CN113570555B - Two-dimensional segmentation method of multi-threshold medical image based on improved grasshopper algorithm - Google Patents
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Abstract
A two-dimensional segmentation method of a multi-threshold medical image based on an improved grasshopper algorithm comprises the following steps: step 8: based on the first position updating of grasshoppers, the position updating of each grasshopper is performed again according to the position updating method of the triangle replacement strategy; step 9: based on the updated grasshopper population, the cauchy variation is carried out on the population individuals, and the local development is increased; step 10: checking whether the iteration termination condition is met, if so, executing the step 11, otherwise, returning to the step 5 to continue iteration; step 11: returning the optimal grasshopper position and the fitness value as an optimal threshold value and a maximum Kapur entropy; step 12: and dividing the medical image by using the obtained optimal threshold value. According to the invention, the triangular substitution strategy and the cauchy variation are adopted, so that the grasshopper algorithm searching capability and optimization precision can be improved, the situation that local optimization is involved in the segmentation process is avoided, and the segmentation quality of medical images can be improved.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to a two-dimensional segmentation method of a multi-threshold medical image based on an improved grasshopper algorithm.
Background
The recognition and understanding of images are core technologies of modern medical imaging equipment, wherein the recognition and understanding of images are mostly dependent on the quality of image segmentation. Image segmentation, which is a classical problem in computer vision research and has become a focus of attention in the field of image understanding, is the first step of image analysis, is the basis of computer vision, is an important component of image understanding, and is one of the most difficult problems in image processing. Therefore, a segmentation method capable of obtaining a high quality segmentation result is particularly important.
In recent years, various image segmentation techniques have been proposed, in which a multi-threshold image segmentation technique is a very simple and efficient method, the core of which is the selection of a threshold value, which enables a more outstanding segmentation effect to be obtained. It is well known that the conventional gradient method can obtain a segmentation threshold, but the method has large computational complexity and the quality of the obtained segmentation threshold is poor.
Among various multi-threshold image segmentation methods, a histogram-based image segmentation method is one of the most commonly used methods. Image segmentation based on a histogram is mainly divided into a one-dimensional histogram and a two-dimensional histogram, wherein the one-dimensional histogram cannot effectively utilize spatial information of an image, and the segmentation is easy to be interfered by noise. Accordingly, abutaleb proposes a multi-threshold image segmentation method based on a two-dimensional histogram, which combines the original gray values with the local average of the pixels. However, when a two-dimensional histogram is applied to multi-threshold image segmentation, if the exhaustion method is directly adopted to find the optimal threshold, the computational complexity of the segmentation is very high. To effectively avoid this phenomenon, many researchers apply swarm intelligence algorithms to assist in finding the optimal threshold and achieve significant results. However, the method proposed by Abutaleb for image segmentation is a way of using local means, which does not take into account certain details of the picture, such as certain points and edges.
The non-local mean value is a new denoising technology which is proposed by Buades and the like in recent years, fully utilizes redundant information in an image, and maximally reflects the detail characteristics of the image while denoising. The basic idea is that the estimate of the current pixel is obtained by a weighted average of the values of pixels in the image that have a similar neighborhood structure. Assuming that I (p) and I (q) are gray values for pixels p and q in image I, a non-local average of image I can be calculated from Eq. (1) -Eq. (4).
Where O (p) is a filtered value of the non-local average, μ (p) and μ (q) are local averages, σ is a standard deviation, ω (p, q) is the weights of pixel p and pixel q, and L (p) and L (q) are m pixel blocks centered on pixel p and pixel q, respectively.
As shown in fig. 1, by the non-local mean image and the gray scale image, a corresponding non-local mean two-dimensional histogram may be generated. Assuming that the gray value level of the original gray image I (x, y) is [0, l-1] and the image size is mxn, the gray value level of the generated non-local mean image g (x, y) is also [0, l-1] and the image size is mxn. Then, a preliminary two-dimensional histogram can be formed from I (x, y) and g (x, y). If the point (I, j) is formed by I (X, y) and g (X, y), where I represents the pixel value of a certain pixel in I (X, y) and j represents the pixel value of a certain pixel in g (X, y). H (i, j) represents the number of times point (i, j) appears on the gray value vector (s, t). Thus, the joint probability density of the point (i, j) is obtained by Eq. (5), and a final two-dimensional histogram can be obtained.
