CN111340823B - Mammary image segmentation method based on fuzzy entropy and differential evolution - Google Patents

Mammary image segmentation method based on fuzzy entropy and differential evolution Download PDF

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CN111340823B
CN111340823B CN202010112442.0A CN202010112442A CN111340823B CN 111340823 B CN111340823 B CN 111340823B CN 202010112442 A CN202010112442 A CN 202010112442A CN 111340823 B CN111340823 B CN 111340823B
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柳培忠
柳垚
范宇凌
蔡盛
杜永兆
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Quanzhou Huagong Intelligent Technology Co ltd
Huaqiao University
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Abstract

The invention provides a mammary gland image segmentation method based on fuzzy entropy and differential evolution in the field of image processing, which comprises the following steps: s1, acquiring a mammary gland image, and setting segmentation parameters of a fuzzy entropy threshold; s2, initializing a population; s3, based on the segmentation parameters, calculating a fuzzy entropy membership function of the individuals in the initialized population, and further solving adaptive values of the individuals to generate an optimized population; s4, carrying out variation, crossing and selection operations on the optimized population; s5, judging whether the current iteration times are larger than the maximum iteration times, if so, outputting the optimal fuzzy entropy membership parameter corresponding to each individual, and entering the step S6; if not, the step S3 is carried out; and S6, segmenting the mammary gland image by using the optimal fuzzy entropy membership parameter and a dual-threshold segmentation method. The invention has the advantages that: the accuracy and the speed of mammary gland image segmentation are greatly improved, and the treatment effect of a patient is further improved.

Description

Mammary image segmentation method based on fuzzy entropy and differential evolution
Technical Field
The invention relates to the field of image processing, in particular to a mammary image segmentation method based on fuzzy entropy and differential evolution.
Background
Breast cancer occurs in renal epithelial tissue, and the accuracy of gland segmentation is crucial for the diagnosis of doctors, so that breast image segmentation becomes one of the most important tasks in tumor detection. With the progress of the technology, breast images obtained by the techniques such as mammography, ultrasound, magnetic Resonance (MR), and Computed Tomography (CT) are widely used in breast lesion detection.
For the segmentation of mammary gland images, there are conventionally a threshold method, a region growing and splitting merging algorithm, a watershed transform method, a fuzzy C-means clustering algorithm, a K-means clustering algorithm, a method based on an active contour model, and the like. However, the conventional method cannot segment the breast image accurately and rapidly, for example, the watershed transform can generate a closed contour of a single pixel when segmenting the breast image, but an over-segmentation phenomenon exists; the extraction of the target contour can be realized based on the active contour model, but the target contour is sensitive to the initial position and is easy to fall into a local extreme value, and the solving speed is reduced.
Therefore, how to provide a mammary gland image segmentation method based on fuzzy entropy and differential evolution to improve the accuracy and speed of mammary gland image segmentation and further improve the treatment effect of patients becomes a problem to be solved urgently.
Disclosure of Invention
The invention aims to provide a mammary gland image segmentation method based on fuzzy entropy and differential evolution, so that the precision and speed of mammary gland image segmentation are improved, and the treatment effect of a patient is further improved.
