CN109712149B - Image segmentation method based on wavelet energy and fuzzy C-means - Google Patents

Abstract

An image segmentation method based on wavelet energy and fuzzy C-means comprises the following steps: calculating a two-layer wavelet energy coefficient of the image in a window by adopting two-dimensional wavelet transform, and establishing energy characteristics; calculating a space distance constraint factor and a gray distance constraint factor of the SAR image pixel, and defining a weighted segmentation fuzzy factor; introducing a weighted segmentation fuzzy factor into an object function of the FCM, establishing a kernel function fuzzy C-means segmentation method based on pixel gray scale and spatial position information, and deducing a kernel function required by the fuzzy C-means segmentation method; calculating updated membership and a segmentation class center analytic expression; iteratively calculating the final membership degree and the segmentation class center; and classifying the SAR image into a corresponding class with the maximum membership degree pixel by pixel to finish image segmentation. On the basis of SAR image wavelet energy feature extraction, pixel gray scale and position information are considered, fuzzy C-means segmentation is carried out on the basis of a weighting kernel function, and robustness is achieved on speckle noise.

Description

Image segmentation method based on wavelet energy and fuzzy C-means

Technical Field

The invention belongs to the field of remote sensing image interpretation, and particularly relates to an image segmentation method based on wavelet energy and a fuzzy C-means, which is used for calculating the wavelet energy characteristics of an image and providing a way for the segmentation of a synthetic aperture radar remote sensing image containing speckle noise, thereby providing important target segmentation information for image content analysis and image classification.

Background

Synthetic Aperture Radar (SAR) remote sensing images become an important component of current remote sensing data with all-weather, all-day, high resolution and large-area data acquisition capability, and have been widely applied in the aspects of resources, environment, urban construction, military and the like. As an important work for understanding and interpreting image content, image segmentation is a technique of dividing an input image into several regions that are mutually disjoint according to different attributes and contents. The remote sensing image is quickly, effectively and accurately segmented, the accuracy of understanding the image content can be further improved, and the operation complexity of a subsequent image processing algorithm can be remarkably reduced. Compared with a common optical image, the SAR remote sensing image has the characteristics of obvious speckle noise, complex geometric deformation, unclear texture edge and the like, so that great challenges are brought to image segmentation work.

At present, SAR image segmentation methods are mainly classified into the following categories, namely histogram threshold method, clustering-based method, model-based method and morphological method. The fuzzy C-means (FCM) algorithm is used as an unsupervised image segmentation method, has a simple principle, is easy to implement, has a high running speed, is widely applied to image segmentation, and has a steady segmentation effect. However, the FCM algorithm is sensitive to a lot of noises, and aiming at the defect, Ahmed and the like introduce image space neighborhood information into an FCM target function, the FCM-S algorithm is provided. In order to overcome the defect of slow running speed of the algorithm, researchers further provide FCM-S1 and FCM-S2 algorithms, and the two methods respectively carry out mean filtering and median filtering on the image. Based on the same idea, szilaggyi et al propose an enhanced FCM algorithm (EnFCM) aiming at accelerating FCM-S, which does not take image pixels as clustering objects, but takes the gray levels contained in the images as clustering objects according to the gray histogram of the images, thus greatly reducing the amount of clustering computation. In addition, an FCM segmentation algorithm based on non-local spatial information is also available, which introduces non-local information for suppressing image noise interference, but increases the amount of computation, and thus has high computation complexity. Cai and the like utilize the local spatial distance and the gray difference of pixels in a window, apply the local spatial distance and the gray difference to an EnFCM algorithm, and provide an FGFCM algorithm, so that the blurring of the image edge is weakened to a certain extent. The methods are effective for optical image noise such as gaussian noise and salt and pepper noise, but are not suitable for speckle noise of SAR images, and therefore cannot be directly applied to SAR remote sensing images.