According to the definition of the non-local mean two-dimensional histogram described above, a corresponding two-dimensional plane histogram is given in FIG. 1, where { t } 1 ，t 2 …, L-1} represents a gray scale imageOf { s }, a value of 1 ，s 2 …, L-1} represents the value of the non-local mean image. In the two-dimensional histogram, the main diagonal contains the largest amount of image information, and therefore only Kapur entropy of n sub-regions on the main diagonal is calculated, which can be defined as Eq. (6).
Wherein,
taking the entropy of Kapur as an objective function, then find the cause based on grasshopper optimization algorithmMaximized threshold set { t } 1 ，t 2 ，...，t n-1 ]Then the optimal segmentation threshold is considered.
However, in the process of searching the optimal segmentation threshold, the grasshopper optimization algorithm is unbalanced in exploration and development, so that the situation of local optimization is easy to occur and fall into, and the segmentation quality of the final medical image is low.
Therefore, there is an urgent need to study a two-dimensional segmentation method of multi-threshold medical images based on an improved grasshopper algorithm to obtain better image segmentation quality.
Disclosure of Invention
In order to solve one or more problems in the prior art, the applicant finds that, through research, the search capability and optimization accuracy of grasshopper algorithm can be improved by adopting a triangular replacement strategy and cauchy variation, wherein grasshopper firstly completes the position update of the first round according to an original search mechanism, then completes the position update of a population by utilizing a position update mechanism of the triangular replacement strategy, so as to balance the search and development capability of the algorithm, then mutates the population by utilizing cauchy variation, and improves the possibility of searching the optimal solution of the population, so as to avoid trapping local optimization in the segmentation process and improve the segmentation quality of medical images.
Specifically, according to an aspect of the present invention, there is provided a two-dimensional segmentation method of a multi-threshold medical image based on an improved grasshopper algorithm, including the steps of:
step 1: inputting a medical image to be segmented, and initializing a threshold segmentation Level;
step 2: initializing parameters, namely, the size of grasshopper population is pop, and the maximum Iteration number max_iteration is equal to that of grasshopper population;
step 3: graying an input image to obtain a corresponding gray image, and obtaining a non-local mean value image by using a non-local mean value filtering mode;
step 4: initializing grasshopper population X i (i＝1，2，...，n)；
Step 5: calculating the fitness value of all grasshoppers, namely Kapur entropy;
step 6: determining the optimal grasshopper position and fitness value;
step 7: according to the position updating mode of the grasshopper, finishing the first position updating of the grasshopper population;
step 8: based on the first position updating of grasshoppers, the position updating of each grasshopper is performed again according to the position updating method of the triangle replacement strategy;
step 9: based on the updated grasshopper population, the cauchy variation is carried out on the population individuals, and the local development is increased;
step 10: checking whether the iteration termination condition is met, if so, executing the step 11, otherwise, returning to the step 5 to continue iteration;
step 11: returning the optimal grasshopper position and the fitness value as an optimal threshold value and a maximum Kapur entropy;
step 12: and dividing the medical image by using the obtained optimal threshold value.
According to yet another aspect of the present invention, step 8 specifically includes: based on the first position updating of grasshoppers, the position updating method of the triangle replacement strategy according to the formula (7) carries out the position updating of each grasshopper again;
wherein t is the current iteration number, i represents the ith individual in the population, bp t Is the optimal solution of the t-th iteration, r 2 ，r 3 And r 4 Are all random numbers, r 2 In the range of 0-2 pi, r 3 In the range of 0-2, r 4 Is in the range of 0-1; a is a constant set to 2.
According to yet another aspect of the present invention, step 9 specifically includes: based on the updated grasshopper population, carrying out local development on population individuals according to the cauchy variation of formulas (9) - (11), and increasing the possibility of finding an optimal solution;
wherein f of formula (9) t (x) Representing the Cauchy density function, θ being a proportional parameter and θ > 0, F of equation (10) t (x) Representing the cauchy distribution function,representing the ith individual in the population of the t-th iteration, r is a random number between 0 and 1, and C represents a random number subject to the Coxie distribution.
