although multi-scale Frangi filtering can enhance images of blood vessels of different thicknesses, impurities in the background are inevitably enhanced at the same time, making it unsuitable for direct use in the construction of prior terms and the extraction of contours.

[0098] S2.2 TM-Frangi Filtering and Initial Contour Acquisition

[0099] By comparing the gray-level histograms of the multi-scale Frangi filter enhancement images, it can be seen that the gray-level value of the vascular region usually reaches above 0.8, while the gray-level value of tubular impurities in the background region is often lower than this value. Therefore, threshold segmentation can be performed on the multi-scale Frangi filter first, defining the segmentation threshold as 0.8 and performing binarization processing, thus obtaining the following results: Figure 4 The result.

[0100] The threshold processing results are labeled using an eight-neighbor connection method, and the area of ​​each connected region is statistically analyzed. Figure 4 Taking image (1) as an example, the results are as follows: Figure 5 As shown in the figure. For ease of display, only connected components with an area of ​​20 or more are counted in the figure.

[0101] In this embodiment, the area threshold is set to 100.

[0102] By processing the image using the TM-Frangi filtering method described above, a more accurate vascular enhancement map F can be obtained, such as... Figure 6 As shown.

[0103] Edge extraction is performed on F, which serves as the initial contour and prior shape curve for the segmentation process. like Figure 7 As shown.

[0104] (S3) Construct adaptive prior constraint terms, adaptive edge indicator functions, length regularization terms, and data fitting terms;

[0105] (S31) Adaptive prior constraint terms

[0106] A prior constraint term that can adaptively adjust prior weights is proposed, as shown in Equation (3.2).

[0107]

[0108] In the formula, H ε (·) is the regularized step function. and Let represent the shape formed by the evolution curve and the prior shape, respectively; η is the adaptive weight parameter of the prior term, defined as follows:

[0109]

[0110] Where m and n are the length and width of the image, s ij Let t be an element in the local gray-level mean matrix S calculated under the current evolution curve. ij The elements in the local gray-level mean matrix T calculated under the prior curve are shown below:

[0111]

[0112]

[0113] pass Figure 8 The effect of the adaptive parameter η can be clearly seen from Table 1.

[0114] Table 1 Values ​​of parameter η under different images

[0115]

[0116] from Figure 8 As shown in Table 1, the adaptive weight parameters proposed in this embodiment have an impact on curve evolution:

[0117] (S32) Adaptive edge indicator function

[0118] Commonly used indicator functions are shown below:

[0119]

[0120]

[0121]

[0122] The existing comparison method quantizes and compares the proposed edge indicator functions, limiting the maximum value of each g to 1. The comparison results are as follows: Figure 9 As shown. Among them, This is the influence function.

[0123] For the image after Gaussian filtering, the edge indication function proposed in this embodiment is defined as follows:

[0124]

[0125]

[0126] Where C is the normalized smooth gradient matrix, c ij Let κ be an element in matrix C, and let κ be a local minimum.

[0127] To further improve the indication effect, an adaptive edge indication function based on a logarithmic function is proposed:

[0128]

[0129]

[0130]

[0131] Where γ is the adjustment parameter. When the evolution curve is far from the target edge, the value of L will be much greater than ζ, and g will take a larger value. The edge indicator function will drive the curve to evolve rapidly. When the curve is at the target boundary, L≈ζ. At this time, the image gradient value is larger, so g will take a smaller value, which allows for a fine segmentation process.

[0132] Indicator functions:

[0133]

[0134]

[0135] like Figure 10The image shows a comparison of the changes in different edge stopping functions and gradient magnitude thresholds provided by this invention. Based on the comparison method in the prior art, g1, g2, and g are quantized and compared, and the changes in the edge stopping function and gradient magnitude threshold L are plotted, as shown below. Figure 11 As shown.

[0136] The indicative effect of g on blood vessel images in this embodiment is compared with g2 and g0 (i.e., the edge indicator function proposed in Equation 3.10) with a constant gradient magnitude threshold parameter. The results are as follows: Figure 12 As shown.

