CN101551864A - Image classification method based on feature correlation of frequency domain direction - Google Patents

Abstract

The invention discloses an image classification method based on frequency-domain direction feature correlation, which mainly solves the shortcomings of the existing method, such as high computational complexity, low classification accuracy, and poor robustness to image size changes. The implementation process includes: (1) selecting texture sample images and dividing them into two image data sets of training samples and test samples; (2) performing 2-dimensional fast Fourier transform on the training sample images, and dividing them according to the frequency and direction of the Fourier plane (3) According to the correlation between the subband features of the frequency domain direction feature matrix, obtain the correlation pair sequence; (4) apply the unary linear regression model to calculate the classification of each correlation pair The feature parameters form a classifier; (5) the frequency domain direction feature of the test sample image is fitted with the classifier parameters to obtain the class label of the test sample; (6) repeat step (5) to obtain the class of all test sample images mark. The invention can be used to classify Brodatz texture images and SAR images.

Description

Image Classification Method Based on Directional Feature Correlation in Frequency Domain

technical field

The invention belongs to the technical field of image processing, in particular to an image classification method which can be used for classifying texture images and synthetic aperture radar (SAR) images.

Background technique

Image classification is an important branch of pattern recognition. It is an image processing method that distinguishes different types of objects according to their different features reflected in image information. The main research content of image classification is how to properly describe images, extract features that can effectively represent image attributes, propose effective classification and recognition methods, and classify images accurately and efficiently on this basis.

The application fields of image classification mainly include the following aspects: image texture analysis, image content retrieval, target detection and recognition, etc. Among them, image texture analysis and classification is an important research direction in image processing and pattern recognition, and plays a vital role in the fields of image classification, segmentation, computer graphics and image coding. In the 1980s, many traditional classification methods were produced, such as gray co-occurrence matrix, second-order statistical method, Gauss-Markov random field, local linear transformation, etc. With the deepening of the research on the human visual system, many multi-resolution texture analysis models have been developed, such as wavelet transform, Gabor transform, Brushlet, Contourlet and so on. Researchers combined multi-channel Gabor filtering, wavelet transform and other methods to propose a lot of innovations and improvements to texture analysis, which greatly improved the accuracy of texture analysis. For example, Jasperetal uses the wavelet base suitable for texture analysis to detect textile texture defects, Ajay Kumar and Grantan K.H Pang et al. use Gabor filtering for object structure defect detection with texture phenomena, and K.N.Bhanu Prakash et al. use gray-scale co-occurrence matrix to detect matrix Ultrasound images of the lungs of the inner fetus to detect whether it has reached maturity. A large number of experiments have proved that this multi-resolution analysis method can get better classification results, so it has been widely used in image analysis and classification research.

Traditional image classification methods generally use the vector distance or statistical difference of texture features to judge category attributes, while image classification based on feature correlation is based on the fact that an image is composed of texture information of a specific frequency band and direction. This is visually reflected as images of different classes have significantly different correlations on different feature channels. Therefore, this correlation is a salient feature to distinguish different classes of textures. Zhi-Zhong Wang and Jun-Hai Yong et al. analyzed the correlation between the subbands of the wavelet packet and proposed corresponding image retrieval methods. This method first obtains the energy characteristics of each sub-band, and then analyzes the correlation between each feature channel to obtain the classification parameters. During the test, by comparing the fitting degree of the correlation model between the test sample and the training sample, they are excluded in turn until the correct class label is obtained. Methods similar to this idea include using wavelet, contourlet and other transformations for feature extraction and correlation analysis, but the common disadvantage of this type of transformation is that the frame is fixed and the sub-bands after transformation are not divided carefully in terms of frequency and direction. These shortcomings lead to insufficient feature correlation, limited classification performance and insufficient robustness to image size changes, and high computational complexity.

Contents of the invention

The purpose of the present invention is to overcome above-mentioned deficiencies in prior art, propose a kind of image classification method based on frequency domain direction characteristic correlation not limited to transformation such as wavelet, wavelet packet and multi-scale geometric analysis tool frame, to improve image classification The robustness of size changes and the accuracy of classification reduce the computational complexity.