The invention has the beneficial effects that:
1. according to the invention, the grasshopper algorithm searching capability and optimization accuracy can be improved by adopting a triangle replacement strategy and the cauchy variation;
2. grasshoppers firstly finish the position updating of the first round according to the original searching mechanism, and then finish the position updating of the population by utilizing the position updating mechanism of the triangle replacement strategy so as to balance the searching and developing capabilities of the algorithm;
3. the method has the advantages that the Kexi variation is utilized to carry out variation on the population, the possibility of searching the optimal solution by the population is improved, so that the situation that local optimization is involved in the segmentation process is avoided, and the segmentation quality of medical images is improved.
Drawings
The invention will be described in further detail with reference to the drawings and the detailed description.
FIG. 1 is a plan view of a two-dimensional histogram;
FIGS. 2-4 are three example medical images to be segmented;
fig. 5-7 are the results of the segmentation of the three medical images of fig. 2-4, respectively, according to the two-dimensional segmentation method of the multi-threshold medical image based on the modified grasshopper algorithm of the present invention.
Detailed Description
The present invention is described in its best mode by the following preferred embodiments with reference to the accompanying drawings, and the detailed description herein is to be construed as limiting the invention, since various changes and modifications can be made without departing from the spirit and scope of the invention.
Example 1
The applicant finds that the search capability and the optimization precision of the grasshopper algorithm can be improved by adopting a triangular replacement strategy and the cauchy variation, wherein the grasshopper firstly completes the position update of the first round according to an original search mechanism, then completes the position update of the population by utilizing the position update mechanism of the triangular replacement strategy, so as to balance the search and development capability of the algorithm, then mutates the population by utilizing the cauchy variation, and improves the possibility of searching the optimal solution of the population, so as to avoid the local optimization and improve the segmentation quality of medical images in the segmentation process.
According to a preferred embodiment of the present invention, there is provided a two-dimensional segmentation method of multi-threshold medical images based on an improved grasshopper algorithm, comprising the steps of:
step 1: inputting a medical image to be segmented, and initializing a threshold segmentation Level;
step 2: initializing parameters, namely, the size of grasshopper population is pop, and the maximum Iteration number max_iteration is equal to that of grasshopper population;
step 3: graying an input image to obtain a corresponding gray image, and obtaining a non-local mean value image by using a non-local mean value filtering mode;
step 4: initializing grasshopper population X i (i＝1，2，...，n)；
Step 5: calculating the fitness value of all grasshoppers, namely Kapur entropy;
step 6: determining the optimal grasshopper position and fitness value;
step 7: according to the position updating mode of the grasshopper, finishing the first position updating of the grasshopper population;
step 8: based on the first position updating of grasshoppers, the position updating of each grasshopper is performed again according to the position updating method of the triangle replacement strategy;
step 9: based on the updated grasshopper population, the cauchy variation is carried out on the population individuals, and the local development is increased;
step 10: checking whether the iteration termination condition is met, if so, executing the step 11, otherwise, returning to the step 5 to continue iteration;
step 11: returning the optimal grasshopper position and the fitness value as an optimal threshold value and a maximum Kapur entropy;
step 12: and dividing the medical image by using the obtained optimal threshold value.
According to a further preferred embodiment of the present invention, step 8 specifically comprises: based on the first position updating of grasshoppers, the position updating method of the triangle replacement strategy according to the formula (7) carries out the position updating of each grasshopper again;
wherein t is the current iteration number, i represents the ith individual in the population, bp t Is the optimal solution of the t-th iteration, r 2 ，r 3 And r 4 Are all random numbers, r 2 In the range of 0-2 pi, r 3 In the range of 0-2, r 4 Is in the range of 0-l; a is a constant set to 2.
According to a further preferred embodiment of the present invention, step 9 specifically comprises: based on the updated grasshopper population, carrying out local development on population individuals according to the cauchy variation of formulas (9) - (11), and increasing the possibility of finding an optimal solution;
wherein f of formula (9) t (x) Representing the Cauchy density function, θ being a proportional parameter and θ > 0, F of equation (10) t (x) Representing the cauchy distribution function,representing the ith individual in the population of the t-th iteration, r is a random number between 0 and 1, and C represents a random number subject to the Coxie distribution.
