CN104123561A - Spatial gravity model based fuzzy c-means remote sensing image automatic classification method - Google Patents

Abstract

A kind of fuzzy C-mean algorithm remote sensing image automatic classification method based on spatial attraction model, the automatic segmentation suitable for remote sensing image, medical image and other images are used with when classifying. Step are as follows: determine the pixel number of Remote Sensing Digital Image, and image is clustered using standard FCM model and is initialized, the spatial attraction and space constraint penalty factor between other pixels in each pixel and its neighborhood window are successively sought later, finally obtain fuzzy factor By by fuzzy factor Addition standard FCM model recycles to obtain new cluster objective function and seeks fuzzy matrix And cluster centre Until cluster centre do not continue to variation or operation reach maximum number of iterations, then the fuzzy membership matrix U finally acquired={ uki } c × N is utilized, classification described in each pixel is determined each pixel point progress category label of remote sensing image using subordinated-degree matrix criterion is maximized, classification of remote-sensing images thematic map is formed, to realize the automatic classification of Remote Sensing Digital Image. Its method is simple, high degree of automation, is influenced by picture noise that small, classification of image segmentation accuracy is high.

Description

Fuzzy C-mean algorithm remote sensing image automatic classification method based on spatial attraction model

Technology neighborhood

The present invention relates to a kind of remote sensing image automatic classification method, the fuzzy C-mean algorithm remote sensing image automatic classification method based on spatial attraction model using in the auto Segmentation that is particularly useful for remote sensing image, medical image and other images and classification.

Background technology

Remotely-sensed data classification is an important technology that extracts thematic categorical data from remotely-sensed data, for every profession and trade information extraction provides abundant Data Source.Current sorting technique is mainly divided into supervised classification and not supervised classification, compared with supervised classification method, not supervised classification can not need the priori can information extraction from remotely-sensed data, and therefore, not supervised classification has very important status in remotely-sensed data classification.

Existing not supervised classification mainly contains ISODATA, KNN, K-means, the methods such as Markov random field (MRF) and Fuzzy C-Means Clustering Algorithm (FCM).Wherein, FCM is a kind of clustering algorithm based on prototype, there is the features such as simple, efficient, data strong adaptability, and compare with hard sorting technique, FCM can obtain the degree of membership that each pixel belongs to each classification, can retain as much as possible the information of image, be more suitable for the remote sensing image for representing to have a large amount of mixed pixels.Standard FC M algorithm is to be proposed by Dune, after promoted by Bezdek, be a kind of iteration optimization method.But, in standard FC M cluster process, do not consider the impact between adjacent picture elements, in the time cutting apart the lower image of signal to noise ratio (S/N ratio), can produce very large error.In order to overcome standard FC M algorithm to responsive this problem of peak of noise, a lot of researchists have added the space constraint of image in the FCM of standard simulated target function, have proposed many improved FCM clustering algorithms, as FCM_S, FCM_S1, FCM_S2, BCFCM, GG-FCM, EnFCM, FGFCM etc.These improvement algorithms have improved the performance of standard FC M to a certain extent, but the effect of these methods be subject to window size, scale factor isoparametric affect very serious, and the selection of these parameters has very large uncertainty, therefore the versatility of these algorithms awaits further checking.At present, occurred a kind of fuzzy local message C means clustering algorithm FLICM, the local restriction of employing can integrate local spatial information and pixel characteristic simultaneously, and does not need additional parameter to calculate.But, in the time that picture noise is larger, FLICM algorithm to cut apart accuracy still lower, main cause is because just simply considered the degree of membership value of space length and the neighborhood pixel of center pixel and neighborhood pixel in FLICM, and do not consider the degree of membership value of center pixel, and the fuzzy factor computing method that propose are without any physical significance.In the segmentation and classification result of FLICM, domain of the existence edge is excessively level and smooth, and has lost a large amount of detailed information.Therefore, be badly in need of one and both retained edge details information, considered again the efficient FCM algorithm of local spatial information.

Summary of the invention

Technical matters: fundamental purpose of the present invention is the weak point overcoming in prior art, provides that a kind of method is simple, automaticity is high, be subject to picture noise to affect the fuzzy C-mean algorithm remote sensing image automatic classification method based on spatial attraction model little, classification of image segmentation accuracy is high.