Due to the speckle multiplicative noise characteristic of the SAR image, the intensity distribution of homogeneous regions in the image is not uniform, which brings difficulty to image segmentation. The method improves the segmentation precision by optimizing a spatial information influence factor, but also increases the time complexity of the algorithm.

Disclosure of Invention

The invention aims to provide an image segmentation method based on wavelet energy and fuzzy C-means, which considers pixel gray scale and position information on the basis of SAR image wavelet energy feature extraction, performs fuzzy C-means segmentation based on a weighting kernel function, has robustness on speckle noise, and can be effectively applied to SAR image segmentation.

In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:

calculating a two-layer wavelet energy coefficient of the image in a window by adopting two-dimensional wavelet transform, and establishing energy characteristics;

calculating a space distance constraint factor and a gray distance constraint factor of the SAR image pixel, and defining a weighted segmentation fuzzy factor;

introducing a weighted segmentation fuzzy factor into an object function of the FCM, establishing a kernel function fuzzy C-means segmentation method based on pixel gray scale and spatial position information, and deducing a kernel function required by the fuzzy C-means segmentation method;

calculating updated membership and a segmentation class center analytic expression;

iteratively calculating the final membership degree and the segmentation class center;

and classifying the SAR image into a corresponding class with the maximum membership degree pixel by pixel to finish image segmentation.

Preferably, a window with a size of 8 × 8 is used to perform two-dimensional wavelet transform on the SAR image to obtain 7 sub-images, and the wavelet energy of each sub-image is defined as:

where MN represents the corresponding sub-image size, x (m, n) is the gray scale value of the sub-image at the (m, n) position, establishing a set of 7-dimensional energy features (e)₁,e₂,…e₇)。

Pixel space distance constraint factor reflecting neighborhood pixels and centersThe approximation of the pixel in spatial distance is calculated as:

wherein the pixel i is a local region N_iThe center pixel in, pixel j is a neighborhood of pixel i,

the Euclidean distance of the two; setting a local region N_iThe size of (a) is 3 × 3; the gray scale distance constraint factor reflects the gray scale similarity of the adjacent pixels, and the calculation formula considering the gray scale ratio distance among the pixels of the SAR image is as follows:

wherein

And

are respectively two local windows N with the same size_iAnd N_jIn the gray scale vector, the center of a local area is still a pixel i and a pixel j, a variable M is the number of pixels in the local area, and a natural logarithm function is adopted to map the gray scale ratio distance into the traditional distance measure:

then, the weighted segmentation ambiguity factor is represented as w_ij＝w_sd·w_id。

The objective function definition of the kernel function fuzzy C-means segmentation method based on the pixel gray scale and the space position information is as follows:

in the formula, N is the number of pixels of the image to be segmented, c is the number of segmentation categories, and c is more than or equal to 2 and less than N, u_kiRepresenting the fuzzy membership process of the segmentation result by the membership degree of the pixel i belonging to the class k and m being the weight of the membership degreeDegree, p_iAnd v_kA 7-dimensional wavelet energy feature vector representing pixel i and class center k; i | · | | is Euclidean distance measure, phi (·) is a characteristic nonlinear mapping function;

due to phi (p)_i) And Φ (v)_k) The product in feature space is defined as the kernel function Φ (p)_i)^TΦ(v_k)＝K(p_i,v_k) Then, there are:

the similarity of the feature space is defined by the above formula, and considering the gaussian radial basis function kernel, there are:

wherein the parameter sigma is the bandwidth of the kernel function and is obtained by calculating the variance of the characteristic distance; suppose that

As feature vectors p_iAnd class-centric feature vectors

Then the average feature distance is:

the parameter σ is calculated according to:

under the Gaussian radial basis function kernel condition, the kernel function is expressed as 2(1-K (p)_i,v_k))；

Thus weighting the blur distance G_kiIs defined as:

to obtain an objective function J_mAnd the calculation formula of the updated membership degree and the center of the segmentation class is as follows:

iterative computation is performed according to the following procedure:

1) setting the number c of clustering centers, membership weight m and iteration termination condition epsilon;

2) randomly setting a clustering center, and setting an iteration count b to be 0;

3) computing a weighted segmentation blur factor w for any two pixels_ijAnd a feature similarity distance;

4) updating membership u_kiAnd a segmentation class center v_k；

5) If { U^(b)-U^(b+1)F is } < epsilon, where U ═ U_kiIf the result is the membership matrix, the iteration is terminated;

otherwise, setting b to b +1 and jumping to the step 4);

after the loop is terminated, the final segmentation class C of the pixel i_iIs the class with the greatest degree of membership, i.e. C_i＝arg_k{max{u_ki}}. Compared with the prior art, the method comprises the steps of firstly calculating the wavelet energy characteristics of the SAR image, then defining the weighting fuzzy factor based on the spatial position and the gray level information of the pixel neighborhood of the SAR image, introducing the weighting fuzzy factor into the FCM, and establishing the kernel function fuzzy C-means segmentation method based on the pixel gray level and the spatial position information, so that the defect that the FCM cannot be directly applied to image segmentation due to speckle noise of the SAR image is overcome. The invention provides a fuzzy C-means segmentation method based on a weighting kernel function by considering pixel gray scale and position information on the basis of SAR image wavelet energy feature extraction, and the method has robustness to speckle noiseThe method can be effectively applied to the urban region segmentation of the SAR image, and the segmentation result is more stable and accurate.

Drawings

FIG. 1 is a flow chart of the operation of the image segmentation method of the present invention;

FIG. 2 is a graph of fuzzy segmentation results of simulated SAR images by different methods:

(a) an original image; (b) adding a speckle noise image; (c) KWFLICM segmentation result graph;

(d) NLEP-FCM segmentation result graph; (e) the invention ILKFCM cuts apart the result chart; (f) KGC segmentation result graph;

FIG. 3 is a line graph of accuracy of segmentation of a simulated SAR image according to methods under different noise intensities;

fig. 4 is a fuzzy segmentation result diagram of an actual measurement SAR image:

(a) an original SAR image; (b) KWFLICM segmentation result graph; (c) NLEP-FCM segmentation result graph;

(d) the invention ILKFCM cuts apart the result chart; (e) KGC segmentation result graph.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings.

Referring to fig. 1, the image segmentation algorithm of the present invention is implemented as follows:

step one, carrying out two-dimensional wavelet transformation on the SAR image by adopting an 8 x 8 window to obtain 7 sub-images, wherein the wavelet energy of each sub-image is defined as

MN denotes the corresponding sub-image size, x (m, n) is the gray value of the sub-image at the (m, n) position. Obtaining a set of 7-dimensional energy characteristics (e) by performing two-layer wavelet transform on the SAR image₁,e₂,…e₇)；

Step two, the spatial distance constraint factor of the SAR image reflects the approximation degree of the neighborhood pixel and the central pixel on the spatial distance, and the calculation formula is as follows:

wherein the pixel i isA local area N_iThe center pixel in, pixel j is a neighborhood of pixel i,

is the euclidean distance between the two. Since the eight neighborhoods may reflect most of the information of the central pixel, here the local region N_iThe size is set to 3 × 3; the gray scale distance constraint factor reflects the gray scale similarity of the adjacent pixels, and the Euclidean distance of the pixel gray scale is not applicable any more because multiplicative speckle noise exists in the pixels of the SAR image.