It will be appreciated that the number of components,new individuals who are cauchy residual; x in equations (9) and (10) is the argument in the cauchy function. Preferably, if->And if the global optimal solution is larger than the current global optimal solution, replacing the global optimal solution, otherwise, discarding the global optimal solution.
Example 2
According to a preferred embodiment of the present invention, there is provided a two-dimensional segmentation method of multi-threshold medical images based on an improved grasshopper algorithm, comprising the steps of:
step 1: inputting an image to be segmented, and initializing a threshold segmentation Level;
step 2: user initialization parameters, grasshopper population size pop, maximum Iteration number Max_iteration, setting a global optimal fitness value best, initializing and assigning best to minus infinity, and setting a global optimal individual to be bp;
step 3: and graying the input image to obtain a corresponding gray image, and obtaining a non-local mean value image by using a non-local mean value filtering mode.
Step 4: initializing grasshopper population X i (i＝1，2，...，n)
Step 5: calculating the fitness value of all grasshoppers, namely Kapur entropy;
step 6: updating an optimal grasshopper position bp and an optimal fitness value best;
step 7: and according to the position updating mode of the grasshopper, completing the first position updating of the grasshopper population.
Step 8: based on the first position updating of grasshoppers, the position updating method of the triangle replacement strategy according to the formula (7) carries out the position updating of each grasshopper again;
wherein t is the current iteration number, i represents the ith individual in the population, bp t Is the optimal solution of the t-th iteration, r 2 ，r 3 And r 4 Are all random numbers, r 2 In the range of 0-2 pi, r 3 In the range of 0-2, r 4 Is in the range of 0-1.a is a constant set to 2.
According to the trigonometric function, updating individuals of the population, wherein the exploration and development of the original grasshopper optimization algorithm are unbalanced, the trigonometric transformation strategy utilizes the fluctuation of the trigonometric function, so that the exploration and development can be well balanced in the iterative process, the updated population calculates the fitness value, and the fitness value is compared with the fitness value before updating, and the individuals with large fitness values are selected to be reserved.
Step 9: based on the updated grasshopper population, the individuals in the population are locally developed according to the cauchy variation of formulas (9) - (11), so that the possibility of finding the optimal solution is increased.
Wherein, the formula (9) represents the cauchy density function, θ > 0 is a proportional parameter, the formula (10) represents the cauchy distribution function,representing the ith individual in the population of the t-th iteration, r is a random number between 0 and 1, and C represents a random number subject to the Coxie distribution.
The Cauchy variation is wider in the horizontal direction than the Gaussian, which means that the local development capacity of the population individuals can be increased, and the possibility that the population finds the optimal solution is increased. And the individual calculates the fitness value according to the new neighborhood generated by the cauchy variation, compares the fitness value with the current global optimal solution, updates the global optimal solution if the fitness value is larger than the global optimal solution, and otherwise, the global optimal solution and population individual information are unchanged.
Step 10: checking whether the iteration termination condition is met, if so, executing the step 11, otherwise, returning to the step 5 to continue iteration;
step 11: returning the optimal grasshopper position and the fitness value as an optimal threshold value and a maximum Kapur entropy;
step 12: and dividing the medical image by using the obtained optimal threshold value.
5-7, which illustrate the results of segmenting the three example medical images of FIGS. 2-4 according to the two-dimensional segmentation method of the multi-threshold medical image based on the modified grasshopper algorithm of the present invention.
According to the invention, an improved grasshopper optimization algorithm is adopted, and first, grasshoppers finish updating own positions in an original mode to finish preliminary foraging behaviors; and then, the position updating mechanism of the triangle replacement strategy is utilized to complete the position updating of the population, so that the searching and developing capability of an algorithm is balanced, the Kexi variation is utilized to mutate the population, the possibility of searching an optimal solution of the population is improved, and the situation that the population is trapped into local optimal in the segmentation process is avoided, and the segmentation quality of medical images is improved. Grasshoppers will obtain better quality foods through triangle replacement strategies and cauchy variations, which can improve the quality of multi-threshold medical image segmentation.
