CN103473786A - Gray level image segmentation method based on multi-objective fuzzy clustering - Google Patents

Abstract

The invention discloses a gray level image segmentation method based on multi-objective fuzzy clustering, relating to the technical field of image processing and mainly solving the problem of lower accuracy rate of gray level image segmentation. The gray level image segmentation method comprises the steps of: after graying an image, randomly generating a plurality of clustering centers according to a generated grey level histogram, and constituting the clustering centers into a parent antibody population. The gray level image segmentation method is characterized in that a dense separation effectiveness function as an evaluation criteria is combined with a fuzzy optimization function in a fuzzy C-mean value method to form a multi-objective optimization problem, the whole parent population is iterated for multiple times by adopting an immune clone multi-objective evolutionary algorithm, simultaneously searched from multiple directions, and calculated in parallel so as to finally acquire an optimum clustering center, and a classifying result is output. Therefore, the detail information in the gray level image is effectively reserved, the wrong fraction is reduced, the gray level image segmentation precision is improved, and a good platform is provided for subsequent operation of gray level image segmentation. The gray level image segmentation method can be used for extracting and obtaining the detail information of the gray level image.

Description

Gray-scale image segmentation method based on the multi objective fuzzy cluster

Technical field

The invention belongs to image processing field, relate generally to gray-scale image segmentation method, a kind of gray-scale image segmentation method based on the multi objective fuzzy cluster specifically, can be used for extracting the detailed information of gray level image, the work such as follow-up target identification, feature extraction of processing for image provide Information base preferably.

Background technology

Along with the development of various imaging techniques, people increase day by day to the requirement and application of processing image.For example: network image, remote sensing images, diameter radar images etc. have all become important field of research.It is a major issue during image is processed that image is cut apart, and it is the check to all image pretreating effects, is also follow-up basis of carrying out graphical analysis and decipher.Some feature that image is cut apart exactly according to image separates the zones of different that has special connotation in image, such as the different grey-scale according between the gray level image pixel is not cut apart, after cutting apart, make the grey scale pixel value in the same area close, and the gray-scale value between adjacent area have obvious difference.

Recent years, by combination that original image partition method and Other subjects are intersected, people have proposed the effective image partition method of many novelties, mainly comprise: the methods such as thresholding method, region growing method, morphological segment method and evolution clustering.These methods, due to ambiguity and the uncertainty of not considering that image has, therefore are difficult to obtain result accurately.And the method for fuzzy clustering is that the concept of fuzzy set is applied in cluster analysis, the uncertainty degree that it belongs to each cluster centre by each pixel in Description Image carrys out the ambiguity of presentation video, so is widely applied.Especially FCM method FCM, it is the most typical a kind of non-supervisory fuzzy clustering method in clustering algorithm, and is widely used in the fields such as image is cut apart, data clusters, pattern-recognition.

FCM is a kind of clustering method based on the Optimization of Fuzzy objective function, its main implementation procedure is that the sample point of vector space in image is divided and is clustered into the K sub spaces that will ask for according to certain Rule measure, the feature of passing judgment on each pixel in cluster result is the subjection degree according to these data and cluster centre, this degree of membership is to mean with the numerical value in 0～1 interval, increased the ambiguity between classification, therefore FCM cluster segmentation algorithm has good local convergence, and is adapted at carrying out in high-dimensional feature space the classification of pixel.Yet the weak point of FCM algorithm when the processing image is cut apart is: (1) FCM algorithm does not take into full account the spatial information of image, only all samples are carried out to cluster as the sample point disperseed, cause last segmentation result very poor on regional consistance, there is assorted point in intra-zone; (2) the FCM algorithm is more responsive to initial value and noise ratio, easily is absorbed in local optimum, causes segmentation effect poor.

Look into newly through network, find no the technical scheme identical with the present invention.

Summary of the invention

The object of the invention is to overcome above-mentioned existing methods deficiency, a kind of gray-scale image segmentation method based on the multi objective fuzzy cluster has been proposed, cut apart the reservation of middle detail section to improve gray level image, improve the precision that image is cut apart, process good Information base is provided for successive image, and then reduce error for whole Image Information Processing process.

The technical scheme that realizes the object of the invention comprises the steps:

(1) read in the not gray level image I of Noise of a width, and add up the grey level histogram GH of this gray level image I, GH={n _l, l=0,1 ..., 255}, l is the gray level of gray level image I, n _lit is the pixel number of gray level l.

(2) generate at random cluster centre C, C={c according to the grey level histogram GH of gray level image I _i, i=1 ..., K}, cluster centre C is also referred to as antibody in the present invention, c _ibe the cluster centre of i class, K be gray level image I cut apart the classification number.

(3) according to step (2), gray level image I is operated, generate N antibody, the parent antibody population V that forms gray level image I is V={C _j, j=1 ..., N}, the population number that wherein N is gray level image I, establishing the population iterations is t, the initial value of t is that 1, j is loop variable.