The technical solution of the present invention is to perform 2-dimensional fast Fourier transform on the sub-graphs in the training sample set, and then divide the Fourier plane into sub-bands in different frequency domain directions according to the frequency and direction, calculate the energy characteristics of each sub-band, and analyze the relationship between the features. Correlation, and using linear regression to obtain classification parameters, and finally by comparing the characteristics of the test sub-graph and the classification parameter models of various types of images, the classification results are obtained. The specific implementation process is as follows:

(1) Select sample images of various textures, and divide these sample images into two data sets of training sample images and test sample images;

(2) Carry out 2-dimensional fast Fourier transform respectively to the training sample image data set, divide the Fourier plane into different frequency domain direction subbands according to the frequency and direction of the Fourier plane;

(3) Calculate the energy characteristics of each subband to obtain the frequency domain direction feature matrix M of the image;

(4) Calculate the correlation coefficient between each sub-band feature of the frequency-domain direction feature matrix M, and arrange in descending order according to the correlation coefficient of each sub-band pair to obtain a correlation pair sequence;

(5) Apply the linear regression model of one element to obtain the classification feature parameters of each feature correlation pair in the correlation pair sequence to form a classifier;

(6) Compare the frequency-domain direction feature of the test sample image with the fitting degree of all parameters in the classifier, calculate the probability that the test sample belongs to each type of image, and take the class label corresponding to the maximum probability as the class of the sample mark;

(7) Step (6) is repeated to obtain the class labels of all sample images in the test sample image dataset.

Compared with the prior art, the present invention has the following advantages:

1. Due to the direct operation and sector adjustment of the Fourier plane in the present invention, the framework limitations of wavelet, wavelet packet and other transformations are overcome, so that features can be divided more carefully in multi-frequency bands, multi-directions, etc., and the classification performance based on correlation is remarkable improve;

2. Since the sub-band parameters of the frequency domain direction feature extraction method of the present invention are adjustable, the invention does not limit the minimum size of the image, and has better robustness to images of different sizes;

3. Since the present invention adopts fast Fourier transform, the computational complexity is greatly reduced, and the feature extraction time is significantly lower than other transforms.

Description of drawings

Fig. 1 is the realization flow schematic diagram of the present invention;

Fig. 2 is a schematic diagram of subband division in the frequency domain direction in the present invention;

3 is a schematic diagram of the corresponding subband center position r(n) when α takes different values in the present invention;

Fig. 4 is a schematic diagram of the feature distribution of subband correlation pairs 28 and 29 of Brodatz texture image D6;

Fig. 5 is the SAR texture data map used in the simulation experiment.

Detailed ways

With reference to Fig. 1, the concrete implementation process of the present invention is as follows:

Step 1, select sample images of various textures, and divide these sample images into two data sets of training sample images and test sample images.

The present invention uses two image data sets for performance testing: Brodatz texture image and SAR texture image.

1a) The selection method of the Brodatz texture image sample dataset is described as follows:

Select 77 types of uniform texture images in the standard Brodatz texture library as test data. These 77 types of textures are: D1, D3, D4, D5, D6, D8, D9, D11, D14, D16, D17, D18, D19, D20, D21, D22, D23, D24, D25, D26, D27, D28, D29, D32, D33, D34, D35, D36, D37, D38, D46, D47, D48, D49, D50, D51, D52, D53, D54, D55, D56, D57, D64, D65, D66, D68, D74, D75, D76, D77, D78, D79, D80, D81, D82, D83, D84, D85, D87, D88, D92, D93, D94, D95, D96, D98, D100, D101, D102, D103, D104, D105, D106, D109, D110, D111, D112.