[0137] (S33), Length regularization term

[0138] The curve C(s) can be represented as a time-dependent function: C(s,t), where s represents the parameters of the curve, typically taking values ​​[0,1], and t is a non-negative number representing the evolution time of the curve. The energy functional E(C) of the curve can be expressed using loop integration:

[0139]

[0140] By using the variational level set method, a level set function is introduced. as well as The way to transform E(C) into about Energy functional And obtain about through variational methods The partial differential equation.

[0141] This method defines a special function called Heaviside:

[0142]

[0143] And there are:

[0144]

[0145] In this way, the energy functional (3.17) of the curve can be rewritten as a surface integral in the image domain Ω:

[0146]

[0147] The energy functional of the area positioning model can then be rewritten as a function of the level set. Format:

[0148]

[0149] For ease of practical calculation, it is usually... and Use regularization and Approximately expressed as:

[0150]

[0151]

[0152] The parameter ε is used to control The effective width.

[0153] (S34), Data Fitting Term

[0154] When using UM energy as the internal energy term:

[0155]

[0156] Where s1 and s2 are represented as:

[0157]

[0158]

[0159] (S4) Fusion Model

[0160] For the LR model using UM internal energy:

[0161]

[0162]

[0163]

[0164] Combining the shape prior E in (3.2) above... Auto-Shape In addition to the edge indicator function g in (3.12), the fusion model FPLRE based on TM-Frangi filtering is proposed:

[0165]

[0166] Where ν and η are the adaptive weight parameters of the local term and prior term of the LR model, respectively.

[0167] Fusion models can systematically consider region information, edge information, and prior information, thus achieving higher segmentation accuracy.

[0168] (S5) Solve the model using variational methods and gradient descent flow methods, and determine whether the cutoff condition has been met.

[0169] The gradient descent flow equation obtained through variational method is as follows:

[0170]

[0171]

[0172] Numerical calculations of the FPLRE model using the finite difference upwind form yield the discretized iterative equation of the gradient descent flow equation:

[0173]

[0174]

[0175]

[0176]

[0177]

[0178] Where n is the nth iteration; h represents the distance between grid points; Δt is the iteration step size, used to control the speed of curve evolution: when Δt takes a small value, the curve evolution speed is slow and the iteration efficiency is low; when Δt takes a large value, the curve is prone to oscillation at the edge or directly crosses the target edge.

[0179] The central difference is represented and calculated as follows:

[0180]

[0181]

[0182] Indicates forward difference, Indicates backward difference, The calculation is as follows:

[0183]

[0184]

[0185] The calculation is as follows:

[0186]

[0187]

[0188] The result of the judgment Does the deadline condition S meet? If satisfied, output the result. Otherwise, recalculate S31-S34.

[0189] (S6) Output the segmentation result

[0190] Will As a segmentation result, it is usually displayed above the blood vessel image to visually show the state of the blood vessel outline.

[0191] Results after implementation:

[0192] Experimental environment:

[0193] The hardware conditions for the experiment of this invention are: HP Pavilion Laptop 15-cc5xx, Intel(R) Core(TM) i5-7200U CPU@2.50GHz 2.71GHz, NVIDIA GeForce 940MX GPU, 8.00GB RAM; the software environment for implementing the active contour model is: Matlab R2021a.

[0194] Evaluation indicators:

[0195] Objective evaluation metrics for segmentation accuracy include the Dice (Dice similarity coefficient) and the VOE (Volumetric Overlap Error) coefficient, which are used to measure the quality of the segmentation results.

[0196] Parameter settings:

[0197] In the FPLRE model, the fixed parameters are set as follows:

[0198] In formulas (2.4) and (2.5), the parameter ε = 1; the scale range of the multi-scale Frangi filter is (0.5, 2.5); in formulas (3.6) and (3.10), K = 1 and κ = 0.01. The iteration cutoff condition S is set to 0.1; in formulas (3.34)-(3.37), the grid point distance h = 1, and in formula (3.38), the iteration step size Δt = 1.