(4) according to any antibody C in the parent antibody population V of gray level image I, the fuzzy membership matrix U of calculating gray level image I is:

U＝{u _ib,i＝1,...,K,b＝1,...,M}，

Wherein, M is the total number of the pixel of gray level image I, u _ibb pixel x in gray level image I _bthe fuzzy membership that belongs to the i class is expressed as:

$u_{\mathrm{ib}}=\frac{1}{{(d(x_b,c_i)/d(x_b,c_1))}^2+{(d(x_b,c_i)/d(x_b,c_2))}^2+\·\·\·+{(d(x_b,c_i)/d(x_b,c_K))}^2},$

Wherein, d (x _b, c _i) be pixel x _bwith cluster centre c _ibetween Euclidean distance, i=1 ..., K, c _iit is the cluster centre of the i class of antibody C;

(5) according to step (4), all N antibody in the parent antibody population V of gray level image I is calculated respectively to its fuzzy membership, the fuzzy membership matrix group U that forms whole population is U={U _j, j=1 ..., N};

(6) according to the parent antibody population V of gray level image I and the fuzzy membership matrix group U of whole population, calculate two target function values of antibody C in population, the efficiency evaluation criterion of weighing the fuzzy clustering of picture element global division is the first aim function, and the fine and close efficiency evaluation criterion of separating is as the second target function;

(7) according to step (6), all N antibody in the parent antibody population V of gray level image I is calculated respectively to its target function value f ₁with target function value f ₂;

(8) according to objective function f ₁with objective function f ₂, find non-dominated antibody population V in the parent antibody population V of gray level image I _f, V _fall non-dominated antibody C in the parent antibody population V of gray level image I ^*set;

(9) according to the non-dominated antibody population V of gray level image I _fcarry out the grade clone operations, generate the rear population V of clone _c;

(10) according to population V after the clone of gray level image I _ccarry out the nonuniformity mutation operation, generate the rear population V of variation _r;

(11) according to population V after the variation of gray level image I _rcarry out dynamic crowding distance deleting mechanism, select the new population V of m antibody as gray level image I;

(12) judge whether iterations t has reached the highest iterations g _maxif meet t>g _max, execution step (13), otherwise return to step (4), t=t+1, carry out next iteration;

(13), in the parent antibody population V of the gray level image I obtained, select optimum antibody C according to third party evaluation index PBM from parent antibody population V after circulation finishes _eas the Optimal cluster centers of gray level image I, wherein PBM is expressed as:

$\mathrm{PBM}={\left(\frac{\left(\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\underset{b=1}{\overset{m}{\mathrm{\Σ}}}{u}_{\mathrm{ib}}\right||x_b-c_i|\left|\right)\×d_{\max }}{\left(\underset{i=1}{\overset{K}{\mathrm{\Σ}}}\underset{b=1}{\overset{M}{\mathrm{\Σ}}}{u}_{\mathrm{ib}}\right||x_b-c_i|\left|\right)\×K}\right)}^2,$

Wherein, d _max={ max||c _i-c _j|| ², i=1 ..., K, j=1 ..., Ki, ≠ j} is antibody C _ethe maximal value of the gray scale difference value between each cluster centre.

(14) according to the grey level histogram GH of gray level image I and optimum cluster centre C _e, calculate each gray level l of gray level image I to each cluster centre c _igray scale difference value d _il;

(15) according to the gray scale difference value d of gray level image I _il, calculate each gray level l of gray level image I to each cluster centre c _iwhat comprise is less than this gray level l to this cluster centre c _ithe pixel number S of all gray levels _il:

Wherein, n _kthe number of the gray level pixel that is k, d _ikthat gray level k is to each cluster centre c _igray scale difference value, d _ilthat gray level l is to cluster centre c _igray scale difference value;

(16) at the pixel number S of gray level image I _ilin, take gray level l as benchmark, find gray level l and each cluster centre c _ipixel number S _ilthe cluster centre c of middle minimum _f, and gray level l is assigned to minimum cluster centre c _fcorresponding f class, obtain the classification results G of gray level image I thus.

Realization of the present invention also is: two target function values described in step (6) are expressed as:

$f_1={\mathrm{\Σ}}_{b=1}^M{\mathrm{\Σ}}_{i=1}^K{\left(u_{\mathrm{ib}}\right)}^2{d}^2(x_b,c_i),$

$f_2=\frac{{\mathrm{\Σ}}_{b=1}^M{\mathrm{\Σ}}_{i=1}^K{\left(u_{\mathrm{ib}}\right)}^2{d}^2(x_b,c_i)}{M}\×\frac{1}{d_{\min }},$

Wherein, d _min={ min||c _i-c _j|| ², i=1 ..., K, j=1 ..., K, i ≠ j} is the minimum value of the gray scale difference value between each cluster centre of antibody C, d ²(x _b, c _i) be the cluster centre c of i class in antibody C _iwith b pixel x in gray level image I _bbetween Euclidean distance.

In the present invention, utilize two objective functions to weigh the quality of cutting apart image, therefore selected two objective functions must be mutually exclusive, mutually complementary.The efficiency evaluation criterion of the fuzzy clustering that the measurement picture element global is divided is as the first aim function, and densification separates the efficiency evaluation criterion as the second target function, less f ₂mean densification and the good cluster of separation property are arranged, and f ₂minimize and depend on f ₁minimize and the arest neighbors class between separation property d _minmaximization.Therefore, f ₁and f ₂can not reach and minimize simultaneously, they can provide one group of non-domination solution.