Technical scheme: for achieving the above object, the fuzzy C-mean algorithm remote sensing image automatic classification method based on spatial attraction model of the present invention, comprises the following steps

Step 1: obtain Remote Sensing Digital Image to be sorted, obtain the pixel number of Remote Sensing Digital Image according to picture size and wave band number, need to determine cluster classification number c and the Fuzzy Exponential m of Remote Sensing Digital Image according to actual classification, and utilize the FCM model of standard to carry out cluster to Remote Sensing Digital Image to obtain initialization fuzzy membership matrix U ₀={ u _ki} _{c × N}with cluster centre V ₀={ v _k} _c;

Step 2: set neighborhood window size, determine the pixel in the neighborhood window using each pixel in Remote Sensing Digital Image as center pixel in Remote Sensing Digital Image according to the neighborhood window size of setting, pass through formula spatial attraction NA between other pixel in each pixel and its affiliated neighborhood window in calculating Remote Sensing Digital Image _ij,

Wherein, G is constant, is used for representing to regulate the contribution of space constraint to cluster objective function, generally establishes G=1, u _kirepresent neighborhood window center pixel x _ibelong to the degree of membership of k classification, u _kjrepresent j pixel x in neighborhood window _jbelong to the degree of membership of k classification, R _ijrepresent pixel x _iwith pixel x _jbetween theorem in Euclid space distance;

Step 3: utilize each pixel in Remote Sensing Digital Image and the spatial attraction NA between other pixel in neighborhood window under it _ij, pass through formula obtain the space constraint penalty factor w between pixel in Remote Sensing Digital Image _ij,

Wherein, w _ijrepresent j pixel x in neighborhood window _jthe x of centering imago unit _iweighing factor, N _ipixel in the neighborhood window of expression center pixel, NA _ijfor each pixel x in the image calculating in step 2 _iwith by pixel x _ias x in the neighborhood window of center pixel _iall the other pixel x _jbetween spatial attraction, | x _i-x _j| represent pixel x _iwith by pixel x _ias the pixel x in the neighborhood window of center pixel _jbetween gray-scale value poor;

Step 4: pass through formula $G_{\mathrm{ki}}^{*}=\underset{j\∈N_i}{\mathrm{\Σ}}{w}_{\mathrm{ij}}{\left|\right|x_j-v_k\left|\right|}^2$ Obtain fuzzy factor

Step 5: pass through formula $J_m^{*}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{k=1}{\overset{c}{\mathrm{\Σ}}}[u_{\mathrm{ki}}^m{\left|\right|x_i-v_k\left|\right|}^2+G_{\mathrm{ki}}^{*}]$ By fuzzy factor join standard FC M model, obtain cluster objective function

Wherein, the pixel number that N is Remote Sensing Digital Image to be sorted, c is the cluster number of classification Remote Sensing Digital Image, represent that the pixel of i in Remote Sensing Digital Image to be sorted belongs to the degree of membership of k class, the Fuzzy Exponential that m is Remote Sensing Digital Image to be sorted, x _irepresent i pixel of Remote Sensing Digital Image to be sorted, v _kfor the central point of Remote Sensing Digital Image k class to be sorted;

The initial fuzzy matrix U obtaining in integrating step 1 ₀with cluster centre V ₀, utilize formula calculate the cluster centre that remote sensing image to be sorted is new count represent the current new cluster centre obtaining;

Recycling formula $u_{\mathrm{ki}}^{*}=\underset{j=1}{\overset{c}{\mathrm{\Σ}}}{\left(\frac{{\left|\right|x_i-v_k\left|\right|}^2+G_{\mathrm{ki}}^{*}}{{\left|\right|x_i-v_j\left|\right|}^2+G_{\mathrm{ji}}^{*}}\right)}^{\frac{-1}{m-1}}$ Calculate the degree of membership matrix that remote sensing image to be sorted is new count represent the current new fuzzy matrix obtaining; Now for passing through initial cluster centre V ₀obtain, represent before the cluster centre that once obtains; for passing through initial fuzzy matrix U ₀obtain, represent before the fuzzy matrix that once obtains;

