CN107220978B - Multi-target threshold image segmentation method fusing interval fuzzy information and statistical information - Google Patents
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Abstract
The invention discloses a multi-target threshold image segmentation method fusing interval fuzzy information and statistical information, which comprises the following steps: inputting an image to be segmented, and converting the image into a gray image; setting the initial population number M, the maximum iteration number G and the maximum threshold number S of the imagemaxThen dividing the population into a plurality of grouped populations Q with the same size according to the threshold numbers(ii) a The obtained grouping population QsPerforming multi-objective evolution by adopting a simultaneous optimization interval modulus entropy function and an inter-class variance function based on a linear intercept histogram, so that each grouping population obtains a group of non-dominated solution sets, and an optimal solution is selected from the non-dominated solution sets of each grouping population according to the weighting ratio of inter-class difference to inter-class difference, wherein the optimal solution is the optimal threshold number and the optimal threshold; and marking and assigning the pixel points in the original image according to the obtained optimal solution to obtain a final segmentation result. The method can realize self-adaptive threshold image segmentation, and can obtain satisfactory segmentation results for noisy images.
Description
Technical Field
The invention belongs to the technical field of image processing, relates to a multi-target threshold image segmentation method fusing interval fuzzy information and statistical information, and particularly relates to a multi-target evolution self-adaptive multi-threshold segmentation method based on image interval value fuzzy entropy and improved OTSU.
Background
Image segmentation is one of the most fundamental and important techniques in image processing and pre-vision. Image segmentation is the process of dividing an image into specific regions with unique properties and extracting the object of interest. Over the twentieth century, researchers have proposed many image segmentation methods, mainly including a threshold method, a region method, a clustering method, and the like. Among many image segmentation techniques, the threshold method is one of the most important and effective techniques because of its simplicity in implementation, small amount of calculation, and stable performance.
Most of the existing researches pay attention to the selection of the optimal threshold after the threshold number of the image is fixed and the application of the optimal threshold are less mentioned for the research on how to adaptively select the threshold number, and the manual intervention of the algorithm is larger. In 2012, Djerou et al proposed that under the framework of binary particle swarm optimization, multi-objective optimization was performed by using inter-class variance, entropy and error rate functions as objective functions, and proposed that optimal thresholds and optimal threshold numbers were selected by using a uniformity metric (U index). A large number of experiments show that the U index has preference to individuals with different threshold numbers, and the optimal threshold number cannot be accurately selected. Moreover, the algorithm does not introduce any image space information, so that the algorithm is sensitive to noise in the image and cannot obtain a satisfactory segmentation result in the segmentation of the image containing the noise. In 2012, the heroic et al proposed a threshold segmentation method based on OTSU criterion and a straight line intercept histogram, where two-dimensional information of the straight line intercept histogram is the gray level of a pixel and the neighborhood average gray level composition. Although the above method can suppress noise in an image to some extent, the image segmentation speed and performance are not ideal. Moreover, the threshold number of the above method is set in advance, and the appropriate threshold number cannot be adapted according to the change of the image.
Disclosure of Invention
The invention aims to provide a multi-target threshold image segmentation method fusing interval fuzzy information and statistical information; the method can realize self-adaptive threshold image segmentation, and can obtain satisfactory segmentation results for noisy images.
The purpose of the invention is solved by the following technical scheme:
the multi-target threshold image segmentation method fusing interval fuzzy information and statistical information comprises the following steps:
Step 3, grouping population Q obtained in the step 2sPerforming multi-objective evolution by adopting a simultaneous optimization interval modulus entropy function and an inter-class variance function based on a linear intercept histogram, so that each grouping population obtains a group of non-dominated solution sets;
step 4, selecting an optimal solution in the non-dominant solution set of each grouping population according to the weighting ratio of the inter-class difference to the inter-class difference, wherein the optimal solution is the optimal threshold number and the optimal threshold;
and 5, marking and assigning the pixel points in the original image according to the optimal solution obtained in the step 4 to obtain a final segmentation result.