Realization of the present invention also is: find non-dominated antibody C in step (8) from the parent antibody population V of gray level image I ^*, and form non-dominated antibody population V _fprocess comprise:

8.1 choose any one the antibody C in the parent antibody population V of gray level image I ^*;

8.2 judgement antibody C ^*whether meet following condition:

C _j≠C ^*(f ₁(C ^*)≥f ₁(C _j)&f ₂(C ^*)＞f ₂(C _j))||(f ₁(C ^*)＞f ₁(C _j)&f ₂(C ^*)≥f ₂(C _j))，

F wherein ₁(C ^*) and f ₂(C ^*) be respectively antibody C ^*objective function f ₁with objective function f ₂value, f ₁(C _j) and

F ₂(C _j) be respectively antibody C _jobjective function f ₁with objective function f ₂value, j=1 ..., N;

8.3 meet the antibody C of above-mentioned condition ^*be called non-dominated antibody, V _fall non-dominated antibody C in the parent antibody population V of gray level image I ^*set.

In the present invention, adopt non-domination criterion can better choose the more excellent antibody in current population.

Realization of the present invention also is: the highest iterations g described in step (12) _maxspan be that [50,100] effect is better.G _maxvalue causes calculated amount large than conference, is difficult for observing and the waste computational resource g _maxthe less meeting of value has influence on segmentation precision, g _maxvalue usually according to segmentation precision, require determine, g in the emulation experiment situation _maxget 50 and usually can meet the demands, the present invention is through repeatedly testing and research has provided effect span preferably.

Compared with prior art there is following advantage in the present invention:

1. the present invention separates densification first Validity Function and is applied to gray level image as interpretational criteria and cuts apart field, and it is combined with the fuzzy optimization function in the FCM method, form multi-objective optimization question, this complexity of clustering problem cut apart to(for) the processing image can be searched for from multiple directions simultaneously, the possibility of the more excellent solution of search, improved the accuracy rate that image is cut apart effectively.

2. the present invention is owing to immune clone algorithm, realizing multiple-objection optimization, changed the inhomogeneous shortcoming of sentencing class that in the FCM, the random initializtion cluster centre brings, increased ability of searching optimum on the characteristic of FCM local convergence, can effectively improve the precision that image is cut apart simultaneously.

3. the present invention, after finally obtaining Optimal cluster centers, adds up the number of pixels of each gray level to the distance of cluster centre by gray level in histogram, can retain the detailed information of image, effectively reduces wrong minute rate.

The accompanying drawing explanation

Fig. 1 is realization flow figure of the present invention;

Fig. 2 is to two classification of gray level image House and three classification experiments comparison diagram as a result, g in experiment by the present invention and FCM method _maxget 50, wherein Fig. 2 (a) is the House original-gray image, Fig. 2 (b) is the two classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 2 (c) is the three classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 2 (d) is the two classification segmentation result figure that adopt the inventive method to obtain, and Fig. 2 (e) is the three classification segmentation result figure that adopt the inventive method to obtain;

Fig. 3 is to two classification of gray level image lena and three classification experiments comparison diagram as a result, g in experiment by the present invention and FCM method _maxget 50, wherein Fig. 3 (a) is the lena original-gray image, Fig. 3 (b) is the two classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 3 (c) is the three classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 3 (d) is the two classification segmentation result figure that adopt the inventive method to obtain, and Fig. 3 (e) is the three classification segmentation result figure that adopt the inventive method to obtain;

Fig. 4 is to two classification of gray level image House and three classification experiments comparison diagram as a result, g in experiment by the present invention and FCM method _maxget 100, wherein Fig. 4 (a) is the House original-gray image, Fig. 4 (b) is the two classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 4 (c) is the three classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 4 (d) is the two classification segmentation result figure that adopt the inventive method to obtain, and Fig. 4 (e) is the three classification segmentation result figure that adopt the inventive method to obtain;

Fig. 5 is to two classification of gray level image lena and three classification experiments comparison diagram as a result, g in experiment by the present invention and FCM method _maxget 75, wherein Fig. 5 (a) is the lena original-gray image, Fig. 5 (b) is the two classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 5 (c) is the three classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 5 (d) is the two classification segmentation result figure that adopt the inventive method to obtain, and Fig. 5 (e) is the three classification segmentation result figure that adopt the inventive method to obtain.

Embodiment

Below in conjunction with accompanying drawing, specific embodiment of the invention step and effect are described in further detail:

Embodiment 1

Image is cut apart the important step belonged in image processing process, and it is processed the work such as follow-up target identification, feature extraction Information base is provided for image.Realize that the minimum hardware that the image cutting procedure needs is configured to: personal computer processor 1GHz, internal memory 1GB, software environment is: the softwares such as matlab or VC.

With reference to Fig. 1, the present invention is a kind of gray-scale image segmentation method based on the multi objective fuzzy cluster, and implementation procedure comprises the steps:

Step 1, read in the not gray level image I of Noise of a width, and gray level image can be processed to obtain by the gray processing of digital picture, and gray level image is preserved with the Nonlinear Scale of 8 of each sampled pixel usually, and 256 grades of gray scales can be arranged like this.