Step 6: judge cluster centre whether continuation changes exclusive disjunction reaches maximum iteration time, and setting iteration stopping threshold epsilon=1e-5 is a little positive number, t the cluster centre that Remote Sensing Digital Image to be sorted is tried to achieve with t-1 cluster centre compare, if meet or b > T both one of condition, iteration finishes, described b initial value is that 0, T is 100, otherwise, set b=b+1, with the current fuzzy matrix obtaining and cluster centre substitute respectively initial fuzzy matrix U ₀with cluster centre V ₀, and be set as with turn back to step 2, repeated execution of steps 2～step 6, until meet or b > T both one of condition;

Step 7: utilize the fuzzy membership matrix U={ u finally obtaining _ki} _{c × N}, determine each pixel x according to following formula _iaffiliated classification, for each pixel x _i, classification c under it _ifor degree of membership u _kithat classification of middle maximum;

C _i＝arg _k{max(u _ki)},k＝1,2,3,…,c

Step 8: according to each pixel x _iaffiliated classification c _igive different colors by different cluster classifications, form classification of remote-sensing images thematic map, thereby realize the automatic classification of Remote Sensing Digital Image.

Beneficial effect: the present invention is by calculating the space constraint penalty factor w between pixel in Remote Sensing Digital Image _ij, consider the gray-scale relation of local pixel in Remote Sensing Digital Image, the fuzzy factor based on spatial attraction model of the spatial context characteristic that can reflect each pixel has comprehensively been proposed be used for suppressing noise.Except having considered the degree of membership value of space length and neighborhood pixel of center pixel and neighborhood pixel, also consider the degree of membership value of center pixel, and the fuzzy factor of introducing there is physical significance, both retained edge details information, considered again local spatial information.The present invention has used the spatial attraction NA between other pixel in center pixel and its corresponding neighborhood window _ijself-adaptation is determined the influence degree of neighborhood pixel centering imago unit, without learning experience value; Introduce the fuzzy factor based on spatial attraction model in objective function, this classification is had the processing containing noisy Remote Sensing Digital Image is had to robustness, and image detail is handled well; Its method is simple, and desired parameters is identical with the FCM of standard, without other parameters, be subject to picture noise affect little, classification of image segmentation accuracy is high, has practicality widely.

Brief description of the drawings:

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is pixel neighborhood window structure signal of the present invention;

Fig. 3 is segmentation result on the embodiment of the present invention 1 remote sensing image and the comparison diagram of prior art;

Fig. 4 is segmentation result on the embodiment of the present invention 2 remote sensing images and the comparison diagram of prior art.

Embodiment:

Below in conjunction with accompanying drawing, embodiments of the invention are further described:

As shown in Figure 1, the fuzzy C-mean algorithm remote sensing image automatic classification method based on spatial attraction model of the present invention, comprises that step is as follows:

Step 1: obtain Remote Sensing Digital Image to be sorted (P, Q, S), the line number that wherein P is image; Q is the columns of image, the wave band number of S image, according to picture size and wave band number, Remote Sensing Digital Image (P, Q, S) is converted to 2 dimension matrix (S, P × Q) form, only consider pixel number and the wave band number of Remote Sensing Digital Image to be sorted, need to determine cluster classification number c and the Fuzzy Exponential m of sense digitized video (S, P × Q) according to actual classification; Utilize the FCM model of standard to carry out cluster to Remote Sensing Digital Image (S, P × Q) and obtain initialization fuzzy membership matrix U ₀={ u _ki} _{c × N}with cluster centre V ₀={ v _k} _c;

Step 2: set neighborhood window size, be illustrated in figure 2 the window that a window size is 5, numeral 1 in figure, 2,4 ... represent the neighborhood scope of center pixel x, determine in Remote Sensing Digital Image (S, P × Q) according to the neighborhood window size of setting, pixel in neighborhood window using each pixel in Remote Sensing Digital Image as center pixel, passes through formula calculate the spatial attraction NA between other pixel in each pixel in Remote Sensing Digital Image and affiliated neighborhood window _ij,

Wherein, G is constant, is used for representing to regulate the contribution of space constraint to cluster objective function, generally establishes G=1, u _kirepresent neighborhood window center pixel x _ibelong to the degree of membership of k classification, u _kjrepresent j pixel x in neighborhood window _jbelong to the degree of membership of k classification, R _ijrepresent pixel x _iwith pixel x _jbetween theorem in Euclid space distance;

Step 3: utilize the spatial attraction NA between other pixel in each pixel and affiliated neighborhood window in Remote Sensing Digital Image _ij, pass through formula obtain the space constraint penalty factor w between pixel in Remote Sensing Digital Image _ij,