Furthermore, the invention is characterized in that:
in step 3, the specific process of performing multi-objective evolution on each group population is as follows:
step 3.1, carrying out chromosome coding and initialization on each grouping population;
step 3.2, calculating 2 fitness function values of each group population individual, and performing non-dominated sorting to select chromosomes to enter respective matching pools;
step 3.3, carrying out self-adjusting crossover and mutation operation on chromosomes in a matching pool corresponding to each grouping population to obtain offspring populations, dividing the offspring populations into a plurality of offspring grouping populations according to the threshold number, and finally obtaining new grouping populations by adopting an elite strategy;
and 3.4, circularly performing the steps 3.2 and 3.3 to obtain the maximum iteration number G.
The specific process of chromosome coding and initialization for each grouping population in step 3.1 is as follows: chromosome coding is the use of real number coding for solving threshold, and each chromosome in the population is composed of [2Imin,2Imax]S is a threshold number, where IminAnd ImaxRespectively representing the maximum and minimum values of the image gray scale.
Wherein the 2 fitness function values in the step 3.2 are an interval fuzzy entropy function and an inter-class variance function based on a straight line intercept histogram.
Wherein the self-regulating crossover and mutation operation in step 3.3 is to subject all the cohorts of the cohort to mixed crossover mutations.
The method for selecting the optimal solution in the step 4 specifically comprises the following steps: firstly, calculating the weighting ratio F of the inter-class difference and the intra-class difference corresponding to the individuals in each grouping population, selecting the individual with the maximum value of F as the optimal solution of the grouping population, and then utilizing the difference F of the weighting ratios F of the inter-class difference and the intra-class difference of the individualsΔTo determine the final solution.
Compared with the prior art, the invention has the beneficial effects that: defining a new nonlinear weighted sum image by utilizing the gray values and the space positions in the original image and the pixel neighborhood window, and forming a linear intercept histogram by utilizing the gray values of the original image and the obtained nonlinear weighted sum image. And designing a multi-threshold inter-class variance function as a fitness function on the basis of the straight line intercept histogram so as to overcome the influence of noise on the segmentation effect in the image segmentation process. The designed multi-threshold interval fuzzy entropy function obtains more detailed information of image segmentation by increasing the fuzziness of the multi-threshold interval fuzzy entropy function. And the segmentation performance and the segmentation speed of the algorithm are improved by adopting the mixed intersection of all individuals and the self-adjusting intersection mutation probability. And finally, determining the optimal solution of each grouping population by using a weighting ratio index of the intra-class difference and the inter-class difference, and then evaluating the optimal solutions of the grouping populations to select a final solution, namely the optimal threshold and the number of the corresponding thresholds. Therefore, the self-adaption of image segmentation is realized, and the target can be automatically segmented and extracted in the image processing.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a comparison graph of the segmentation results using the Berkeley image database image #55067 in the embodiment of the present invention;
FIG. 3 is a comparison graph of the segmentation results using the Berkeley image database image #241004 in an embodiment of the present invention.
Wherein a is an original drawing; b is a Gaussian noise-containing map; c is a noise graph of salt and pepper; d is a standard segmentation chart; e is the OTSU segmentation map (gaussian noise); f is a fuzzy entropy segmentation graph (Gaussian noise); g is a fuzzy entropy segmentation graph (Gaussian noise) based on difference optimization; h is the adaptive segmentation map (Gaussian noise) of the method of the invention; i is OTSU segmentation map (salt and pepper noise); j is a fuzzy entropy segmentation graph (salt and pepper noise); k is a fuzzy entropy segmentation graph (salt and pepper noise) based on difference optimization; l is the adaptive segmentation result (salt and pepper noise) of the method.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
the invention provides a multi-target threshold image segmentation method fusing interval fuzzy information and statistical information, as shown in figure 1, the specific process comprises the following steps:
Step 3, dividing the initial population into a plurality of grouped populations Q with the same size according to the threshold numbersEncoding and initializing chromosomes of each individual; the specific process is that the chromosome coding mode is to use real number coding for the solved threshold, and the initialization method of the grouping population with the threshold number s is as follows: each chromosome in the population is composed of [2Imin,2Imax]S different random integers within the interval, wherein IminAnd ImaxRespectively representing the maximum and minimum values of the image gray scale.