Considering the inter-pixel gray scale ratio distance of the SAR image, the calculation formula is as follows:

wherein,

and

are respectively two local windows N with the same size_iAnd N_jAnd (3) inner gray level vector, wherein the center of the local area is still the pixel i and the pixel j, and the variable M is the number of pixels in the local area. The distance of the ratio

The method has certain robustness on the SAR image multiplicative speckle, and when the SAR image multiplicative speckle is close to 1, the gray scale distance is smaller, otherwise, the gray scale distance is larger; finally, the ratio distance is mapped into the traditional distance measure by adopting a natural logarithm function

Then, the ambiguity factor can be expressed as w_ij＝w_sd·w_id。

Introducing fuzzy factors based on space constraint and gray scale constraint into the FCM to obtain a kernel function fuzzy C-means segmentation method (ILKFCM) combining pixel gray scale and position information, wherein the target function formula is

Wherein N is the number of image pixels to be segmented, c is the number of segmentation categories, and c is more than or equal to 2 and less than N, u_kiIs the degree of membership that pixel i belongs to class k. m is a membership weight, which indicates the fuzzy membership degree of the segmentation result and is generally set to 2. p is a radical of_iAnd v_kA 7-dimensional wavelet energy feature vector representing pixel i and class center k. And | l | · | | is Euclidean distance measure, and phi (·) is a characteristic nonlinear mapping function. Due to phi (p)_i) And Φ (v)_k) The product in feature space is defined as the kernel function Φ (p)_i)^TΦ(v_k)＝K(p_i,v_k) Then, the following formula is given:

the similarity of the feature space can be defined by the above formula, wherein the Gaussian radial basis function kernel is considered, and the formula is

The parameter σ is the bandwidth of the kernel function, and can be obtained by calculating the variance of the characteristic distance.

Suppose that

As feature vectors p_iAnd class-centric feature vectors

The average characteristic distance is

The parameter σ can be calculated as

Under the Gaussian radial basis function kernel constraint, the kernel function can be expressed as 2(1-K (p)_i,v_k))，Weighted fuzzy distance G_kiIs calculated by the formula

Step four, solving an objective function J_mAnd the calculation formula of the updated membership degree and the center of the segmentation class is as follows:

wherein u is_kiTo updated membership, v_kIs a segmentation class center;

step five and step six, the ILKFCM segmentation algorithm iteration flow proposed by the invention is as follows:

1) setting the number c of clustering centers, membership weight m and iteration termination condition epsilon;

2) randomly setting a clustering center, and setting an iteration count b to be 0;

3) computing a weighted blurring factor w for any two pixels_ijAnd a feature similarity distance;

4) updating membership u_kiAnd a segmentation class center v_k；

5) If { U^(b)-U^(b+1)F is } < epsilon, where U ═ U_kiIf the result is the membership matrix, the iteration is terminated; otherwise, setting b to b +1 and jumping to the step 4);

after the loop is terminated, the final segmentation class C of the pixel i_iIs the class with the greatest degree of membership, i.e. C_i＝arg_k{max{u_ki}}。

The fuzzy C-means algorithm is a classical clustering method and is widely applied to image segmentation, and the FCM cannot be directly applied to SAR image segmentation due to speckle noise in SAR images. In order to solve the problem, the invention provides a fuzzy C-means segmentation method based on a weighting kernel function by considering pixel gray scale and position information on the basis of SAR image wavelet energy feature extraction. The method has the basic principle that the method has robustness to speckle noise of the SAR image due to the fact that the gray scale and the position information of the image pixels are considered at the same time, and the similarity between the pixels can be effectively measured. The method improves the FCM segmentation algorithm, and the result obtained on SAR image segmentation is necessarily more reasonable, effective and accurate, thereby meeting the current precision application requirement.

The fuzzy segmentation method is verified by respectively adopting simulated and actually measured SAR images.

The simulated SAR image is a texture map with the size of 244 rows by 244 columns, contains three gray values, namely three different categories, which are respectively 10, 120 and 250, and is added with the result of 8-view Gamma distribution speckle noise. The actually measured SAR image is a TerrraSAR X-band single-polarized SAR image in the hong Kong area, the spatial resolution is 3 meters, the image size is 1578 lines multiplied by 1126 columns, and the area mainly contains three types of ground objects of the hong Kong urban area, the water area and the farmland.