The invention is realized by the following steps: a mammary gland image segmentation method based on fuzzy entropy and differential evolution comprises the following steps:
s10, obtaining a mammary gland image, wherein the mammary gland image is a gray image; setting segmentation parameters of a fuzzy entropy threshold, wherein the segmentation parameters comprise a population size NP, an individual dimension D, a maximum iteration number FES, a current iteration number FES, an evolution algebra G and an evaluation function f (); wherein NP, D, FES and FES are positive integers, and FES = NP 1000; evaluating the function f (·) as a maximum fuzzy entropy;
step S20, using formula
Figure BDA0002390489920000021
Initializing the population; wherein x i G Representing the G generation population; i represents the number of the individual; />
Figure BDA0002390489920000022
Representing individuals, each of which consists of B-dimensional fuzzy entropy membership parameters, and the B =6,B-dimensional fuzzy entropy membership parameters comprise a 1 、b 1 、c 1 、a 2 、b 2 、c 2 And are all positive numbers; each individual was randomly selected at [ x ] L ,x U ]，x L Representing the lower bound of the pixel value, and taking the value as 0; x is the number of U Represents the upper bound of the pixel value, and takes 255;
s30, based on the segmentation parameters, calculating a fuzzy entropy membership function Q of individuals in the initialized population t Further, the adaptive value of the individual is obtained to generate an optimized population;
step S40, using formula
Figure BDA0002390489920000023
Mutating the optimized population to produce variant individuals; wherein->
Figure BDA0002390489920000024
Represents the G th generation variant individuals; />
Figure BDA0002390489920000025
Representing a population; f represents a scale factor, F ∈ [0,1](ii) a Index r 1 ,r 2 ,r 3 Represents the combination of any three fuzzy entropy membership degree parameters in the population, and each variant individual with different values and randomly generated will generate r once 1 ,r 2 ,r 3 ；
S50, carrying out differential evolution on the current population x i G And variant individuals of
Figure BDA0002390489920000026
Performing crossing operation to generate crossing individual>
Figure BDA0002390489920000027
Figure BDA0002390489920000028
Wherein j rand Denotes a random integer between 1 and B, rand j Represents a uniformly distributed random number between 0 and 1; CR represents a crossing factor, which is a positive number;
step S60, crossing individuals are subjected to evaluation function
Figure BDA0002390489920000029
And current population x i G The individual(s) of (1) performs a selection operation, and the individual(s) with the better fitness value are retained: />
Figure BDA00023904899200000210
Step S70, judging whether the current iteration time FES is larger than the maximum iteration time FES, if so, outputting the optimal fuzzy entropy membership parameter corresponding to each individual, and entering step S80; if not, the step S30 is carried out;
and S80, segmenting the mammary gland image by using the optimal fuzzy entropy membership parameter and a dual-threshold segmentation method.
Further, the step S30 specifically includes:
step S31, representing the breast image as:
Figure BDA0002390489920000031
wherein I (x, y) represents the gray scale value of the breast image at coordinate point (x, y); k represents a gray value, H represents a set of gray values, and H = {0,1, ·, l-1},1 ≦ l ≦ 256;
step S32, setting n k Represents D k The pixel ratio is as follows:
Figure BDA0002390489920000032
wherein h is k Represents the pixel scale; r represents the number of line pixels of the breast image; c represents the mammary glandThe number of column pixels of the image; h is not less than 0 k ≤1；
Is provided with h k ＝{h 0 ,h 1 ,...,h l-1 H and k if =1 is the gray level histogram of the breast image, then
Figure BDA0002390489920000033
Representing that the breast image regions of different gray values have no intersection;
step S33, calculating a division threshold t 1 And t 2 ：
If (x) i,1 +x i,3 )/2≤x i,2 ≤x i,3 Then, then
Figure BDA0002390489920000034
If x i,1 ≤x i,2 ＜(x i,1 +x i,3 ) /2, then
Figure BDA0002390489920000035
If (x) i,4 +x i,6 )/2≤x i,5 ≤x i,6 Then, then
Figure BDA0002390489920000036
If x i,4 ≤x i,5 ＜(x i,4 +x i,6 ) /2, then
Figure BDA0002390489920000037
Wherein x i,1 、x i,2 、x i,3 、x i,4 、x i,5 、x i,6 Respectively represent a 1 、b 1 、c 1 、a 2 、b 2 、c 2 The parameters correspond to 6 dimensions of an individual;
using said segmentation threshold t 1 And t 2 Dividing the gray value of the mammary gland image into bright level regions E b Middle zone E m And dark level region E d ；
Calculating the bright level region E b Middle zone E m And dark level region E d The ratio of the breast images:
Figure BDA0002390489920000038
wherein p is d Representing the proportion of dark regions in the breast image, p m Representing the proportion of the median region in the mammary image, p b Representing the proportion of the bright level area in the mammary gland image;
step S34, setting
Figure BDA0002390489920000041
Then->
Figure BDA0002390489920000042
Wherein D kd Representing dark regions in the breast image, D km Representing a mid-level region in the breast image, D kb Representing bright level regions in the breast image, p k Representing the probability of the gray value k in the entire breast image, p d|k 、p m|k 、p b|k Respectively representing a pixel with a gray value k belonging to E d 、E m 、E b Conditional probability of, p kd 、p km 、p kb Respectively representing the conditional probability that a region with a gray value k belongs to a dark level region, a middle level region and a bright level region in the mammary gland image;
step S35, making a pixel with k gray value belong to the bright level area E b Middle zone E m And dark level region E d Are respectively equal to p d|k 、p m|k 、p b|k I.e. mu d (k)＝p d|k ，μ m (k)＝p m|k ，μ b (k)＝p b|k Then:
Figure BDA0002390489920000043
step S36, setting Q d 、Q m And Q b Respectively corresponding dark, medium and bright values of the fuzzy entropy, then:
Figure BDA0002390489920000044
fuzzy entropy membership function Q t ＝Q d +Q m +Q b (ii) a Wherein Q t Is given by a 1 、b 1 、c 1 、a 2 、b 2 、c 2 Parameter determination, using maximum entropy to determine a 1 、b 1 、c 1 、a 2 、b 2 、c 2 Obtaining the adaptive value of the individual, and further generating the optimized population.