[0199] The dynamic parameter ν needs to be adjusted according to different images to obtain the best segmentation result. Its value is within a range. For the FPLRE model, ν can be approximately 0.01-0.06. For the dynamic parameter ν in Table 2, the values ​​given in the table are the optimal values, but other values ​​can also produce approximate segmentation results, with only slight differences in details.

[0200] Table 2 shows the dynamic parameter settings for different experimental images in the FPLRE model.

[0201]

[0202] Blood vessel image segmentation experiment:

[0203] This embodiment selects Figure 12 A segmentation experiment was conducted on the blood vessel image in (a). The segmentation results of the FPLRE model proposed in this embodiment were compared with those of TM-Frangi filtering, LR model, CVXB model, U-Net model, ABC model, HLFRA model, and GLMF model on the above blood vessel image. The results are as follows: Figure 12 As shown; the average segmentation accuracy and computational efficiency of various models are presented in the form of a bar chart. Figure 13 and Figure 14 middle;

[0204] FPLRE model analysis:

[0205] For the FPLRE model, it ranked first in the average of both accuracy evaluation metrics, demonstrating good segmentation results. Furthermore, the FPLRE model showed a more significant improvement in computational efficiency. On the other hand, the FPLRE model incorporates TM-Frangi information as prior information into the LR model, making model adjustment more flexible and easier to select the parameter ν for the data fitting term. Even when ν is set to different values ​​within the parameter range, the model's segmentation accuracy does not change significantly. Using Image2 as the experimental image, setting the parameter ν to 0.01-0.06 yielded the following results: Figure 15 The segmentation results are shown in Table 3. The Dice coefficients of the segmentation results under each parameter are listed in Table 3.

[0206] Table 3 Dice values ​​under different parameters

[0207]

[0208]

[0209] Subjective evaluations and Dice coefficients show that, within the parameter value range, the model maintains high segmentation accuracy, with a maximum difference in accuracy of only 0.7%. Figure 12 As shown in (c), the prior information obtained by TM-Frangi filtering is relatively reliable, so the overall image segmentation accuracy is high. Even the lower segmentation accuracy of 90.26% is higher than that of the LR model of 90.14%.

[0210] In summary, the FPLRE model proposed in this invention provides more flexible adjustment space for parameter ν while ensuring high segmentation accuracy and computational efficiency. Furthermore, the model can accommodate various types of prior information, exhibiting excellent scalability. However, from another perspective, the segmentation results of this invention depend to some extent on the accuracy of the prior information. Therefore, selecting appropriate prior information is crucial for this invention.

[0211] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the improved blood vessel segmentation method based on shape constraints and edge indicator functions described above. The storage medium may be a magnetic disk, optical disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk drive (HDD), or solid-state drive (SSD), etc.; the storage medium may also include combinations of the above types of memory.

[0212] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the improved blood vessel segmentation method based on shape constraints and edge indicator functions described above.

[0213] like Figure 16As shown, the computer device may include: at least one processor 121, such as a CPU (Central Processing Unit), at least one communication interface 123, memory 124, and at least one communication bus 122. The communication bus 122 is used to enable communication between these components. The communication interface 123 may include a display screen and a keyboard; optionally, the communication interface 123 may also include a standard wired interface or a wireless interface. The memory 124 may be high-speed RAM (Random Access Memory) or non-volatile memory, such as at least one disk drive. Optionally, the memory 124 may also be at least one storage device located remotely from the processor 121. The memory 124 stores application programs, and the processor 121 calls the program code stored in the memory 124 to execute any of the above-described method steps. The communication bus 122 may be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus, etc. The communication bus 122 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 16The term 124 is represented by a single line, but this does not imply a single bus or a single type of bus. The memory 124 may include volatile memory, such as random-access memory (RAM); it may also include non-volatile memory, such as flash memory, hard disk drive (HDD), or solid-state drive (SSD); or a combination of the above types of memory. The processor 121 may be a central processing unit (CPU), a network processor (NP), or a combination of a CPU and an NP. The processor 121 may further include a hardware chip. This hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The aforementioned PLD can be a complex programmable logic device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL), or any combination thereof. Optionally, the memory 124 is also used to store program instructions. The processor 121 can call the program instructions to implement the improved blood vessel segmentation method based on shape constraints and edge indication functions as described in this embodiment.