In the present embodiment, reading in a width gray level image House, referring to Fig. 2 (a), is the gray level image I that this example will be cut apart, and its size is 227 * 227, adds up the grey level histogram GH:GH={n of this gray level image I _l, l=0,1 ..., 255}, l is the gray level of gray level image I, n _lit is the pixel number of gray level l.The information of reading in image all the mode of two bit matrix mean.

Step 2, according to grey level histogram GH random initializtion cluster centre, C is: C={c _i, i=1 ..., K}, using C as initial antibodies, c _ibe the cluster centre of i class, K be gray level image I cut apart the classification number.Grey level histogram GH is generated to cluster centre at random and may also be referred to as the random initializtion cluster centre, to count the theoretic span of K be [1 to the classification of cutting apart of gray level image, 255], yet the K value causes calculated amount large than conference, be difficult for observing and the waste computational resource, the less meeting of K value has influence on segmentation precision, and the value of K requires definite usually according to segmentation precision, and in the emulation experiment situation, K gets 2 or 3.

In the present embodiment, the random initial antibodies C=(c generated ₁, c ₂), the classification of cutting apart of gray level image I is counted K=2.

Step 3, generate N initial antibodies C according to step 2 is random, and take this, to form parent antibody population V be V={C _j, j=1 ..., N}, the number that wherein N is initial population, establishing population iterations t value is that 1, j is loop variable.

In this example, the number N=10 of initialization population, because K=2, this parent antibody initial population V is 10 * 2 matrix.

Step 4, according to antibody C arbitrarily in population V, the fuzzy membership matrix U of calculating gray level image I is:

U＝{u _ib,i＝1,...,K,b＝1,...,M}，

Wherein, M is the total number of the pixel of gray level image I, u _ibb pixel x in gray level image I _bthe fuzzy membership that belongs to the i class is expressed as:

$u_{\mathrm{ib}}=\frac{1}{{(d(x_b,c_i)/d(x_b,c_1))}^2+{(d(x_b,c_i)/d(x_b,c_2))}^2+\·\·\·+{(d(x_b,c_i)/d(x_b,c_K))}^2},$

Wherein, d (x _b, c _i) be pixel x _bwith cluster centre c _ibetween Euclidean distance, i=1 ..., K, c _iit is the cluster centre of the i class of antibody C.

In the present embodiment, the total number M of the pixel of gray level image I is 227 * 227, and the classification of cutting apart of gray level image I is counted K=2, so b pixel x of antibody C in population V _bthe fuzzy membership that belongs to the i class, u _ibbe expressed as:

$u_{\mathrm{ib}}=\frac{1}{{(d(x_b,c_i)/d(x_b,c_1))}^2+{(d(x_b,c_i)/d(x_b,c_2))}^2},$

In population, the fuzzy membership of all pixels of all antibody is identical with the above formula representation.

Step 5, operated according to all N antibody in step 4 pair population, and the fuzzy membership matrix group U that forms whole population is U={U _j, j=1 ..., N}, be that 10 antibody are carried out to this operation in this example.

Step 6, according to the parent antibody population V of gray level image I and the fuzzy membership matrix group U of whole population, calculate two target function values of antibody C in population, the efficiency evaluation criterion of weighing the fuzzy clustering of picture element global division is the first aim function, and the fine and close efficiency evaluation criterion of separating is as the second target function.

Wherein in population, the first object function representation of antibody C is:

$f_1={\mathrm{\Σ}}_{b=1}^M{\mathrm{\Σ}}_{i=1}^K{\left(u_{\mathrm{ib}}\right)}^2{d}^2(x_b,c_i),$

The fine and close second target function representation that separates the efficiency evaluation criterion is:

$f_2=\frac{{\mathrm{\Σ}}_{b=1}^M{\mathrm{\Σ}}_{i=1}^K{\left(u_{\mathrm{ib}}\right)}^2{d}^2(x_b,c_i)}{M}\×\frac{1}{d_{\min }},$

Wherein, d _min={ min||c _i-c _j|| ², i=1 ..., K, j=1 ..., K, i ≠ j} is the minimum value of the gray scale difference value between each cluster centre of antibody C, d ²(x _b, c _i) be the cluster centre c of i class in antibody C _iwith b pixel x in gray level image I _bbetween Euclidean distance.

Middlely can more effectively search for more outstanding splitting scheme in order to cut apart at image, improve the accuracy rate that image is cut apart, the present invention utilizes two objective functions to construct Model for Multi-Objective Optimization, therefore selected two objective functions must be mutually exclusive, mutually complementary, can from a plurality of angles, be cut apart image simultaneously.The efficiency evaluation criterion of the fuzzy clustering that the measurement picture element global is divided is as the first aim function, and the fine and close efficiency evaluation criterion of separating is as second target function, f ₂for meaning the ratio of the fuzzy mean square distance sum of pixel and the minimum separation of cluster centre, expect densification and separation property segmentation result preferably, the fine and close validity objective function f that separates of expectation ₂value less.And f ₂minimize and depend on f ₁minimize and the arest neighbors class between separation property d _minmaximization.Therefore, f ₁and f ₂can not reach and minimize simultaneously, they can provide one group of non-domination solution.In this example, the classification of cutting apart of gray level image I is counted K=2.

Step 7, calculate respectively its target function value according to all N antibody in step 6 pair population, comprises the first object function f ₁with the second objective function f ₂.