Taking three medical images (hereinafter, respectively represented by image 1, image 2 and image 3) of fig. 2-4 as an example, the comparison analysis is performed by using the method of the present invention and using the grasshopper optimization algorithm, respectively, and the following results are obtained:
with the entropy of Kapur as the objective function, SCGOA (method of the present invention) is compared with the results of the objective function values obtained by GOA (grasshopper optimization algorithm) respectively (threshold=8):
when the objective function value is the largest, comparing the obtained results of the optimal segmentation threshold values:
the overall ranking Mean level of the 'Mean' representation and the ranking rating of the method are represented by the friedman 'using analysis results of 20 evaluations of Feature Similarity (FSIM), peak signal-to-noise ratio (PSNR), and Structural Similarity (SSIM) by friedman' test. According to the result of Friedman test analysis, in the 20 evaluations of PSNR, SSIM, FSIM, the SCGOA-based multi-threshold medical image segmentation method is obviously superior to the GOA-based multi-threshold medical image segmentation method, and the performance is greatly improved. This also fully demonstrates that the SCGOA-based multi-threshold image segmentation method is a multi-threshold image segmentation method that can obtain high quality segmentation results and is quite stable.
Friedman test of FSIM:
friedman test for PSNR:
friedman test of SSIM:
the invention has the beneficial effects that:
1. according to the invention, the grasshopper algorithm searching capability and optimization accuracy can be improved by adopting a triangle replacement strategy and the cauchy variation;
2. grasshoppers firstly finish the position updating of the first round according to the original searching mechanism, and then finish the position updating of the population by utilizing the position updating mechanism of the triangle replacement strategy so as to balance the searching and developing capabilities of the algorithm;
3. the method has the advantages that the Kexi variation is utilized to carry out variation on the population, the possibility of searching the optimal solution by the population is improved, so that the situation that local optimization is involved in the segmentation process is avoided, and the segmentation quality of medical images is improved.
Those of ordinary skill in the art will appreciate that all or a portion of the steps in implementing the methods of the above embodiments may be implemented by a program to instruct related hardware, where the program may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc.
The foregoing disclosure is illustrative of the present invention and is not to be construed as limiting the scope of the invention, which is defined by the appended claims.
Claims (1)
1.A method for two-dimensional segmentation of a multi-threshold medical image based on an improved grasshopper algorithm, comprising the steps of:
step 1: inputting a medical image to be segmented, and initializing a threshold segmentation Level;
step 2: initializing parameters, namely, the size of grasshopper population is pop, and the maximum Iteration number max_iteration is equal to that of grasshopper population;
step 3: graying an input image to obtain a corresponding gray image, and obtaining a non-local mean value image by using a non-local mean value filtering mode;
step 4: initializing grasshopper population X i (i＝1,2,…,n)；
Step 5: calculating the fitness value of all grasshoppers, namely Kapur entropy;
step 6: determining the optimal grasshopper position and fitness value;
step 7: according to the position updating mode of the grasshopper, finishing the first position updating of the grasshopper population;
step 8: based on the first position updating of grasshoppers, the position updating of each grasshopper is performed again according to the position updating method of the triangle replacement strategy;
step 9: based on the updated grasshopper population, the cauchy variation is carried out on the population individuals, and the local development is increased;
step 10: checking whether the iteration termination condition is met, if so, executing the step 11, otherwise, returning to the step 5 to continue iteration;
step 11: returning the optimal grasshopper position and the fitness value as an optimal threshold value and a maximum Kapur entropy;
step 12: dividing the medical image by using the obtained optimal threshold;
the step 8 specifically includes: based on the first position updating of grasshoppers, the position updating method of the triangle replacement strategy according to the formula (7) carries out the position updating of each grasshopper again;
wherein t is the current iteration number, i represents the ith individual in the population, bp t Is the optimal solution of the t-th iteration, r 2 ,r 3 And r 4 Are all random numbers, r 2 In the range of 0-2 pi, r 3 In the range of 0-2, r 4 Is in the range of 0-1; a is a constant, set to 2;
the step 9 specifically comprises the following steps: based on the updated grasshopper population, carrying out local development on population individuals according to the cauchy variation of formulas (9) - (11), and increasing the possibility of finding an optimal solution;
wherein f of formula (9) t (x) Represents a cauchy density function, θ is a scale parameter and θ>0, F of formula (10) t (x) Representing the cauchy distribution function,representing the ith individual in the population of the t-th iteration, r is a random number between 0 and 1, and C represents a random number subject to the Coxie distribution.
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