Further, in the step S40, the F uses cauchy inverse cumulative distribution, and F i,j ＝Cauchy i,j (Fm j ,0.1)；
Wherein F i,j Representing the cross probability of each dimension in an individual; f mj A position parameter representing a Cauchy's inverse cumulative distribution and a scale factor of a current individual; fm j ＝(1-c)·Fm j +c·mean F (S F,j )；S F,j Represents a successful cross-parent scaling factor; c represents a constant between 0 and 1; mean is a measure of F (.) represents the Lehmer averaging operation:
Figure BDA0002390489920000051
F mj is 0.5 and the scale parameter is 0.1.
Further, in the step S50, the CR determines the possibility that the target individual inherits the gene from the variant individual
Figure BDA0002390489920000052
A normal distribution is used; />
CR i,j ＝randn i,j (CRm j ,0.1)；
CRm j ＝(1-c)·CRm j +c·mean CR (S CR,j )；
Wherein CR i,j Representing the cross probability, S, of each individual dimension CR,j Indicating the crossover probability, CRm, of successful crossover parents j Mean, representing the probability of individual cross CR (-) represents an arithmetic mean operation.
Further, the step S80 specifically includes:
utilizing the optimal fuzzy entropy membership parameter a 1 、b 1 、c 1 、a 2 、b 2 、c 2 Get the corresponding x i,1 、x i,2 、x i,3 、x i,4 、x i,5 、x i,6 And then calculating mu d (k)、μ m (k) And mu b (k)：
Figure BDA0002390489920000053
Figure BDA0002390489920000054
Figure BDA0002390489920000061
By said μ d (k)、μ m (k) And mu b (k) The breast image is segmented.
The invention has the advantages that:
the mammary gland image is segmented by a double-threshold segmentation method, a low pixel value is weakened, a high pixel value is strengthened to highlight a critical area, burrs and irregular edges of which the pixel values are at critical values are highlighted, and the accuracy of the mammary gland image segmentation is greatly improved; through the differential evolution method, the individuals and the variant individuals of the current population are subjected to cross operation, namely, the rapid convergence and the strong robustness of the differential evolution method are utilized, the global optimal solution is rapidly obtained, the situation that the individuals and the variant individuals fall into a local extreme value is avoided, the mammary gland image segmentation speed is greatly improved, the treatment effect of a patient is greatly improved, the optimal parameter combination is obtained through the iterative evolution population, and the principle is simple and easy to achieve.
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The invention will be further described with reference to the following examples with reference to the accompanying drawings.
FIG. 1 is a flow chart of a mammary gland image segmentation method based on fuzzy entropy and differential evolution.
FIG. 2 is a diagram of the fuzzy entropy membership function of the present invention.
FIG. 3 is a schematic diagram of the differential evolution method of the present invention for optimizing the segmentation process.
Fig. 4 is a graph of the segmentation effect of the present invention compared to other algorithms.
Detailed Description
The technical scheme in the embodiment of the application has the following general idea: firstly, constructing a maximum fuzzy entropy evaluation function as a population evolution direction by combining the fuzzy entropy of an image; then initializing fuzzy entropy parameters as individuals of population evolution, establishing a variation strategy to enable the population to generate variation, and performing cross operation on the individuals and the variation individuals of the current population by a differential evolution method to avoid falling into local optimal parameter combination; then, according to the evolution mode of the superior and the inferior, the overall parameters of the population are close to the optimal parameter combination; and finally, outputting the optimal parameter combination of the fuzzy entropy and the optimal threshold value of the segmented image when the iteration times are reached.