[0214] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A blood vessel segmentation method based on shape constraints and edge indicator functions, characterized in that, Includes the following steps: S1: Acquire a blood vessel image, and perform noise reduction processing on the blood vessel image to obtain a blood vessel image to be segmented; S2: Based on the blood vessel image to be segmented, use TM The Frangi filtering method is used for preprocessing to obtain the initial contour; S3: Obtain the local activity contour model, and construct the adaptive prior constraint term, adaptive edge indicator function, length regularization term and data fitting term of the local activity contour model based on the initial contour. S4: Obtain the LR model using UM internal energy. Based on the LR model using UM internal energy, the adaptive prior constraint term, adaptive edge indicator function, length regularization term, and data fitting term of the local active contour model, obtain the TM-based model. The fusion model of Frangi filtering is shown in the formula: in, For TM-based Frangi filtering fusion model Let g be the weight parameter of the local term, and g be the adaptive edge indicator function. Here is the regularized impulse function. For local data fitting, For adaptive prior constraints, Here, Ω represents the length regularization term, and Ω represents the image domain. It is a piecewise function. Let be the regularized step function, I be the grayscale image of the blood vessel, s1 be the local grayscale mean of the curve inside the grayscale image of the blood vessel, and s2 be the local grayscale mean of the curve outside the grayscale image of the blood vessel. For gradient operators; S5: Using variational methods and gradient descent flow methods, the TM-based... The final evolution curve is obtained by solving the fusion model of Frangi filtering; S6: Based on the final evolution curve and the blood vessel image, obtain the segmentation result.

2. The improved blood vessel segmentation method based on shape constraints and edge indicator functions according to claim 1, characterized in that, Step S2 includes the following steps: S21: Based on the blood vessel image to be segmented, use TM The Frangi filtering method is used to obtain multi-scale Frangi filter enhancement maps. S22: According to the preset segmentation threshold, the multi-scale Fragi filter enhancement image is subjected to threshold segmentation and binarization to obtain the threshold processing result; S23: The threshold processing result is marked using an eight-neighbor connection method to obtain a marked image; connected regions in the marked image whose area is less than a preset area threshold are filtered out to obtain a blood vessel enhancement image; S24: Extract the edges of the enhanced blood vessel image to obtain an initial contour, which is used as a priori shape curve.

3. The improved blood vessel segmentation method based on shape constraints and edge indicator functions according to claim 1, characterized in that, Step S3 includes the following steps: S31: Obtain the local activity contour model. Based on the initial contour, construct adaptive prior constraints for the local activity contour model, as shown in the formula: in, For adaptive prior constraints, The level set function corresponding to the evolution curve. Let Ω be the level set function corresponding to the prior shape curve, and let Ω be the image domain. For local image domain, For regularized step functions, η Here, exp[] represents the adaptive weight parameters for the prior terms, and exp[] represents the natural exponent. m The length of the image. n The width of the image. This refers to the element in the i-th row and j-th column of the local gray-level mean matrix calculated under the current evolution curve. Let be the element in the i-th row and j-th column of the local gray-level mean matrix calculated under the prior curve. S This is the local gray-level mean matrix calculated under the current evolution curve. T This is the local gray-level mean matrix calculated under the prior curve. It is a piecewise function. This is a grayscale image of blood vessels. S32: An adaptive edge indicator function for constructing a local activity contour model, as shown in the formula: Where g is an adaptive edge indicator function based on a logarithmic function. The parameters are used to adjust the indication range of the indicator function. The normalized smooth image gradient matrix, The gradient magnitude threshold, For matrix The element in the i-th row and j-th column, It is the minimum value. For gradient operators, For Gaussian kernel function, For a grayscale image of blood vessels, max(.) is the maximum value function, and |.| is the absolute value. To control the constant of noise sensitivity, This represents the mean gray level of the curve within the blood vessel grayscale image. This represents the mean gray level of the curve outside the blood vessel grayscale image. A constant used to control the convergence rate of the curve; S33: Length regularization term for constructing the local activity profile model; S34: Data fitting terms for constructing the local activity contour model, as shown in the formula: in, For local data fitting, The impulse function is a regularized function. For the image domain, For local image domain, It is a piecewise function, F is the internal energy term, F UM For the internal energy term using UM (Uniform Modeling) energy, Let be the regularized step function, I be the grayscale image of the blood vessel, s1 be the local grayscale mean of the curve inside the grayscale image of the blood vessel, and s2 be the local grayscale mean of the curve outside the grayscale image of the blood vessel. ε is the regularized impulse function, and ε is a parameter that controls the effective width.

