CN107220978A - The multiple target threshold image segmentation method of the interval fuzzy message of fusion and statistical information - Google Patents
The multiple target threshold image segmentation method of the interval fuzzy message of fusion and statistical information Download PDFInfo
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Abstract
The invention discloses the multiple target threshold image segmentation method of the interval fuzzy message of fusion and statistical information, comprise the following steps：Input image to be split, and convert the image into gray level image；The initial population number N of image, maximum iteration G and max-thresholds number S are setmax, population is then divided into several size identicals packet population Q according to threshold numbers；By obtained packet population QsMulti-target evolution is carried out using the interval modulus entropy function of optimization simultaneously and based on the histogrammic inter-class variance function of Linear intercept, each packet population is obtained one group of non-dominant disaggregation and one optimal solution of selection is concentrated in the non-domination solution of each packet population by the weighting ratio of class inherited and class inherited, the optimal solution is optimal threshold number and optimal threshold；Assignment is marked to the pixel in original image according to obtained optimal solution, final segmentation result is obtained.This method can realize that adaptive threshold image is split, and satisfied segmentation result can be also obtained to noisy image.
Description
Technical field
The invention belongs to technical field of image processing, it is related to the multiple target threshold value of the interval fuzzy message of fusion and statistical information
Image partition method, it is particularly a kind of based on image interval value fuzzy entropy and the adaptive many thresholds of multi-target evolution for improving OTSU
It is worth dividing method.
Background technology
Image segmentation is one of the most basic and important technology in image procossing and early vision.Image segmentation is exactly handle
Image is divided into several regions specific, with unique properties, and the process that Objective extraction interested is come out.20
Since century, researchers propose many image partition methods, mainly include the method, the method in region, cluster of threshold value
Method etc..In numerous image Segmentation Technologies, threshold method is simple because of its realization, and amount of calculation is small, and performance is stable and turns into most heavy
Want and one of effective technology.
How certainly the existing selection and its application for studying optimal threshold after concern image threshold number fixation mostly for
Adapt to selected threshold number research it is then rare carries, and and cause algorithm human intervention it is larger.Djerou in 2012 et al. is carried
Go out under the framework of binary particle swarm algorithm, multiple target is carried out using inter-class variance, entropy and error rate function as object function
Optimization, and propose to select optimal threshold and optimal threshold number using homogeneity module (U indexs).Sent out by many experiments
The existing U indexs individual different to threshold number has Preference, and optimal threshold number can not be selected exactly.And above-mentioned algorithm
Any image space information is not introduced so that algorithm is more sensitive for the noise in image, it is impossible in noisy acoustic image point
Cut the middle segmentation result for obtaining satisfaction.What will is brave et al. proposed in 2012 it is histogrammic based on OTSU criterions and Linear intercept
Threshold segmentation method, the histogrammic two-dimensional signal of the method cathetus intercept is the gray scale and its neighborhood averaging gray scale group of pixel
Into.Although the above method can play certain inhibitory action, its image segmentation speed and performance to the noise in image
It is unsatisfactory.And the threshold number of the above method is set in advance, it is impossible to which it is suitable adaptively to go out with the change of image
Threshold number.
The content of the invention
It is an object of the invention to provide the multiple target threshold Image Segmentation side of the interval fuzzy message of fusion and statistical information
Method；This method can realize that adaptive threshold image is split, and satisfied segmentation result can be also obtained to noisy image.
The purpose of the present invention is solved by the following technical programs：
The multiple target threshold image segmentation method of this interval fuzzy message of fusion and statistical information, comprises the following steps：
Step 1, image to be split is inputted, and converts the image into gray level image；
Step 2, the initial population number N of image, maximum iteration G and max-thresholds number S are setmax, then will plant
Group is divided into several size identicals packet population Q according to threshold numbers；
Step 3, the packet population Q to being obtained in step 2sCut using the interval modulus entropy function of optimization simultaneously and based on straight line
Multi-target evolution is carried out away from histogrammic inter-class variance function, each packet population is obtained one group of non-dominant disaggregation；
Step 4, concentrated and selected in the non-domination solution of each packet population by the weighting ratio of class inherited and class inherited
An optimal solution is selected, the optimal solution is optimal threshold number and optimal threshold；
Step 5, assignment is marked to the pixel in original image according to the optimal solution obtained in step 4, obtains final
Segmentation result.