The experimental procedure was as follows:

the invention and other two improved fuzzy segmentation algorithms and a classical Kernel function graph segmentation method are respectively utilized for verification aiming at simulated and actually measured SAR images, the two improved fuzzy segmentation algorithms are respectively a Kernel function enhancement type local fuzzy C mean value segmentation method (KWFLICM) proposed by Gong and the like and a non-local fuzzy C mean value segmentation method (NLEP-FCM) proposed by Feng and the like and based on edge preservation, and in addition, the classical Kernel function graph segmentation algorithm (Kernel GraphCuts, KGC) is also used as a comparison method. In three FCM-based iteration segmentation methods, the iteration termination condition is set to be epsilon 10^-3。

The experimental results and analysis are set forth below:

fig. 2(a) is a texture map of size 244 rows by 244 columns containing three gray values, i.e. three different classes, 10, 120 and 250 respectively. FIG. 2(b) shows the results of adding 8-view Gamma distributed speckle noise, and FIGS. 2(c) - (f) show the results of KWFLICM, NLEP-FCM, the inventive method and KGC segmentation, respectively. It can be seen that KWFLICM, NLEP-FCM and KGC are all robust to speckle noise. Because the kwvlicm considers the spatial distance of the pixels in the local neighborhood and the local variance coefficient at the same time, most of the noise can be effectively suppressed, but a part of isolated points still exist in fig. 2(c), which affects the segmentation accuracy. The boundary retentivity and the regional homogeneity of the NLEP-FCM segmentation result are good, but partial information is lost in the image detail-rich region, because the method is not based on the segmentation of the original image. The KGC segmentation result is inferior to other methods, and although the method has better robustness to noise, the loss of detail information is serious, so that the method is not suitable for SAR image complex urban region segmentation. The ILKFCM segmentation method has the best segmentation effect, and can keep complete image details while achieving good noise resistance.

In order to further compare the robustness of different segmentation methods to speckle noise of different degrees, Gamma noise of different views is added to the simulated image, wherein the Gamma noise is 1-5 views respectively, and the higher the view is, the weaker the noise degree is.

As can be seen from FIG. 3, ILKFCM, NLEP-FCM and KGC are all more robust to coherent plaques than KWFLICM. With the serious speckle noise, the segmentation precision of the KWFLICM is greatly reduced, the other three methods change slowly, and meanwhile, as can be seen from the figure, the segmentation precision of the ILKFCM provided by the invention is kept highest and SA is more stable with the change of the noise degree, which shows that the segmentation method provided by the invention has better robustness on the speckle noise of the SAR image.

Fig. 4(a) is a TerraSAR X-band single-polarized SAR image of hong kong, which has a spatial resolution of 3 m and a size of 1578 rows × 1126 columns and mainly contains three types of ground features of hong kong city, water area and farmland. FIGS. 4(b) - (e) are KWFLICM, NLEP-FCM, the method of the present invention and the KGC segmentation results, where different gray values represent different segmentation ground object results. It can be seen that the kwvlicm segmentation result is poor and the image detail information is also lost seriously due to the speckle noise effect. The NLEP-FCM, the method and the KGC segmentation result are good, the visual effect of the result obtained by the method is good, the robustness on noise is good, meanwhile, more details of urban areas and natural ground objects can be obtained, so that the main information of the original image is kept, and the remote sensing image fuzzy segmentation method provided by the invention can be proved to be effective.