4. The improved blood vessel segmentation method based on shape constraints and edge indicator functions according to claim 3, characterized in that, Step S33 specifically includes: constructing a length regularization term for the local activity contour model, as shown in the formula: in, For length regularization terms, For level set functions, For the image domain, For gradient operators, It is a step function. ε is the regularized step function, and ε is a parameter that controls the effective width.

5. The improved blood vessel segmentation method based on shape constraints and edge indicator functions according to claim 1, characterized in that, Step S5 includes: S51: According to the TM-based The Frangi filter fusion model uses variational methods to derive the gradient descent flow equation, and employs a finite difference upwind form to apply the TM-based... The Frangi filter fusion model is numerically calculated to obtain the discretized iterative form of the gradient descent flow equation; S52: Based on the discretized iterative formula of the gradient descent flow equation, obtain the evolution curve for each iteration; when the difference between the evolution curves of two adjacent iterations is greater than a preset threshold, return to step S3; when the difference between the evolution curves of two adjacent iterations is not greater than the preset threshold, obtain the final evolution curve.

6. The improved blood vessel segmentation method based on shape constraints and edge indicator functions according to claim 1, characterized in that, Step S51 specifically includes: according to the TM-based... The Frangi filter fusion model uses variational methods to derive the gradient descent flow equation, and employs a finite difference upwind form to apply the TM-based... The Frangi filter fusion model is numerically calculated to obtain the discretized iterative form of the gradient descent flow equation, as shown in the formula: in, The level set function corresponding to the evolution curve. For TM-based The Frangi filtering fusion model, where g is the adaptive edge indicator function. Here, is the regularized impulse function, and div(.) is the divergence function. For gradient operators, Here, μ1 represents the weight parameters of the local term in the LR model, μ2 represents the data fitting term inside the curve, and μ1 represents the data fitting term outside the curve. These are the adaptive weight parameters for the prior terms of the LR model. For regularized step functions, Let Ω be the level set function corresponding to the prior shape curve. y For local image domain, Let be a piecewise function, where I is the grayscale image of the blood vessel, s1 is the local mean grayscale value of the curve inside the grayscale image of the blood vessel, and s2 is the local mean grayscale value of the curve outside the grayscale image of the blood vessel. This is a discrete scheme combining forward and backward differences of the divergence operator in the x-direction. Indicates backward difference, h Indicates the distance between grid points. Indicates forward difference, For the nth iteration S1 is Discrete scheme combining forward difference and central difference in the x-direction. Indicates central difference. This is a discrete scheme combining forward and backward differences of the divergence operator in the y-direction. Indicates backward difference, Indicates forward difference, S2 is Discrete scheme combining forward difference and central difference in the y-direction. Indicates central difference. n For the nth iteration, The iteration step size, This is the adaptive gradient indicator function.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the improved blood vessel segmentation method based on shape constraints and edge indicator functions as described in any of claims 1-6.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the improved blood vessel segmentation method based on shape constraints and edge indicator functions as described in any one of claims 1-6.

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