Referring to fig. 1 to 4, a preferred embodiment of a mammary gland image segmentation method based on fuzzy entropy and differential evolution of the present invention includes the following steps:
s10, acquiring a mammary gland image, wherein the mammary gland image is a gray image and is a two-dimensional matrix formed by pixel value points in a range of 0-255; setting segmentation parameters of a fuzzy entropy threshold value by combining the fuzzy entropy of the mammary gland image, wherein the segmentation parameters comprise population scale NP, individual dimension D, maximum iteration number FES, current iteration number FES, evolution algebra G and an evaluation function f (); wherein NP, D, FES and FES are positive integers, and FES = NP 1000; evaluating the function f (·) as the maximum fuzzy entropy; the population size NP indicates that N kinds (a) are set 1 ,b 1 ,c 1 ,a 2 ,b 2 ,c 2 ) Combining; the evolution algebra G is a population evolution completion algebra; the current iteration time fes is the time for carrying out variation, crossing or selection strategies in a generation of population, and one evolution needs to be carried out for 3 times of iteration (variation, crossing and selection);
step S20, using formula
Figure BDA0002390489920000071
Initializing the population; wherein x i G Representing the G generation population; i represents the number of the individual; />
Figure BDA0002390489920000072
Representing individuals, each of which consists of B-dimensional fuzzy entropy membership parameters, and the B =6,B-dimensional fuzzy entropy membership parameters comprise a 1 、b 1 、c 1 、a 2 、b 2 、c 2 And are all positive numbers; each individual was randomly selected at [ x ] L ,x U ]，x L Representing the lower bound of the pixel value, and taking the value as 0; x is the number of U Represents the upper bound of the pixel value, and takes 255;
s30, based on the segmentation parameters, calculating a fuzzy entropy membership function Q of individuals in the initialized population t Further, the adaptive value of the individual is obtained to generate an optimized population;
step S40, using formula
Figure BDA0002390489920000073
Mutating the optimized population to produce variant individuals; wherein +>
Figure BDA0002390489920000074
Represents G generation variant individuals; />
Figure BDA0002390489920000075
Representing a population; f represents a scale factor, F ∈ [0,1](ii) a Index r 1 ,r 2 ,r 3 Represents the combination of any three fuzzy entropy membership degree parameters in the population, and the values of the fuzzy entropy membership degree parameters are different and are randomly generatedWill all generate r once 1 ,r 2 ,r 3 ；
Step S50, utilizing a Differential Evolution (DE) method to perform comparison on the current population x i G And variant individuals of
Figure BDA0002390489920000076
Performing crossing operation to generate crossing individual>
Figure BDA0002390489920000077
/>
Figure BDA0002390489920000078
Wherein j rand Denotes a random integer between 1 and B, rand j Represents a uniformly distributed random number between 0 and 1; CR represents a crossing factor, which is a positive number;
step S60, crossing individuals are subjected to evaluation function
Figure BDA0002390489920000079
And current population x i G The individual(s) of (1) performs a selection operation, and the individual(s) with the better fitness value are retained: />
Figure BDA0002390489920000081
Namely, a greedy selection mode with the advantages and the disadvantages is adopted, so that the filial generation better individuals replace the parent individuals, and the population is always close to the optimal segmentation threshold;
through three strategies of variation, intersection and selection, the individuals of the population are continuously subjected to iterative evolution;
step S70, judging whether the current iteration time FES is larger than the maximum iteration time FES, if so, outputting the optimal fuzzy entropy membership parameter corresponding to each individual, and entering step S80; if not, the step S30 is carried out;
s80, segmenting the mammary gland image by using the optimal fuzzy entropy membership parameter and a dual-threshold segmentation method; traditionally, the segmentation of the breast image uses a single threshold method, but the breast image is mainly composed of three types of background, fat and gland outside the breast, and has three distinct types of features, and the dual threshold facilitates changing the classification of the image pixel gray level from two types to three types.