Further, the features of the present invention is also resided in：
Wherein in step 3, it is to the detailed process that each packet population carries out multi-target evolution：
Step 3.1, chromosome coding and initialization are carried out to each packet population；
Step 3.2,2 fitness function values of each packet population at individual are calculated, and carry out non-dominated ranking and then choosing
Chromosome is selected into respective match-pool；
Step 3.3, the intersection and variation being self-regulated to the chromosome in the corresponding match-pool of each packet population are grasped
Make, obtain progeny population, progeny population then is divided into some filial generations according to threshold number is grouped population, finally using elite plan
Slightly obtain new packet population；
Step 3.4, circulation carries out step 3.2 and 3.3, obtains maximum iteration G.
It is to the detailed process that each packet population carries out chromosome coding and initialization wherein in step 3.1：Chromosome
It is encoded to and uses each chromosome in real coding, population to be by [2I to solving threshold valuemin,2Imax] s in interval is different
Random integers are constituted, and s is threshold number, wherein IminAnd ImaxThe maximum and minimum value of gradation of image are represented respectively.
2 fitness function values are for Interval Fuzzy entropy function and based on the histogrammic class of Linear intercept wherein in step 3.2
Between variance function.
The intersection and mutation operation being wherein self-regulated in step 3.3 are that all packet populations are carried out into mixing intersection to dash forward
Become.
The method of selection optimal solution is specially wherein in step 4：Individual corresponding class in each packet population is calculated first
Between in difference and class difference weighting ratio F, choose the individual that causes F to take maximum as the optimal solution for being grouped population, then
Utilize the difference F of the weighting ratio F of difference in the class inherited and class of individualΔTo determine last solution.
Compared with prior art, the beneficial effects of the invention are as follows：Utilize the gray value in original image and neighborhood of pixels window
And locus defines a new nonlinear weight and image, with original image gray scale and obtained nonlinear weight and image
Gray scale constitutes Linear intercept histogram.Multi thresholds inter-class variance function conduct is designed on the basis of above-mentioned Linear intercept is histogrammic
Fitness function, to overcome influence of the noise to segmentation effect in image segmentation process.The multi thresholds Interval Fuzzy entropy letter of design
Count by increasing its ambiguity to obtain the detailed information of more images segmentations.Intersected using all individual mixing and self-regulation is handed over
Furcula changeable probability improves the segmentation performance and splitting speed of algorithm.Finally referred to the weighting ratio of difference in class and class inherited
Mark to determine the optimal solution of each packet population, then evaluated to choose one most in the optimal solution of these packet populations
Solve eventually, i.e. optimal threshold and its corresponding threshold number.Then the adaptive of image segmentation is realized, can be in image procossing
To the automatic segmentation of target and extraction.
Brief description of the drawings
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is the segmentation result contrast in embodiment in the present invention using Berkeley image data base images #55067
Figure；
Fig. 3 is the segmentation result contrast in embodiment in the present invention using Berkeley image data base images #241004
Figure.
Wherein, a is artwork；B is the noisy figure of Gauss；C is the noisy figure of the spiced salt；D is Standard Segmentation figure；E is OTSU segmentation figures
(Gaussian noise)；F is fuzzy entropy figure (Gaussian noise)；G is the fuzzy entropy figure (Gaussian noise) optimized based on difference；
H is the inventive method adaptivenon-uniform sampling figure (Gaussian noise)；I is OTSU segmentation figures (salt-pepper noise)；J is fuzzy entropy figure
(salt-pepper noise)；K is the fuzzy entropy figure (salt-pepper noise) optimized based on difference；L is the inventive method adaptivenon-uniform sampling knot
Really (salt-pepper noise).
Embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings：
The invention provides the multiple target threshold image segmentation method of the interval fuzzy message of fusion and statistical information, such as Fig. 1
Shown, its detailed process comprises the following steps：
Step 1, image to be split is inputted, and converts the image into gray level image.
Step 2, the initial population number N of the image to be split, maximum iteration G and max-thresholds number S are setmax,
Then population is divided into several size identicals packet population Q according to threshold numbers, control parameter K is set1And K2。
Step 3, initial population is divided into several size identicals packet population Q according to threshold numbers, and to per each and every one
The chromosome coding of body and initialization；Specific process is that the mode of chromosome coding is that the threshold value of solution is compiled using real number
Code, threshold number is as follows for the initial method of s packet population：Each chromosome is by [2I in populationmin,2Imax] interval
S interior different random integers compositions, wherein IminAnd ImaxThe maximum and minimum value of gradation of image are represented respectively.
Step 4,2 fitness function Interval Valued Fuzzy entropy f of each packet population at individual are calculated1(t1,t2,…,tn) and
Based on the histogrammic inter-class variance f of Linear intercept2(t1,t2,…,tn) value, and its value is emitted on to the gene of chromosome successively
On position, the chromosome in the corresponding match-pool of above-mentioned 2 fitness function values is then intersected into mutation probability p according to self-regulationc
And pmMixing intersection is carried out to the chromosome in match-pool and produces progeny population with mutation, then according to the number of threshold values of progeny population
Mesh is divided into some filial generation packet populations, finally obtains new packet population using elitism strategy.
Step 5, circulation performs step 3 and step 4, when iterations reaches maximum G, and each packet population can obtain
To one group of non-dominant disaggregation, then obtained using the weighting ratio index of difference in class inherited and class in each packet population
An optimal solution is selected in non-dominant disaggregation；Selection optimal solution method be specially：Individual in each packet population is calculated first
Corresponding class inherited and the weighting ratio F of difference in class, choose the individual for causing F to take maximum as the optimal of packet population
Solution, then utilizes the difference F of the weighting ratio F of difference in the class inherited and class of individualΔTo determine last solution.
Step 6, two parameters of optimal threshold number and optimal threshold obtained using step 5 are to the pixel in original image
Assignment is marked, final segmentation result is obtained.
2 fitness function Interval Valued Fuzzy entropy f in the present invention1(t1,t2,…,tn) and it is histogrammic based on Linear intercept
Inter-class variance f2(t1,t2,…,tn) be designed specifically to：
Multi thresholds (t1,t2,…,tn) under Interval Fuzzy entropy function specific design it is as follows：
f1(t1,t2,…,tn)=H1+H2+…Hn+Hn+1
In above formulaPoint,1It is not calculated as follows：
Wherein Represent under Interval Fuzzy membership function
BoundaryThe upper bound of Interval Fuzzy membership function is represented, concrete form is as follows：
Wherein, α is Interval Fuzzy index, can rule of thumb set, and value is 0.8 here, and fuzzy membership function is determined
Justice is as follows：
f1(t1,t2,…,tn) when taking maximum, illustrate information of the image segmentation result comprising artwork in maximum, now can be with
Obtain optimal threshold
Specific design based on the histogrammic inter-class variance function of Linear intercept is first to design Linear intercept histogram, then
Design multi thresholds inter-class variance function.With (xi,εj) represent to be made up of the gray scale and linear weighted function of pixel and the gray scale of image
Two tuples, then xi+εj=l can represent the straight line that and Linear intercept vertical with leading diagonal is l in two-dimensional histogram.Straight line
Intercept is histogrammic to be defined as follows：NlRepresent xi+εjThe number of times that=l occurs, then xi+εjThe Probability p that=l occurslIt can be expressed as
pl=Nl/ N, l=0,1 ..., 2L-1.Wherein linear weighted function and image ε specific configuration are as follows：
Wherein, εjIt is gray values of the image ε at j, SjRepresent the neighborhood window centered on pixel j, EjpRepresent pixel j and
Local similarity between pixel p, it is according to neighborhood window SjThe space coordinate and gray value of interior pixel is calculated, specific shape
Formula is as follows：In above formula, (aj,
bj) and (ap,bp) represent the space coordinate of pixel j and pixel p respectively, max (| aj-ap|,|bj-bp|) represent pixel j and pixel p
Chebyshev's distance, λsAnd λgIt is two scale parameters, σjIt is defined asWherein, SRIt is neighborhood
Window SjThe number of interior pixel.