Step 8, according to objective function f ₁with objective function f ₂, find non-dominated antibody population V in population V _f, to any one the antibody C in population V ^*, and if only if antibody C ^*meet:

C _j≠ C ^*and (f ₁(C ^*)>=f ₁(C _j) & f ₂(C ^*)>f ₂(C _j)) || (f ₁(C ^*)>f ₁(C _j) & f ₂(C ^*)>=f ₂(C _j)), antibody C ^*for non-dominated antibody,

F wherein ₁(C ^*) and f ₂(C ^*) be respectively any one antibody C ^*objective function f ₁with objective function f ₂value, f ₁(C _j) and f ₂(C _j) be respectively antibody C _jobjective function f ₁with objective function f ₂value;

In this example, selected non-dominated antibody population V _fthe antibody number be 5.

Step 9, according to non-dominated antibody population V _fcarry out the grade clone operations, generate the rear population V of clone _c.

The method of existing clone operations has whole clone, and grade clone etc. in embodiments of the present invention, adopt the grand operation of grade, population V after the clone _cnumber be 15.

Step 10, according to population V after the clone _ccarry out the nonuniformity mutation operation, generate the rear population V of variation _r.

The method of existing mutation operation has the single-point variation, the multiple spot variation, and antibody neighbour variation, nonuniformity variation etc., in this example, what mutation operation adopted is the nonuniformity variation, the probability of variation is 0.1, to cloning rear population V _ci the cluster centre c of any one antibody C _icarry out the nonuniformity variation:

$c_i=\left\{\begin{array}{cc}{c}_i-1& r\&GreaterEqual;0\\ c_i+1& r<0\end{array}\right.,$

I=1 wherein ..., K, r is the random real number generated between-1 to 1, in this example, the classification of cutting apart of gray level image I is counted K=2.

Step 11, according to population V after variation _rcarry out dynamic crowding distance deleting mechanism, select m antibody as new population V.

In this example, m gets 10, and dynamic crowding distance deleting mechanism antagonist according to the following rules upgrades operation, i.e. population V after variation _rthe antibody scale is greater than at 10 o'clock, and the antibody in intensive place is deleted.At first to the rear population V that makes a variation _rin all antibody carry out the ascending order arrangement according to first aim function f 1, allow C _jmean the rear population V of drained order variation _rin j antibody, 1≤j≤10, C so _jcrowding distance m (C _j) be expressed as:

$m\left(C_j\right)=\frac{f_1\left(C_{j+1}\right)-f_1\left(C_{j-1}\right)}{{f_1}^{\max }-{f_1}^{\min }}+\frac{f_2\left(C_{j-1}\right)-f_2\left(C_{j+1}\right)}{{f_2}^{\max }-{f_2}^{\min }},$

F wherein ₁ ^maxmean population V _rin the maximal value of all antibody first aim functions, f ₁ ^minmean population V _rin all antibody first aim minimum of a function values, f ₂ ^maxmean population V _rin the maximal value of all antibody second target functions, wherein f ₂ ^minmean population V _rin all antibody second target minimum of a function values.Delete the rear population V of variation _rthe antibody of middle crowding distance value minimum, stop until non-dominated antibody scale reaches at 10 o'clock.

Step 12, judge whether iterations t has reached the highest iterations g _maxif meet t>g _max, performing step 13, otherwise return to step 4, t=t+1, carry out next iteration.

In this example, maximum iteration time g _max=50.

G _maxvalue more calculated amount is large, is difficult for observing and the waste computational resource, and efficiency is low, g _maxthe little meeting of value has influence on segmentation precision, g _maxvalue according to segmentation precision, require to determine, the present invention is through repeatedly testing and research has provided effect span preferably.

Step 13, in the antibody population V obtained after circulation finishes, select optimum antibody C according to third party evaluation index PBM _eas Optimal cluster centers, wherein PBM is expressed as:

$\mathrm{PBM}={\left(\frac{\left(\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}\underset{b=1}{\overset{m}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ib}}\right||x_b-c_i|\left|\right)\&times;d_{\max }}{\left(\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{b=1}{\overset{M}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ib}}\right||x_b-c_i|\left|\right)\&times;K}\right)}^2,$

Wherein, d _max={ max||c _i-c _j|| ², i=1 ..., K, j=1 ... K, i ≠ j} is antibody C _ethe maximal value of the gray scale difference value between each cluster centre.

Step 14, according to grey level histogram GH and optimum cluster centre C _e, calculate each gray level l to each cluster centre c _igray scale difference value d _il.

In the present embodiment, the gray level image House of employing has 256 gray levels, and the classification of cutting apart of gray level image I counts N=2, so d _ilit is 256 * 2 matrix.

Step 15, according to gray scale difference value d _il, calculate each gray level l to each cluster centre c _iwhat comprise is less than this gray level l to this cluster centre c _ithe pixel number S of all gray levels _il:

Wherein, n _kthe number of the gray level pixel that is k, d _ikthat gray level k is to each cluster centre c _igray scale difference value, d _ilthat gray level l is to cluster centre c _igray scale difference value.

Step 16, at pixel number S _ilin, take gray level l as benchmark, find gray level l and each cluster centre c _ipixel number S _ilthe cluster centre c of middle minimum _f, and gray level l is assigned to minimum cluster centre c _fcorresponding f class, obtain classification results G thus.The classification results figure of reduction is referring to Fig. 2 (d).