Step 4, calculating 2 fitness function interval values fuzzy entropy f of each group population individual1(t1,t2,…,tn) And inter-class variance f based on straight line intercept histogram2(t1,t2,…,tn) The values are sequentially arranged on the gene positions of the chromosome, and then the dyeing in the matching pool corresponding to the 2 fitness function values is carried outColor body according to self-adjusting cross mutation probability pcAnd pmAnd performing mixed crossing and mutation on the chromosomes in the matching pool to generate offspring populations, dividing the offspring populations into a plurality of offspring grouping populations according to the threshold number of the offspring populations, and finally obtaining a new grouping population by adopting an elite strategy.
Step 5, circularly executing the step 3 and the step 4, when the iteration times reach the maximum value G, each grouping population can obtain a group of non-dominated solution sets, and then selecting an optimal solution on the non-dominated solution sets obtained by each grouping population by using a weighting ratio index of the inter-class difference and the intra-class difference; the method for selecting the optimal solution specifically comprises the following steps: firstly, calculating the weighting ratio F of the inter-class difference and the intra-class difference corresponding to the individuals in each grouping population, selecting the individual with the maximum value of F as the optimal solution of the grouping population, and then utilizing the difference F of the weighting ratios F of the inter-class difference and the intra-class difference of the individualsΔTo determine the final solution.
And 6, marking and assigning the pixels in the original image by using the optimal threshold number and the optimal threshold parameter obtained in the step 5 to obtain a final segmentation result.
Fuzzy entropy f of 2 fitness function interval values in the invention1(t1,t2,…,tn) And inter-class variance f based on straight line intercept histogram2(t1,t2,…,tn) The specific design of (1) is as follows:
multiple threshold (t)1,t2,…,tn) The following interval fuzzy entropy function is specifically designed as follows:
f1(t1,t2,…,tn)＝H1+H2+…Hn+Hn+1
in the above formula H1,H2,···,Hn,Hn+1The following are calculated respectively:
wherein
Lower bound of fuzzy membership function representing interval
The method represents the upper bound of the interval fuzzy membership function, and the specific form is as follows:
wherein α is an interval fuzzy index, which can be set empirically, and the value here is 0.8, and the definition of the fuzzy membership function is as follows:
f1(t1,t2,…,tn) When the maximum value is obtained, the information indicating that the image segmentation result contains the original image is maximum, and the optimal threshold value can be obtained at the moment
The specific design of the inter-class variance function based on the straight-line intercept histogram is to design the straight-line intercept histogram first and then design a multi-threshold inter-class variance function. With (x)i,εj) Representing a binary set consisting of the gray levels of the pixels and the gray level of the linear weighted sum image, then xi+εjL may denote a straight line in the two-dimensional histogram that is perpendicular to the main diagonal and has a straight line intercept of l. The straight line intercept histogram is defined as follows: n is a radical oflDenotes xi+εjX is the number of occurrences of li+εjProbability of occurrence of ═ llCan be represented as pl＝NlN, L ═ 0,1, …, 2L-1. The specific construction of the linear weighted sum image epsilon is as follows:
wherein epsilonjIs the gray value of the image epsilon at j, SjRepresenting a neighborhood window, E, centered on pixel jjpRepresenting the local similarity between pixel j and pixel p according to the neighborhood window SjThe spatial coordinates and gray values of the inner pixels are calculated, and the specific form is as follows:
in the above formula, (a)j,bj) And (a)p,bp) Representing the spatial coordinates, max (| a), of pixel j and pixel p, respectivelyj-ap|,|bj-bpL) represents the Chebyshev distance, λ, of pixel j and pixel psAnd λgIs a two-dimensional parameter, σjIs defined as
Wherein S isRIs a neighborhood window SjThe number of inner pixels.
The definition of the multi-threshold inter-class variance function based on the straight-line intercept histogram is as follows:
wherein
Such that the between-class variance function f2(t1,t2,…,tn) Taking the maximum threshold as the optimum threshold, i.e.