It is defined as follows based on the histogrammic multi thresholds inter-class variance function of Linear intercept：
Wherein
So that inter-class variance functionIt is optimal threshold to take threshold value during maximum, i.e.,
Intersect mutation strategy in step 4 and use all individual mixing intersection mutation, i.e., the individual of all packet populations
Between can be intersected, and select be two point intersect, crosspoint is also to randomly select to obtain.It is general that self-regulation intersects mutation
Rate pcAnd pmSpecific design it is as follows：
Wherein, σl(ci,cj)=((fi,l-fave,l)+(fj,l-fave,l))/2, (l=1,2 ..., L), fi,lAnd fj,lRespectively
Represent fitness function value of i-th and j-th individual under l-th of target, fave,mRepresent the average fitness of l-th of target
Functional value, L represents the number of fitness function, herein using two fitness functions, so L=2, K1And K2For two controls
Parameter.When the fitness function value of individual is larger, pcAnd pmValue just it is smaller；Conversely, pcAnd pmValue it is bigger.According to certainly
Adjust crossover probability pcWith mutation probability pmIndividual is intersected and made a variation, the gene neither destroyed can guarantee that colony again
Diversity.After the completion of intersecting and making a variation, the progeny population of generation is divided into some filial generations according to threshold number and is grouped populations.Then
Each filial generation is grouped progress non-dominated ranking after population mixes with threshold number identical parent packet population and selects the next generation
Population is grouped, therefore, the Optimum threshold segmentation result found so far will be retained.
The choosing method of optimal threshold number and optimal threshold is to calculate individual right in each packet population first in step 5
The weighting ratio F of difference in the class inherited and class answered, chooses the individual for causing F to take maximum as the optimal of packet population
Solution, then determines last solution using the difference F Δs of the weighting ratio F of difference in the class inherited and class of individual.Weighting ratio F
It is defined as follows with F Δs：
Wherein,S represents threshold number, and N represents the total of image pixel
Number, Nj is the sum of pixel in j classes, and y represents the total average gray value of all pixels, and yj represents that the gray scale of jth class pixel is averaged
Value, xij represents the gray value of the ith pixel in jth class.Fs represents the maximum of F in packet population, and Fmax represents number of threshold values
Maximum when mesh is from 1 to s-1 in all F values.Corresponding s values are optimal threshold number when Fmax is maximum, this packet population
Under optimal solution be this paper algorithms last solution.
Embodiment and progress analysis of simulation experiment
Choose in a and Fig. 3 in #55067 the and #241004 two images in Berkeley image data bases, such as Fig. 2
Shown in a, simulation analysis are carried out by the method for the present invention using the two width picture, effectiveness of the invention is verified, it is specific as follows：
#55067 and #241004 two images two types noise is respectively salt-pepper noise (0,0.001) in the present embodiment,
As shown in the c in Fig. 2 and Fig. 3, Gaussian noise (0,0.001) is as shown in the b in Fig. 2 and Fig. 3.By OTUS methods to two kinds not
Picture with noise split in obtained result figure 2 and Fig. 3 shown in e and i；By fuzzy entropy drawing method to two kinds not
Picture with noise carries out splitting obtained result as shown in f and j in Fig. 2 and Fig. 3；Pass through the fuzzy entropy optimized based on difference
Segmentation drawing method carries out splitting obtained result as shown in g and k in Fig. 2 and Fig. 3 to the picture of two kinds of different noises；Use this
The method of invention carries out splitting obtained result as shown in h and l in Fig. 2 and Fig. 3 to the picture of two kinds of different noises；Use mark
Quasi- segmentation drawing method carries out splitting obtained result as shown in d in Fig. 2 and Fig. 3 to artwork a.By comparison diagram it can be seen that the present invention
Segmentation accuracy to target and background is more accurate than remaining several control methods.The present invention not only overcomes the shadow of noise
Ring, adaptively go out suitable threshold number and achieve highly desirable segmentation result.