Claims (3)

1. An image segmentation method based on wavelet energy and fuzzy C-means is characterized by comprising the following steps:

calculating a two-layer wavelet energy coefficient of the image in a window by adopting two-dimensional wavelet transform, and establishing energy characteristics;

calculating a space distance constraint factor and a gray distance constraint factor of the SAR image pixel, and defining a weighted segmentation fuzzy factor;

introducing a weighted segmentation fuzzy factor into an object function of the FCM, establishing a kernel function fuzzy C-means segmentation method based on pixel gray scale and spatial position information, and deducing a kernel function required by the fuzzy C-means segmentation method;

the pixel spatial distance constraint factor reflects the approximation degree of the neighborhood pixel and the central pixel on the spatial distance, and the calculation formula is as follows:

wherein the pixel i is a local region N_iThe center pixel in, pixel j is a neighborhood of pixel i,

the Euclidean distance of the two; setting a local region N_iThe size of (a) is 3 × 3; the gray scale distance constraint factor reflects the gray scale similarity of the adjacent pixels, and the calculation formula considering the gray scale ratio distance among the pixels of the SAR image is as follows:

wherein

And

are respectively two local windows N with the same size_iAnd N_jInner gray scale vector, localThe center of the partial region is still the pixel i and the pixel j, the variable M is the number of the pixels in the partial region, and the gray ratio distance is mapped into the traditional distance measure by adopting a natural logarithm function:

then, the weighted segmentation ambiguity factor is represented as w_ij＝w_sd·w_id；

The objective function definition of the kernel function fuzzy C-means segmentation method based on the pixel gray scale and the space position information is as follows:

in the formula, N is the number of pixels of the image to be segmented, c is the number of segmentation categories, and c is more than or equal to 2 and less than N, u_kiIs the membership degree of the pixel i belonging to the class k, m is the weight of the membership degree, and represents the fuzzy membership degree of the segmentation result, p_iAnd v_kA 7-dimensional wavelet energy feature vector representing pixel i and class center k; i | · | | is Euclidean distance measure, phi (·) is a characteristic nonlinear mapping function;

due to phi (p)_i) And Φ (v)_k) The product in feature space is defined as the kernel function Φ (p)_i)^TΦ(v_k)＝K(p_i,v_k) Then, there are:

the similarity of the feature space is defined by the above formula, and considering the gaussian radial basis function kernel, there are:

wherein the parameter sigma is the bandwidth of the kernel function and is obtained by calculating the variance of the characteristic distance; suppose that

As feature vectors p_iAnd class-centric feature vectors

Then the average feature distance is:

the parameter σ is calculated according to:

under the Gaussian radial basis function kernel condition, the kernel function is expressed as 2(1-K (p)_i,v_k))；

Thus weighting the blur distance G_kiIs defined as:

calculating updated membership and a segmentation class center analytic expression;

iteratively calculating the final membership degree and the segmentation class center;

iterative computation is performed according to the following procedure:

1) setting the number c of clustering centers, membership weight m and iteration termination condition epsilon;

2) randomly setting a clustering center, and setting an iteration count b to be 0;

3) computing a weighted segmentation blur factor w for any two pixels_ijAnd a feature similarity distance;

4) updating membership u_kiAnd a segmentation class center v_k；

5) If { U^(b)-U^(b+1)F is } < epsilon, where U ═ U_kiIf the result is the membership matrix, the iteration is terminated;

otherwise, setting b to b +1 and jumping to the step 4);

after the loop has ended, the final segmentation of the pixel iClass C_iIs the class with the greatest degree of membership, i.e. C_i＝arg_k{max{u_ki}}；

And classifying the SAR image into a corresponding class with the maximum membership degree pixel by pixel to finish image segmentation.

2. The image segmentation method based on wavelet energy and fuzzy C-means as claimed in claim 1, wherein:

two-dimensional wavelet transformation is carried out on the SAR image by adopting a window with the size of 8 multiplied by 8 to obtain 7 sub-images, wherein the wavelet energy of each sub-image is defined as:

where MN represents the corresponding sub-image size, x (m, n) is the gray scale value of the sub-image at the (m, n) position, establishing a set of 7-dimensional energy features (e)₁,e₂,…e₇)。

3. The image segmentation method based on wavelet energy and fuzzy C-means as claimed in claim 1, wherein:

to obtain an objective function J_mAnd the calculation formula of the updated membership degree and the center of the segmentation class is as follows:

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