Wherein, w _ijrepresent j pixel x in neighborhood window _jthe x of centering imago unit _iweighing factor, N _iexpression center pixel x _ineighborhood window in pixel, NA _ijfor each pixel x in the image calculating in step 2 _iwith by pixel x _ias all the other the pixel x in the neighborhood window of center pixel _jbetween spatial attraction, | x _i-x _j| represent pixel x _iwith by pixel x _ias the pixel x in the neighborhood window of center pixel _jbetween gray-scale value poor;

Step 4: pass through formula $G_{\mathrm{ki}}^{*}=\underset{j\∈N_i}{\mathrm{\Σ}}{w}_{\mathrm{ij}}{\left|\right|x_j-v_k\left|\right|}^2$ Obtain fuzzy factor

Step 5: pass through formula $J_m^{*}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{k=1}{\overset{c}{\mathrm{\Σ}}}[u_{\mathrm{ki}}^m{\left|\right|x_i-v_k\left|\right|}^2+G_{\mathrm{ki}}^{*}]$ By fuzzy factor join standard FC M model, obtain adding fuzzy factor cluster objective function

Wherein, the pixel number that N is Remote Sensing Digital Image to be sorted, both N=P × Q; C is the cluster number of classification Remote Sensing Digital Image, represent that the pixel of i in Remote Sensing Digital Image to be sorted belongs to the degree of membership of k class, the Fuzzy Exponential that m is Remote Sensing Digital Image to be sorted, x _irepresent i pixel of Remote Sensing Digital Image to be sorted, v _kfor the central point of Remote Sensing Digital Image k class to be sorted;

The initial fuzzy matrix U obtaining in integrating step 1 ₀with cluster centre V ₀, utilize formula calculate the cluster centre that remote sensing image to be sorted is new count represent the current new cluster centre obtaining;

Recycling formula $u_{\mathrm{ki}}^{*}=\underset{j=1}{\overset{c}{\mathrm{\Σ}}}{\left(\frac{{\left|\right|x_i-v_k\left|\right|}^2+G_{\mathrm{ki}}^{*}}{{\left|\right|x_i-v_j\left|\right|}^2+G_{\mathrm{ji}}^{*}}\right)}^{\frac{-1}{m-1}}$ Calculate the degree of membership matrix that remote sensing image to be sorted is new count represent the current new fuzzy matrix obtaining; Now for passing through initial cluster centre V ₀obtain, represent before the cluster centre that once obtains; for passing through initial fuzzy matrix U ₀obtain, represent before the fuzzy matrix that once obtains;

Step 6: judge cluster centre whether continuation changes exclusive disjunction reaches maximum iteration time, and the iteration stopping threshold epsilon=1e-5 that sets operation times is a little positive number, t the cluster centre that Remote Sensing Digital Image to be sorted is tried to achieve with t-1 cluster centre compare, if meet or b > T both one of condition, iteration finishes, described b initial value is that 0, T is 100, otherwise, set b=b+1, with the current fuzzy matrix obtaining and cluster centre substitute respectively initial fuzzy matrix U ₀with cluster centre V ₀, and be set as with turn back to step 2, repeated execution of steps 2～step 6, until meet or b > T both one of condition;

Step 7: utilize the fuzzy membership matrix U={ u finally obtaining _ki} _{c × N}, determine each pixel x according to following formula _iaffiliated classification, for each pixel x _i, classification c under it _ifor degree of membership u _kithat classification of middle maximum;

C _i＝arg _k{max(u _ki)},k＝1,2,3,…,c

Step 8: according to each pixel x _iaffiliated classification c _igive different colors by different cluster classifications, form classification of remote-sensing images thematic map, thereby realize the automatic classification of Remote Sensing Digital Image.

All algorithms in the present invention are all that programming realizes under Matlab7.8, choose the remotely-sensed data of two zoness of different as verification msg, the checking sample of classification is by having carried out strict geometric correction to original remote sensing image, and meet rectification error and be less than 0.5 pixel requirement, then on the image of correcting, obtain required checking sample by the method for visual interpretation.Finally utilize production precision, overall accuracy and Kappa coefficient to evaluate classification results precision, and FLNAICM of the present invention and standard FC M and FLICM algorithm have been contrasted.