Claims (6)
1. the multiple target threshold image segmentation method of the interval fuzzy message of fusion and statistical information, it is characterised in that including following
Step：
Step 1, image to be split is inputted, and converts the image into gray level image；
Step 2, the initial population number N of image, maximum iteration G and max-thresholds number S are setmax, then population is pressed
It is divided into several size identicals packet population Q according to threshold numbers；
Step 3, the packet population Q to being obtained in step 2sUsing while optimizing interval modulus entropy function and straight based on Linear intercept
The inter-class variance function of square figure carries out multi-target evolution, each packet population is obtained one group of non-dominant disaggregation；
Step 4, selection one is concentrated in the non-domination solution of each packet population by the weighting ratio of class inherited and class inherited
Individual optimal solution, the optimal solution is optimal threshold number and optimal threshold；
Step 5, assignment is marked to the pixel in original image according to the optimal solution obtained in step 4, obtains final point
Cut result.
2. the multiple target threshold image segmentation method of the interval fuzzy message of fusion according to claim 1 and statistical information,
Characterized in that, in the step 3, being to the detailed process that each packet population carries out multi-target evolution：
Step 3.1, chromosome coding and initialization are carried out to each packet population；
Step 3.2,2 fitness function values of each packet population at individual are calculated, and carries out non-dominated ranking and then selects dye
Colour solid enters respective match-pool；
Step 3.3, the intersection and mutation operation being self-regulated to the chromosome in the corresponding match-pool of each packet population, are obtained
To progeny population, progeny population is then divided into by some filial generations according to threshold number and is grouped population, is finally obtained using elitism strategy
To new packet population；
Step 3.4, circulation carries out step 3.2 and 3.3, obtains maximum iteration G.
3. the multiple target threshold image segmentation method of the interval fuzzy message of fusion according to claim 2 and statistical information,
Characterized in that, being to the detailed process that each packet population carries out chromosome coding and initialization in the step 3.1：Dyeing
Body is encoded to uses each chromosome in real coding, population to be by [2I to solving threshold valuemin,2Imax] interval in s difference
Random integers composition, s is threshold number, wherein IminAnd ImaxThe maximum and minimum value of gradation of image are represented respectively.
4. the multiple target threshold image segmentation method of the interval fuzzy message of fusion according to claim 2 and statistical information,
Characterized in that, 2 fitness function values are Interval Fuzzy entropy function and histogrammic based on Linear intercept in the step 3.2
Inter-class variance function.
5. the multiple target threshold image segmentation method of the interval fuzzy message of fusion according to claim 2 and statistical information,
Characterized in that, the intersection and mutation operation that are self-regulated in the step 3.3 are that all packet populations are carried out into mixing intersection
Mutation.
6. the multiple target threshold image segmentation method of the interval fuzzy message of fusion according to claim 1 and statistical information,
Characterized in that, the method that optimal solution is selected in the step 4 is specially：It is corresponding that individual in each packet population is calculated first
Class inherited and the weighting ratio F of difference in class, choose the individual optimal solution as packet population for causing F to take maximum, so
The difference F of the weighting ratio F of difference in the class inherited and class of individual is utilized afterwardsΔTo determine last solution.
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