The step S30 specifically includes:
step S31, representing the breast image as:
Figure BDA0002390489920000082
wherein I (x, y) represents the gray value of the breast image at coordinate point (x, y); k represents a gray value, H represents a set of gray values, and H = {0,1, ·, l-1},1 ≦ l ≦ 256;
step S32, setting n k Is shown by D k The pixel ratio is as follows:
Figure BDA0002390489920000083
wherein h is k Represents the pixel scale; r represents the number of line pixels of the breast image; c represents the column pixel number of the mammary gland image; h is not less than 0 k Less than or equal to 1; i.e. the size of the breast image is R × C;
is provided with h k ＝{h 0 ,h 1 ,...,h l-1 H and k if =1 is the gray level histogram of the breast image, then
Figure BDA0002390489920000084
Representing that the breast image regions of different gray values have no intersection;
step S33, calculating a division threshold t 1 And t 2 ：
If (x) i,1 +x i,3 )/2≤x i,2 ≤x i,3 Then, then
Figure BDA0002390489920000085
If x i,1 ≤x i,2 ＜(x i,1 +x i,3 ) /2, then
Figure BDA0002390489920000086
If (x) i,4 +x i,6 )/2≤x i,5 ≤x i,6 Then, then
Figure BDA0002390489920000087
If x i,4 ≤x i,5 ＜(x i,4 +x i,6 ) /2, then
Figure BDA0002390489920000088
Wherein x i,1 、x i,2 、x i,3 、x i,4 、x i,5 、x i,6 Respectively represent a 1 、b 1 、c 1 、a 2 、b 2 、c 2 The parameters correspond to 6 dimensions of an individual; segmentation threshold t 1 And t 2 The value range of (1) is 0-255;
using said segmentation threshold t 1 And t 2 Dividing gray value of mammary gland image into bright level regions E b Middle zone E m And dark level region E d ；
Calculating the bright level region E b Middle zone E m And dark level region E d The ratio of the breast images:
Figure BDA0002390489920000091
wherein p is d Representing the proportion of dark regions in the breast image, p m Representing the proportion of the median region in the mammary image, p b Representing the proportion of the bright level area in the mammary gland image;
step S34, setting
Figure BDA0002390489920000092
Then->
Figure BDA0002390489920000093
Wherein D kd Representing dark levels in breast imagesRegion, D km Representing a mid-level region in the breast image, D kb Representing bright level regions in the breast image, p k Representing the probability of the gray value k in the entire breast image, p d|k 、p m|k 、p b|k Respectively representing a pixel with a gray value k belonging to E d 、E m 、E b Conditional probability of (p) kd 、p km 、p kb Respectively representing the conditional probability that a region with a gray value k belongs to a dark level region, a middle level region and a bright level region in the mammary gland image;
step S35, making a pixel with k gray value belong to the bright level area E b Middle zone E m And dark level region E d Are respectively equal to p d|k 、p m|k 、p b|k I.e. mu d (k)＝p d|k ，μ m (k)＝p m|k ，μ b (k)＝p b|k Then:
Figure BDA0002390489920000094
step S36, setting Q d 、Q m And Q b Respectively corresponding dark, medium and bright values of the fuzzy entropy, then:
Figure BDA0002390489920000101
fuzzy entropy membership function Q t ＝Q d +Q m +Q b (ii) a Wherein Q t Is given by a 1 、b 1 、c 1 、a 2 、b 2 、c 2 Parameter determination, using maximum entropy to determine a 1 、b 1 、c 1 、a 2 、b 2 、c 2 Obtaining the adaptive value of the individual by the optimal combination, and further generating an optimized population; i.e. find the minimum Q t Namely to obtain a 1 、b 1 、c 1 、a 2 、b 2 、c 2 The optimum combination of (a).
In the step S40, the F uses a Cauchi-Rev cumulative distribution, and F i,j ＝Cauchy i,j (Fm j ,0.1)；
Wherein F i,j Representing the cross probability of each dimension in an individual; f mj A position parameter representing a Cauchy-Rev cumulative distribution and a scale factor of the current individual; fm j ＝(1-c)·Fm j +c·mean F (S F,j )；S F,j Represents a successful cross-parent scaling factor; c represents a constant between 0 and 1; mean is a measure of F (.) denotes the Lehmer averaging operation:
Figure BDA0002390489920000102
F mj is 0.5 and the scale parameter is 0.1.