Embodiment 1, adopted size be having comprised of 200 × 200 pixels red, green and blue three wave band resolution be 0.61 meter of QuickBird remote sensing image, these data are positioned at the urban area of Jiangsu Province, China Xuzhou City, acquisition time is in August, 2005, as Fig. 3 (a) and (b) respectively original classification image and reference data image, image has been divided into 4 classifications: structures, bare area, water and vegetation, Fuzzy Exponential is 2.

Fig. 3 (c)-(e) represented respectively classification results of FCM, FLICM and FLNAICM, in Fig. 3 (c), due to the similarity of spectrum and the existence of picture noise, FCM has just utilized the spectral characteristic of image, do not consider spatial context information, caused and in classification results, had many " spiced salt " phenomenon.Can find out from Fig. 3 (d) and Fig. 3 (e), the classifying quality of FLICM and FLNAICM is all better than FCM, and the major part " assorted point " in classification chart is removed, and forms good homogeney category regions.From Fig. 3 (d), can find, there is level and smooth phenomenon in classification plot, form the classification plot in larger region, for example, in Fig. 3 (d) mark A, B, C place, lose the details in many classification plot, and than FLICM method, can find out from Fig. 3 (e), FLNAICM has retained many detailed information, for example, in Fig. 3 (e) mark A, B, C place, its reason is because FLNAICM has utilized spatial attraction between center pixel and neighborhood pixel as neighborhood pixel centering imago unit spacial influence degree, and this spatial attraction has taken into full account local space relation and the gray-scale relation of center pixel and neighborhood pixel pixel, and can automatically calculate according to the characteristic of pixel.FLICM just utilizes space length and the degree of membership between center pixel and neighborhood pixel pixel simply.Table 1 provides the classification results precision evaluation result of FCM, FLICM and FLNAICM, and with respect to FCM and FLICM, FLNAICM has provided the highest nicety of grading.

Table 1. is implemented checking sample number, production precision, overall accuracy and the Kappa coefficient in 1

Embodiment 2

In embodiment 2, adopted size be having comprised of 200 × 200 pixels red, green and blue three wave band resolution be 0.61 meter of QuickBird remote sensing image, these data are positioned at the region, outskirts of a town of Jiangsu Province, China Xuzhou City, acquisition time is in August, 2005, if Fig. 4 (a) and Fig. 4 (b) are respectively original classification image and reference data image, image has been divided into 4 classifications: road, bare area, water and vegetation, Fuzzy Exponential is 2.

Fig. 4 (c)-(e) is respectively the classification results of FCM, FLICM and FLNAICM, in Fig. 4 (c), due to the similarity of spectrum and the existence of picture noise, the sorting technique of FCM has only been utilized the spectral characteristic of image, do not consider spatial context information, in classification results, occurred a large amount of " spiced salt " phenomenons.Can find out from Fig. 4 (d) and Fig. 4 (e), the classifying quality of FLICM and FLNAICM is all better than FCM, and the major part " assorted point " in classification chart has all been removed.In Fig. 4 (d), there is level and smooth phenomenon, the loss in detail in many classification plot, for example, in Fig. 4 (d) mark A, B, C place, and than FLICM method, can find out from Fig. 4 (e), FLNAICM has retained many detailed information, for example, in Fig. 4 (e) mark A, B, C place, its reason is because FLNAICM has utilized spatial attraction between center pixel and neighborhood pixel as neighborhood pixel centering imago unit spacial influence degree, and this spatial attraction has taken into full account local space relation and the gray-scale relation of center pixel and neighborhood pixel pixel, can automatically calculate according to the characteristic of pixel.In FLICM, just utilize simply space length and the degree of membership between center pixel and neighborhood pixel pixel.Table 2 provides the classification results precision evaluation result of FCM, FLICM and FLNAICM, and than FCM and FLICM, FLNAICM has provided the highest nicety of grading.

Table 2. is implemented checking sample number, production precision, overall accuracy and the Kappa coefficient in 2

To sum up, the present invention proposes a kind of FLNAICM sorting technique based on neighborhood Pixel domain gravitation, utilize the influence degree of gravitation between center pixel and neighborhood pixel estimation neighborhood pixel centering imago unit, reasonably introduce spatial context information to the FCM of standard to improve its nicety of grading and algorithm to containing the robustness of noisy Images Classification.