The cross mutation strategy in the step 4 adopts the mixed cross mutation of all individuals, namely, the individuals of all the grouping populations can be crossed, and double-point cross is selected, and the cross point also adoptsIs obtained by random selection. Self-adjusting cross mutation probability pcAnd pmThe specific design is as follows:
wherein σl(ci,cj)＝((fi,l-fave,l)+(fj,l-fave,l))/2,(l＝1,2,…,L)，fi,lAnd fj,lRespectively representing the fitness function values of the ith and jth individuals under the ith target, fave,mDenotes the average fitness function value of the ith target, L denotes the number of fitness functions, and two fitness functions are used in this document, so L is 2, K1And K2Two control parameters. When the fitness function value of the individual is larger, pcAnd pmThe smaller the value of (c); otherwise, pcAnd pmThe larger the value of (c). According to self-adjusting cross probability pcAnd the probability of variation pmThe individual is crossed and mutated, good genes are not damaged, and the diversity of the population can be ensured. After crossing and mutation are completed, dividing the generated filial generation population into a plurality of filial generation grouping populations according to the threshold number. Then, each child grouping population is mixed with the parent grouping population with the same threshold number, and then non-dominant sorting is carried out to select the next grouping population, so that the optimal threshold segmentation result discovered so far is retained.
The optimal threshold number and the optimal threshold selection method in step 5 are that firstly, the weighting ratio F of the inter-class difference and the intra-class difference corresponding to the individuals in each grouping population is calculated, the individual which enables the F to take the maximum value is selected as the optimal solution of the grouping population, and then the final solution is determined by utilizing the difference F delta of the weighting ratio F of the inter-class difference and the intra-class difference of the individual. The weighted ratios F and F Δ are defined as follows:
wherein,
s represents the threshold number, N represents the total number of pixels of the image, Nj is the total number of pixels in class j, y represents the average gray scale value of all pixels in total, yj represents the average gray scale value of the class j pixels, and xij represents the gray scale value of the ith pixel in class j. Fs represents the maximum value of F in the grouping population, and Fmax represents the maximum value of all F values when the threshold number is from 1 to s-1. And when Fmax is maximum, the corresponding s value is the optimal threshold number, and the optimal solution under the grouping population is the final solution of the algorithm.
Example and analysis of simulation experiment
Selecting two images of #55067 and #241004 in a Berkeley image database, as shown in a in figure 2 and a in figure 3, using the two images to carry out simulation analysis by the method of the invention, and verifying the effectiveness of the invention, specifically as follows:
in the present embodiment, two types of noise of the two images #55067 and #241004 are salt and pepper noise (0, 0.001), as shown in c in fig. 2 and 3, and gaussian noise (0, 0.001) is shown in b in fig. 2 and 3. The results obtained by segmenting the two pictures with different noises by the OTSU method are shown in fig. 2 and e and i in fig. 3; the results obtained by dividing the pictures with two different noises by the fuzzy entropy division graph method are shown as f and j in fig. 2 and 3; the results obtained by segmenting the two pictures with different noises by the fuzzy entropy segmentation graph method based on the difference optimization are shown as g and k in fig. 2 and 3; the results obtained by segmenting the picture with two different noises by using the method of the present invention are shown as h and l in fig. 2 and 3; the result of dividing the original image a using the standard division diagram method is shown as d in fig. 2 and 3. Compared with the rest comparison methods, the segmentation accuracy of the target and the background is more accurate. The invention not only overcomes the influence of noise, but also obtains ideal segmentation result by self-adapting to proper threshold number.
Claims (5)
1. The multi-target threshold image segmentation method fusing the interval fuzzy information and the statistical information is characterized by comprising the following steps of:
step 1, inputting an image to be segmented, and converting the image into a gray image;
step 2, setting the initial population number M, the maximum iteration number G and the maximum threshold number S of the imagemaxThen dividing the population into a plurality of grouped populations Q with the same size according to the threshold numbers；
Step 3, grouping population Q obtained in the step 2sPerforming multi-objective evolution by adopting a simultaneous optimization interval fuzzy entropy function and an inter-class variance function based on a linear intercept histogram, so that each grouping population obtains a group of non-dominated solution sets;
wherein, the grouping population Q obtained in the step 2sThe specific process of carrying out multi-objective evolution by adopting the simultaneous optimization interval fuzzy entropy function and the inter-class variance function based on the linear intercept histogram is as follows:
step 3.1, carrying out chromosome coding and initialization on each grouping population;
step 3.2, calculating 2 fitness function values of each group population individual, and performing non-dominated sorting to select chromosomes to enter respective matching pools;
wherein: interval fuzzy entropy function f1(t1,t2,…,tn) The specific design of (1) is as follows:
f1(t1,t2,…,tn)＝H1+H2+…Hn+Hn+1
wherein H1,H2,…,Hn,Hn+1The following are calculated respectively:
wherein,
lower bound of fuzzy membership function representing interval
The method represents the upper bound of the interval fuzzy membership function, and the specific form is as follows:
wherein α is interval fuzzy index, and the value is 0.8;
f1(t1,t2,…,tn) When the maximum value is obtained, the optimal threshold value is obtained
Interclass variance function f based on straight line intercept histogram2(t1,t2,…,tn) The specific design of (1) is as follows:
first, a straight line intercept histogram is designed by (x)i,εj) Representing a binary set consisting of the gray levels of the pixels and the gray level of the linear weighted sum image, then xi+εjL represents a straight line which is perpendicular to the main diagonal line and has a straight line intercept of l in the two-dimensional histogram; the straight line intercept histogram is defined as follows: n is a radical oflDenotes xi+εjX is the number of occurrences of li+εjProbability of occurrence of ═ llIs represented by pl＝NlN, L ═ 0,1, …, 2L-1; the specific construction of the linear weighted sum image epsilon is as follows:
wherein epsilonjIs the gray value of the image epsilon at j, SjRepresenting a neighborhood window, E, centered on pixel jjpRepresenting the local similarity between pixel j and pixel p, according to a neighborhood window SjCalculating the spatial coordinates and gray values of the inner pixels：
Wherein (a)j,bj) And (a)p,bp) Representing the spatial coordinates, max (| a), of pixel j and pixel p, respectivelyj-ap|,|bj-bpL) represents the Chebyshev distance, λ, of pixel j and pixel psAnd λgIs a two-dimensional parameter, σjIs defined as
Wherein S isRIs a neighborhood window SjThe number of inner pixels;
then designing a multi-threshold inter-class variance function f based on the linear intercept histogram2(t1,t2,…,tn)：
f2(t1,t2,…,tn)＝w0w1(μ0-μ1)2+w0w2(μ0-μ2)2+…+w0wn(μ0-μn)2+w1w2(μ1-μ2)2+w1w3(μ1-μ3)2+…+w1wn(μ1-μn)2+…+wn-1wn(μn-1-μn)2
Wherein
Between-class variance function f2(t1,t2,…,tn) Taking the maximum threshold as the optimum threshold, i.e.
Step 3.3, carrying out self-adjusting crossover and mutation operation on chromosomes in a matching pool corresponding to each grouping population to obtain offspring populations, dividing the offspring populations into a plurality of offspring grouping populations according to the threshold number, and finally obtaining new grouping populations by adopting an elite strategy;
step 3.4, circularly performing the steps 3.2 and 3.3 to reach the maximum iteration times G;
step 4, selecting an optimal solution in the non-dominated solution set of each grouping population according to the weighting ratio of the inter-class difference and the intra-class difference, wherein the optimal solution is the optimal threshold number and the optimal threshold;
and 5, marking and assigning the pixel points in the original image according to the optimal solution obtained in the step 4 to obtain a final segmentation result.
2. The multi-target threshold image segmentation method fusing interval fuzzy information and statistical information according to claim 1, wherein the specific process of chromosome coding and initialization for each grouping population in step 3.1 is as follows: chromosome coding is the use of real number coding for solving threshold, and each chromosome in the population is composed of [2Imin,2Imax]S is a threshold number, where IminAnd ImaxRespectively representing the maximum and minimum values of the image gray scale.
3. The multi-target threshold image segmentation method fusing interval fuzzy information and statistical information as claimed in claim 1, wherein the 2 fitness function values in the step 3.2 are an interval fuzzy entropy function and an inter-class variance function based on a straight line intercept histogram.
4. The method for multi-objective threshold image segmentation with fusion of interval fuzzy information and statistical information according to claim 1, characterized in that the self-adjusting intersection and mutation operation in step 3.3 is to perform mixed intersection mutation on all grouping populations.
5. The multi-objective threshold image segmentation method fusing interval blur information and statistical information according to claim 1, whichCharacterized in that, the method for selecting the optimal solution in the step 4 specifically comprises the following steps: firstly, calculating the weighting ratio F of the inter-class difference and the intra-class difference corresponding to the individuals in each grouping population, selecting the individual with the maximum value of F as the optimal solution of the grouping population, and then utilizing the difference F of the weighting ratios F of the inter-class difference and the intra-class difference of the individualsΔTo determine the final solution.
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