In the step S50, the CR determines the possibility that the target individual inherits the gene from the variant individual
Figure BDA0002390489920000103
A normal distribution is used; />
CR i,j ＝randn i,j (CRm j ,0.1)；
CRm j ＝(1-c)·CRm j +c·mean CR (S CR,j )；
Wherein CR i,j Representing the cross probability, S, of each individual dimension CR,j Indicating the crossover probability, CRm, of successful crossover parents j Mean, representing the probability of individual cross CR (-) represents an arithmetic mean operation.
The step S80 specifically includes:
utilizing the optimal fuzzy entropy membership parameter a 1 、b 1 、c 1 、a 2 、b 2 、c 2 Get the corresponding x i,1 、x i,2 、x i,3 、x i,4 、x i,5 、x i,6 And then calculating mu d (k)、μ m (k) And mu b (k)：
Figure BDA0002390489920000104
Figure BDA0002390489920000111
Figure BDA0002390489920000112
Using MATLAB compiler, passing said μ d (k)、μ m (k) And μ b (k) The breast image is segmented.
FIG. 2 is a diagram of a fuzzy entropy membership function passing through μ in step S80 d (k)、μ m (k) And mu b (k) To the optimal fuzzy entropy membership parameter a 1 、b 1 、c 1 、a 2 、b 2 、c 2 And (3) segmenting the mammary gland image and extracting a gland region, wherein the mammary gland image consists of three fuzzy entropy membership curves, the x axis is a k value, and the y axis is a membership value under the condition of the k value.
Fig. 4 is a comparison segmentation effect diagram of the invention and other algorithms, through comparison tests, the structural similarity of the invention can reach more than 0.90, the feature similarity is higher than that of other algorithms, and experimental results show that the invention has higher accuracy for segmenting the mammary gland and can meet the clinical requirements of doctors. As can be seen from fig. (b) and (c), the distribution of glands scattered in the fibroglandular type is scattered, but the extraction effect is good, and the structural similarity is 0.94 and 0.93, respectively. From (e) to (g), it can be seen that the extraction effect is significant for the heterogeneous dense type, and the structural similarities are 0.99, 0.92, and 0.93, respectively. Therefore, for gland segmentation results with scattered and uneven distribution, which are significant and close to the expert manual segmentation results, other types of gland segmentation results are closer to the results of manual segmentation than different algorithms. The tumor characteristics in the interior of the gland are more remarkable in the (a) and (e), the structural similarity reaches 0.98 and 0.99, and the structural similarity is higher than that of the segmentation result of other algorithms. In conclusion, the method is superior to other comparison algorithms in two evaluation indexes, and is close to the level of manual segmentation of experts in the contour segmentation of glands.
Table 1 shows the image structure similarity between the fuzzy entropy segmentation result and the manual segmentation result of different optimization algorithms:
Image PSOFE BFOFE ABCFE BATFE FireflyFE DEFE
(a) 0.772585 0.960233 0.951338 0.967582 0.967761 0.983714
(b) 0.767622 0.908242 0.922446 0.931719 0.934276 0.940575
(c) 0.727953 0.872984 0.857899 0.924748 0.924985 0.930942
(d) 0.80175 0.818965 0.823363 0.899649 0.872728 0.900564
(e) 0.711131 0.862833 0.953069 0.968934 0.979494 0.99412
(f) 0.736424 0.928552 0.909655 0.921997 0.925404 0.928391
(g) 0.767985 0.887575 0.938516 0.912257 0.931238 0.93803
(h) 0.695158 0.894295 0.851698 0.90098 0.937426 0.953872
in conclusion, the invention has the advantages that:
the mammary gland image is segmented by a double-threshold segmentation method, a low pixel value is weakened, a high pixel value is strengthened to highlight a critical area, burrs and irregular edges of which the pixel values are at critical values are highlighted, and the accuracy of the mammary gland image segmentation is greatly improved; through the differential evolution method, the individuals and the variant individuals of the current population are subjected to cross operation, namely, the rapid convergence and the strong robustness of the differential evolution method are utilized, the global optimal solution is rapidly obtained, the situation that the individuals and the variant individuals fall into a local extreme value is avoided, the mammary gland image segmentation speed is greatly improved, the treatment effect of a patient is greatly improved, the optimal parameter combination is obtained through the iterative evolution population, and the principle is simple and easy to achieve.