Claims (1)

1. the fuzzy C-mean algorithm remote sensing image automatic classification method based on spatial attraction model, is characterized in that comprising following steps:

Step 1: obtain Remote Sensing Digital Image to be sorted, obtain the pixel number of Remote Sensing Digital Image according to picture size and wave band number, need to determine cluster classification number c and the Fuzzy Exponential m of Remote Sensing Digital Image according to actual classification, and utilize the FCM model of standard to carry out cluster to Remote Sensing Digital Image to obtain initialization fuzzy membership matrix U ₀={ u _ki} _{c × N}with cluster centre V ₀={ v _k} _c;

Step 2: set neighborhood window size, determine the pixel in the neighborhood window using each pixel in Remote Sensing Digital Image as center pixel in Remote Sensing Digital Image according to the neighborhood window size of setting, pass through formula spatial attraction NA between other pixel in each pixel and its affiliated neighborhood window in calculating Remote Sensing Digital Image _ij,

Wherein, G is constant, is used for representing to regulate the contribution of space constraint to cluster objective function, generally establishes G=1, u _kirepresent neighborhood window center pixel x _ibelong to the degree of membership of k classification, u _kjrepresent j pixel x in neighborhood window _jbelong to the degree of membership of k classification, R _ijrepresent pixel x _iwith pixel x _jbetween theorem in Euclid space distance;

Step 3: utilize each pixel in Remote Sensing Digital Image and the spatial attraction NA between other pixel in neighborhood window under it _ij, pass through formula obtain the space constraint penalty factor w between pixel in Remote Sensing Digital Image _ij,

Wherein, w _ijrepresent j pixel x in neighborhood window _jthe x of centering imago unit _iweighing factor, N _iexpression center pixel x _ineighborhood window in pixel, NA _ijfor each pixel x in the image calculating in step 2 _iwith by pixel x _ias all the other the pixel x in the neighborhood window of center pixel _jbetween spatial attraction, | x _i-x _j| represent pixel x _iwith by pixel x _ias the pixel x in the neighborhood window of center pixel _jbetween gray-scale value poor;

Step 4: pass through formula obtain fuzzy factor

Step 5: pass through formula by fuzzy factor join standard FC M model, obtain cluster objective function

Wherein, the pixel number that N is Remote Sensing Digital Image to be sorted, c is the cluster number of classification Remote Sensing Digital Image, represent that the pixel of i in Remote Sensing Digital Image to be sorted belongs to the degree of membership of k class, the Fuzzy Exponential that m is Remote Sensing Digital Image to be sorted, x _irepresent i pixel of Remote Sensing Digital Image to be sorted, v _kfor the central point of Remote Sensing Digital Image k class to be sorted;

The initial fuzzy matrix U obtaining in integrating step 1 ₀with cluster centre V ₀, utilize formula calculate the cluster centre that remote sensing image to be sorted is new count represent the current new cluster centre obtaining;

Recycling formula calculate the degree of membership matrix that remote sensing image to be sorted is new count represent the current new fuzzy matrix obtaining; Now for passing through initial cluster centre V ₀obtain, represent before the cluster centre that once obtains; for passing through initial fuzzy matrix U ₀obtain, represent before the fuzzy matrix that once obtains;

Step 6: judge cluster centre whether continuation changes exclusive disjunction reaches maximum iteration time, and setting iteration stopping threshold epsilon=1e-5 is a little positive number, t the cluster centre that Remote Sensing Digital Image to be sorted is tried to achieve with t-1 cluster centre compare, if meet or b > T both one of condition, iteration finishes, described b initial value is that 0, T is 100, otherwise, set b=b+1, with the current fuzzy matrix obtaining and cluster centre substitute respectively initial fuzzy matrix U ₀with cluster centre V ₀, and be set as with turn back to step 2, repeated execution of steps 2～step 6, until meet or b > T both one of condition;

Step 7: utilize the fuzzy membership matrix U={ u finally obtaining _ki} _{c × N}, determine each pixel x according to following formula _iaffiliated classification, for each pixel x _i, classification c under it _ifor degree of membership u _kithat classification of middle maximum;

C _i＝arg _k{max(u _ki)},k＝1,2,3,…,c

Step 8: according to each pixel x _iaffiliated classification c _igive different colors by different cluster classifications, form classification of remote-sensing images thematic map, thereby realize the automatic classification of Remote Sensing Digital Image.