Contrast experiment of the present invention is classical FCM image partition method, and image segmentation result is contrasted with gray level image.Fig. 2 (a) is the House original-gray image, Fig. 2 (b) is the two classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 2 (d) is the two classification segmentation result figure that adopt the inventive method to obtain, from Fig. 2 (b) and Fig. 2 (d) contrast, can find out: the inventive method can be told the metope Vertical texture information of House image better, the segmentation result that adopts the FCM method to obtain does not have this advantage, divide under shade cutting apart of metope under metope and sunlight for the right side of House image, the inventive method can be told the different detailed information of these two kinds of metopes better, the segmentation result that adopts the FCM method to obtain can not differentiated the difference of these two kinds of metopes, the inventive method intactly has been partitioned into the doorframe marginal information of House image in addition, improved the precision that image is cut apart, and the FCM method has been carried out misclassification by the coboundary of doorframe in the House image.

Embodiment 2

Gray-scale image segmentation method based on the multi objective fuzzy cluster is with embodiment 1, and in embodiment 2, the contrast experiment is classical FCM image partition method, and image segmentation result is contrasted with gray level image.In embodiment 2, adopt gray level image House as input picture, the image size is 227 * 227 pixels, and gray level is 256, maximum iteration time g _maxget 50, image is cut apart classification and is counted K and be set to 3, is gray level image to be carried out to three cut apart.Adopt the present invention to be processed final classification results figure referring to Fig. 2 (e).

Fig. 2 (a) is the House original-gray image, Fig. 2 (c) is the three classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 2 (e) is the three classification segmentation result figure that adopt the inventive method to obtain, from Fig. 2 (c) and Fig. 2 (e) contrast, can find out: method of the present invention can be told the metope of House image and the texture information on roof better, and the segmentation result that adopts the FCM method to obtain can not be told the texture on metope and roof.

Embodiment 3

Gray-scale image segmentation method based on the multi objective fuzzy cluster is with embodiment 1, and in embodiment 3, the contrast experiment is classical FCM image partition method, and image segmentation result is contrasted with gray level image.In embodiment 3, adopt gray level image lena as input picture, the image size is 256 * 256 pixels, and gray level is 256, maximum iteration time g _maxget 50, image is cut apart classification and is counted K and be set to 2, is gray level image to be carried out to two cut apart.Final classification results figure is referring to Fig. 3 (d).

Fig. 3 (a) is the lena original-gray image, Fig. 3 (b) is the two classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 3 (d) is the two classification segmentation result figure that adopt the inventive method to obtain, from Fig. 3 (b) and Fig. 3 (d) contrast, can find out: the inventive method can be told the facial information of lena image better, personage's mouth in Fig. 3 (d) for example, the profile of nose and eyes is more complete, and in the segmentation result figure that adopts the FCM method to obtain, the character facial partial information is lost, as nose, the information dropout at face position, overall segmentation accuracy is lower, secondly the segmentation result for lena image cap part contrasts, also can find out that the inventive method can better more tell shade and non-hatched area, more intactly be partitioned into dash area, the FCM method is to having cutting apart of dash area disappearance and details imperfect.

Embodiment 4

Gray-scale image segmentation method based on the multi objective fuzzy cluster is with embodiment 1, and in embodiment 4, the contrast experiment is classical FCM image partition method, and image segmentation result is contrasted with gray level image.In embodiment 4, adopt gray level image lena as input picture, the image size is 256 * 256 pixels, and gray level is 256, maximum iteration time g _maxget 50, image is cut apart classification and is counted K and be set to 3, is gray level image to be carried out to three cut apart.Final classification results figure is referring to Fig. 3 (e).

Fig. 3 (a) is the lena original-gray image, Fig. 3 (c) is the three classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 3 (e) is the three classification segmentation result figure that adopt the inventive method to obtain, from Fig. 3 (c) and Fig. 3 (e) contrast, can find out: the inventive method can have more stereovision to the processing of gray scale part, process better the detailed information of lena image, effectively be partitioned into the zone of dash area, improved the precision that image is cut apart, the segmentation result that adopts the FCM method to obtain does not have this advantage.

Embodiment 5

Gray-scale image segmentation method based on the multi objective fuzzy cluster is with embodiment 1.In embodiment 5, the contrast experiment is classical FCM image partition method, and image segmentation result is contrasted with gray level image.In embodiment 5, adopt gray level image House as input picture, the image size is 227 * 227 pixels, and gray level is 256, maximum iteration time g _maxget 100, image is cut apart classification and is counted K and be set to 2, is gray level image to be carried out to two cut apart.Final classification results figure is referring to Fig. 4 (d).

Fig. 4 (a) is the House original-gray image, Fig. 4 (b) is the two classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 4 (d) is the two classification segmentation result figure that adopt the inventive method to obtain, from Fig. 4 (b) and Fig. 4 (d) contrast, can find out: the segmentation result of FCM method, for cutting apart of doorframe, be incomplete, and the segmentation result of the present invention shown in Fig. 4 (d) can detect complete doorframe edge effectively, secondly in the House original-gray image, the Vertical texture of metope and the shade of right side metope are resolved out in Fig. 4 (d), these detailed information have been lacked in the segmentation result figure of FCM method.