While specific embodiments of the invention have been described, it will be understood by those skilled in the art that the specific embodiments described are illustrative only and are not limiting upon the scope of the invention, as equivalent modifications and variations as will be made by those skilled in the art in light of the spirit of the invention are intended to be included within the scope of the appended claims.

Claims (1)

1. A mammary gland image segmentation method based on fuzzy entropy and differential evolution is characterized in that: the method comprises the following steps:
s10, acquiring a mammary gland image, wherein the mammary gland image is a gray level image; setting segmentation parameters of a fuzzy entropy threshold, wherein the segmentation parameters comprise a population size NP, an individual dimension D, a maximum iteration number FES, a current iteration number FES, an evolution algebra G and an evaluation function f (); wherein NP, D, FES and FES are positive integers, and FES = NP 1000; evaluating the function f (·) as the maximum fuzzy entropy;
step S20, using formula
Figure FDA0003983136330000011
Initializing the population; wherein x i G Representing the G generation population; i represents the number of the individual; />
Figure FDA0003983136330000012
Representing individuals, each of which consists of B-dimensional fuzzy entropy membership parameters, and the B =6,B-dimensional fuzzy entropy membership parameters comprise a 1 、b 1 、c 1 、a 2 、b 2 、c 2 And are all positive numbers; each individual was randomly selected at [ x ] L ,x U ]，x L Representing the lower bound of the pixel value, and taking the value as 0; x is the number of U Represents the upper bound of the pixel value, and takes 255;
s30, based on the segmentation parameters, calculating a fuzzy entropy membership function Q of individuals in the initialized population t Further, the adaptive value of the individual is obtained to generate an optimized population;
step S40, using formula
Figure FDA0003983136330000013
Mutating the optimized population to produce variant individuals; wherein->
Figure FDA0003983136330000014
Represents G generation variant individuals; />
Figure FDA0003983136330000015
Representing a population; f represents a scale factor, F ∈ [0,1](ii) a Index r 1 ,r 2 ,r 3 Represents the combination of any three fuzzy entropy membership grade parameters in the population, and all variant individuals with different values and generated randomly can generate r once 1 ,r 2 ,r 3 ；
S50, carrying out differential evolution on the current population x i G And variant individuals of
Figure FDA0003983136330000016
Performing crossing operation to generate crossing individual>
Figure FDA0003983136330000017
Figure FDA0003983136330000018
Wherein j rand Denotes a random integer between 1 and B, rand j Represents a uniformly distributed random number between 0 and 1; CR represents a crossing factor, which is a positive number;
step S60, crossing individuals are paired based on the evaluation function
Figure FDA0003983136330000019
And current population x i G The individual(s) of (1) performs a selection operation, and the individual(s) with the better fitness value are retained: />
Figure FDA00039831363300000110
Step S70, judging whether the current iteration time FES is larger than the maximum iteration time FES, if so, outputting the optimal fuzzy entropy membership parameter corresponding to each individual, and entering step S80; if not, the step S30 is carried out;
s80, segmenting the mammary gland image by using the optimal fuzzy entropy membership parameter and a dual-threshold segmentation method;
the step S30 specifically includes:
step S31, representing the breast image as:
Figure FDA0003983136330000021
wherein I (x, y) represents the gray value of the breast image at coordinate point (x, y); k represents a gray value, H represents a set of gray values, and H = {0,1, ·, l-1},1 ≦ l ≦ 256;
step S32, setting n k Represents D k The pixel ratio is as follows:
Figure FDA0003983136330000022
wherein h is k Represents the pixel scale; r represents the number of line pixels of the breast image; c represents the column pixel number of the mammary gland image; h is not less than 0 k ≤1；