Embodiment 6

Gray-scale image segmentation method based on the multi objective fuzzy cluster is with embodiment 1.In embodiment 6, the contrast experiment is classical FCM image partition method, and image segmentation result is contrasted with gray level image.In embodiment 6, adopt gray level image House as input picture, the image size is 227 * 227 pixels, and gray level is 256, maximum iteration time g _maxget 100, image is cut apart classification and is counted K and be set to 3, is gray level image to be carried out to three cut apart.Final classification results figure is referring to Fig. 4 (e).

Fig. 4 (a) is the House original-gray image, Fig. 4 (c) is the three classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 4 (e) is the three classification segmentation result figure that adopt the inventive method to obtain, from Fig. 4 (c) and Fig. 4 (e) contrast, can find out: apply dividing method of the present invention, the texture of the Vertical texture of metope and roof tile is accurately detected, and does not tell these detailed information in the segmentation result figure that the FCM method obtains.

Embodiment 7

Gray-scale image segmentation method based on the multi objective fuzzy cluster is with embodiment 1-6, and in embodiment 7, the contrast experiment is classical FCM image partition method, and image segmentation result is contrasted with gray level image.In embodiment 7, adopt gray level image lena as input picture, the image size is 256 * 256 pixels, and gray level is 256, maximum iteration time g _maxget 75, image is cut apart classification and is counted K and be set to 2, is gray level image to be carried out to two cut apart.Final classification results figure is referring to Fig. 5 (d).

Fig. 5 (a) is the lena original-gray image, Fig. 5 (b) is the two classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 5 (d) is the two classification segmentation result figure that adopt the inventive method to obtain, from Fig. 5 (b), can find out, the FCM method has been lost the part detailed information of lena image, and segmentation result figure lacks stereovision; From Fig. 5 (d), can find out, the inventive method is partitioned into the zone of dash area effectively, has improved the precision that image is cut apart.

Embodiment 8

Gray-scale image segmentation method based on the multi objective fuzzy cluster is with embodiment 1-7, and in embodiment 8, the contrast experiment is classical FCM image partition method, and image segmentation result is contrasted with gray level image.In embodiment 8, adopt gray level image lena as input picture, the image size is 256 * 256 pixels, and gray level is 256, maximum iteration time g _maxget 75, image is cut apart classification and is counted K and be set to 3, is gray level image to be carried out to three cut apart.Final classification results figure is referring to Fig. 5 (e).

Fig. 5 (a) is the lena original-gray image, Fig. 5 (c) is the three classification segmentation result figure that adopt contrast experiment's FCM method to obtain, Fig. 5 (e) is the three classification segmentation result figure that adopt the inventive method to obtain, from Fig. 5 (c) and Fig. 5 (e) contrast, can find out: the inventive method can be told the facial information of lena image better, and in the segmentation result figure that adopts the FCM method to obtain, the character facial partial information is lost, as nose, the information dropout at face position, overall segmentation accuracy is lower.

To sum up, the gray-scale image segmentation method based on Fuzzy Multiobjective that the present invention proposes, mainly solve gray level image and cut apart the problem that accuracy rate is low.The method is after image is carried out to the gray processing processing, according to the grey level histogram generated, generates at random a plurality of cluster centres, and forms the parent antibody population; Key of the present invention is first densification to be separated the fuzzy optimization function of Validity Function in interpretational criteria and FCM method and combines, form multi-objective optimization question, and adopt the immune clone multi-objective Evolutionary Algorithm to carry out repeatedly iteration to whole parent population, from multiple directions, search for simultaneously, parallel computation, finally obtain optimum cluster centre, the output category result.Can effectively retain the detailed information in gray level image, reduce wrong minute rate, effectively improve the precision that gray level image is cut apart, gray level image is partitioned into to comparatively desirable effect, the subsequent operation of cutting apart for gray level image provides better platform.

The present invention has advantages of that the image segmentation precision is high, can be used for extracting and obtaining the detailed information of gray level image.

Claims (4)

1. the gray-scale image segmentation method based on the multi objective fuzzy cluster, is characterized in that including as follows

Step:

(1) read in the not gray level image I of Noise of a width, and the grey level histogram GH of statistics gray level image I is GH={n _l, l=0,1 ..., 255}, l is the gray level of gray level image I, n _lit is the pixel number of gray level l;

(2) generate at random cluster centre C, C={c according to the grey level histogram GH of gray level image I _i, i=1 ..., K}, cluster centre C is also referred to as antibody, c _ibe the cluster centre of i class, K be gray level image I cut apart the classification number;

(3) according to step (2), gray level image I is operated, generate N antibody, the parent antibody population V that forms gray level image I is V={C _j, j=1 ..., N}, the population number that wherein N is gray level image I, establishing the population iterations is t, the initial value of t is that 1, j is loop variable;

(4) according to any antibody C in the parent antibody population V of gray level image I, the fuzzy membership matrix U of calculating gray level image I is:

U＝{u _ib,i＝1,...,K,b＝1,...,M}，

Wherein, M is the total number of the pixel of gray level image I, u _ibb pixel x in gray level image I _bthe fuzzy membership that belongs to the i class is expressed as:

$u_{\mathrm{ib}}=\frac{1}{{(d(x_b,c_i)/d(x_b,c_1))}^2+{(d(x_b,c_i)/d(x_b,c_2))}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(d(x_b,c_i)/d(x_b,c_K))}^2},$

Wherein, d (x _b, c _i) be pixel x _bwith cluster centre c _ibetween Euclidean distance, i=1 ..., K, c _iit is the cluster centre of the i class of antibody C;

(5) according to step (4), all N antibody in the parent antibody population V of gray level image I is calculated respectively to its fuzzy membership, the fuzzy membership matrix group U that forms whole population is U={U _j, j=1 ..., N};

(6) according to the parent antibody population V of gray level image I and the fuzzy membership matrix group U of whole population, calculate two target function values of antibody C in population, the efficiency evaluation criterion of weighing the fuzzy clustering of picture element global division is the first aim function, and the fine and close efficiency evaluation criterion of separating is as the second target function;

(7) according to step (6), all N antibody in the parent antibody population V of gray level image I is calculated respectively to its target function value f ₁with target function value f ₂;

(8) according to objective function f ₁with objective function f ₂, find non-dominated antibody population V in the parent antibody population V of gray level image I _f, V _fall non-dominated antibody C in the parent antibody population V of gray level image I ^*set;

(9) according to the non-dominated antibody population V of gray level image I _fcarry out the grade clone operations, generate the rear population V of clone _c;

(10) according to population V after the clone of gray level image I _ccarry out the nonuniformity mutation operation, generate the rear population V of variation _r;

(11) according to population V after the variation of gray level image I _rcarry out dynamic crowding distance deleting mechanism, select the new population V of m antibody as gray level image I;

(12) judge whether iterations t has reached the highest iterations g _maxif meet t>g _max, execution step (13), otherwise return to step (4), t=t+1, carry out next iteration;

(13), in the parent antibody population V of the gray level image I obtained, select optimum antibody C according to third party evaluation index PBM from parent antibody population V after circulation finishes _eoptimal cluster centers as gray level image I;

(14) according to the grey level histogram GH of gray level image I and optimum cluster centre C _e, calculate each gray level l of gray level image I to each cluster centre c _igray scale difference value d _il;

(15) according to the gray scale difference value d of gray level image I _il, calculate each gray level l of gray level image I to each cluster centre c _iwhat comprise is less than this gray level l to this cluster centre c _ithe pixel number S of all gray levels _il:

Wherein, n _kthe number of the gray level pixel that is k, d _ikthat gray level k is to each cluster centre c _igray scale difference value, d _ilthat gray level l is to cluster centre c _igray scale difference value;

(16) at the pixel number S of gray level image I _ilin, take gray level l as benchmark, find gray level l and each cluster centre c _ipixel number S _ilthe cluster centre c of middle minimum _f, and gray level l is assigned to minimum cluster centre c _fcorresponding f class, obtain the classification results G of gray level image I thus.

2. the gray-scale image segmentation method based on the multi objective fuzzy cluster according to claim 1, it is characterized in that: two target function values described in step (6) are expressed as:

$f_1={\mathrm{\&Sigma;}}_{b=1}^M{\mathrm{\&Sigma;}}_{i=1}^K{\left(u_{\mathrm{ib}}\right)}^2{d}^2(x_b,c_i),$

$f_2=\frac{{\mathrm{\&Sigma;}}_{b=1}^M{\mathrm{\&Sigma;}}_{i=1}^K{\left(u_{\mathrm{ib}}\right)}^2{d}^2(x_b,c_i)}{M}\&times;\frac{1}{d_{\min }},$

Wherein, d _min={ min||c _i-c _j|| ², i=1 ..., K, j=1 ..., K, i ≠ j} is the minimum value of the gray scale difference value between each cluster centre of antibody C, d ²(x _b, c _i) be the cluster centre c of i class in antibody C _iwith b pixel x in gray level image I _bbetween Euclidean distance.

3. the gray-scale image segmentation method based on the multi objective fuzzy cluster according to claim 2, is characterized in that: find non-dominated antibody C in step (8) from the parent antibody population V of gray level image I ^*, form non-dominated antibody population V _f, its process comprises:

8.1 choose any one the antibody C in the parent antibody population V of gray level image I ^*;

8.2 judgement antibody C ^*whether meet following condition:

C _j≠C ^*(f ₁(C ^*)≥f ₁(C _j)&f ₂(C ^*)＞f ₂(C _j))||(f ₁(C ^*)＞f ₁(C _j)&f ₂(C ^*)≥f ₂(C _j))，

F wherein ₁(C ^*) and f ₂(C ^*) be respectively antibody C ^*objective function f ₁with objective function f ₂value, f ₁(C _j) and

F ₂(C _j) be respectively antibody C _jobjective function f ₁with objective function f ₂value, j=1 ..., N;

8.3 meet the antibody C of above-mentioned condition ^*be called non-dominated antibody, V _fall non-dominated antibody C in the parent antibody population V of gray level image I ^*set.

4. the gray-scale image segmentation method based on the multi objective fuzzy cluster according to claim 3, is characterized in that: the highest iterations g described in step (12) _maxvalue between 50 to 100.

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