Is provided with h k ＝{h 0 ,h 1 ,...,h l-1 H and k if =1 is the gray level histogram of the breast image, then
Figure FDA0003983136330000023
Representing that the breast image regions of different gray values have no intersection;
step S33, calculating a division threshold t 1 And t 2 ：
If (x) i,1 +x i,3 )/2≤x i,2 ≤x i,3 Then, then
Figure FDA0003983136330000024
If x i,1 ≤x i,2 ＜(x i,1 +x i,3 ) /2, then
Figure FDA0003983136330000025
If (x) i,4 +x i,6 )/2≤x i,5 ≤x i,6 Then, then
Figure FDA0003983136330000026
If x i,4 ≤x i,5 ＜(x i,4 +x i,6 ) /2, then
Figure FDA0003983136330000027
Wherein x i,1 、x i,2 、x i,3 、x i,4 、x i,5 、x i,6 Respectively represent a 1 、b 1 、c 1 、a 2 、b 2 、c 2 The parameters correspond to 6 dimensions of an individual;
using said segmentation threshold t 1 And t 2 Dividing the gray value of the mammary gland image into bright level regions E b Middle zone E m And dark level region E d ；
Calculating the bright level region E b Middle zone E m And dark level region E d The ratio of each in the mammary gland image:
Figure FDA0003983136330000031
wherein p is d Representing the proportion of dark regions in the breast image, p m Representing the proportion of the median region in the mammary image, p b Representing the proportion of the bright level area in the mammary gland image;
step S34, setting
Figure FDA0003983136330000032
Then->
Figure FDA0003983136330000033
Wherein D kd Representing dark regions in the breast image, D km Representing a mid-level region in the breast image, D kb Representing bright level regions in the breast image, p k Representing the probability of the gray value k in the entire breast image, p d|k 、p m|k 、p b|k Respectively representing a pixel with a gray value k belonging to E d 、E m 、E b Conditional probability of (p) kd 、p km 、p kb Respectively representing the conditional probability that a region with a gray value k belongs to a dark level region, a middle level region and a bright level region in the mammary gland image;
step S35, making a pixel with k gray value belong to the bright level area E b Middle zone E m And dark level region E d Are respectively equal to p d|k 、p m|k 、p b|k I.e. mu d (k)＝p d|k ，μ m (k)＝p m|k ，μ b (k)＝p b|k And then:
Figure FDA0003983136330000034
step S36, setting Q d 、Q m And Q b Respectively corresponding dark, medium and bright values of the fuzzy entropy, then:
Figure FDA0003983136330000035
fuzzy entropy membership function Q t ＝Q d +Q m +Q b (ii) a Wherein Q t Is given by a 1 、b 1 、c 1 、a 2 、b 2 、c 2 Parameter determination, using maximum entropy to determine a 1 、b 1 、c 1 、a 2 、b 2 、c 2 Obtaining the adaptive value of the individual by the optimal combination, and further generating an optimized population;
in the step S40, the F uses a Cauchi-Rev cumulative distribution, and F i,j ＝Cauchy i,j (Fm j ,0.1)；
Wherein F i,j Representing the cross probability of each dimension in an individual; f mj A position parameter representing a Cauchy-Rev cumulative distribution and a scale factor of the current individual; fm j ＝(1-c)·Fm j +c·mean F (S F,j )；S F,j Represents a successful cross-parent scaling factor; c represents a constant between 0 and 1; mean is a measure of F (.) denotes the Lehmer averaging operation:
Figure DA00039831363369829835
F mj 0.5, and the scale parameter 0.1;
in the step S50, the CR determines the possibility that the target individual inherits the gene from the variant individual
Figure FDA0003983136330000042
A normal distribution is used;
CR i,j ＝randn i,j (CRm j ,0.1)；
CRm j ＝(1-c)·CRm j +c·mean CR (S CR,j )；
wherein CR i,j Representing the cross probability, S, of each individual dimension CR,j Indicating the crossover probability, CRm, of successful crossover parents j Mean, representing the probability of individual cross CR (-) represents an arithmetic mean operation;
the step S80 specifically includes:
utilizing the optimal fuzzy entropy membership parameter a 1 、b 1 、c 1 、a 2 、b 2 、c 2 Get the corresponding x i,1 、x i,2 、x i,3 、x i,4 、x i,5 、x i,6 And then calculating mu d (k)、μ m (k) And mu b (k)：
Figure FDA0003983136330000043
/>
Figure FDA0003983136330000044
Figure FDA0003983136330000051
By said μ d (k)、μ m (k) And mu b (k) The breast image is segmented.
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