The size of each texture image above is 640×640. According to the following two sub-image selection methods, two databases are established for 77 types of uniform texture images, as shown in Table 1:

Table 1 Brodatz texture dataset settings

test database Number of texture classes subplot size Number of samples for each category Total number of samples The number of test/training samples per class texture library 128 77 128×128 25 1925 10/15 texture library 64 77 64×64 100 7700 40/60

In Table 1, the texture library 128 evenly divides the 77 types of images into 25 non-overlapping sub-images, the size of each sub-image is 128×128, the total number of sub-images is 1925, and 25 sub-images Among them, 10 images are used as training samples, and 15 images are used as test samples, that is, the total number of sub-images in the training sample image data set is 770, and the total number of sub-images in the test sample image data set is 1155; is divided into 100 non-overlapping sub-images, the size of each sub-image is 64×64, and the total number of sub-images is 7700, of which 100 sub-images, 40 are used as training samples, and 60 are used as test samples, that is The training sample image dataset contains 3080 subimages, and the test sample image dataset contains 4620 subimages.

1b) The selection method of the SAR image sample data set is described as follows:

The SAR image classification database is taken from different texture regions of 3 real SAR images, including 5 types of textures. Figure 5 shows the data maps of these 5 types of SAR textures used in the experiment. From top to bottom, from left to right are mountains, Water, farmland, and urban areas in high and low resolution. Randomly select 2000 points in these five types of uniform SAR texture regions, and perform the operation of sliding window to extract subimages. The database with a subimage size of 128×128 is recorded as SAR128, and the database with a subimage size of 64×64 is recorded as SAR128. For SAR64, each type of texture contains 2000 subimages, 500 are used as training samples, and 1500 are used as test samples. Therefore, the total number of subimages in SAR128 and SAR64 is 10,000, of which the training sample image data set contains 2500 subimages, and the test The sample image dataset contains 7500 subimages, as shown in Table 2:

Table 2 SAR image dataset settings

test database Number of texture classes subplot size Number of samples for each category Total number of samples The number of test/training samples per class SAR128 5 128×128 2000 10000 500/1500 SAR64 5 64×64 2000 10000 500/1500

Step 2, perform 2-dimensional fast Fourier transform on the given training sample image, and divide the Fourier plane into frequency-domain direction subbands according to the frequency and direction of the Fourier plane.

After the 2-dimensional fast Fourier transform is performed on the image, the Fourier plane is obtained. With the DC component of the Fourier plane as the center, K frequency domain direction subbands are obtained by dividing the upper half of the Fourier plane according to the frequency domain direction subbands. The specific implementation process as follows:

2a) The upper half of the Fourier plane is divided into N frequency bands and D directions according to polar coordinates, and K=N×D+2 sectors are obtained, and each sector represents different frequency bands and direction information from low frequency to high frequency, Constitute different sub-bands, as shown in Figure 2. D=8 in Fig. 2, the positions where sectors 13 and 26 are located in Fig. 2, because the contained information is not much, it is processed as a sub-band, D generally takes 16, and N generally takes 6;

2b) Calculate the position of each subband center point (r _n , θ _d ) according to the following formula:

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; N</span>}$

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; D.</span>}$

Among them, n represents the frequency band, N is the total number of frequency bands, d represents the polar coordinate direction of the upper half plane of Fourier, D is the total number of directions, R represents the maximum radius of the Fourier plane, and α is an adjustable parameter. Figure 3 shows the corresponding radius r _n values when α takes different values. When α=1, r _n is a linear function, which means that points are evenly taken on the radius. When α increases, r _n turns into a nonlinear function. The low-frequency position is made denser, and the high-frequency part is sparsely selected, which is in line with the idea of sub-band division in multi-scale geometric analysis. The results of multiple experiments show that the results are more robust when α=1.5, D=16, and N=6;

2c) Calculate the size Δr _n of each subband according to the following formula:

Δr _n =r _n -r _n-1 , n=1,...,N

Wherein, the subbands in different directions of the same frequency band have the same size.

Step 3, calculate the energy features of the K subbands according to the following formula, and obtain the feature vector V={v _k , k=1,...,K}:

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span>}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span>$

Where |c _j | represents the absolute value of the sub-band coefficients, A _k is the coefficient coordinate set of the kth sub-band, and |·| represents the set size.

Step 4, repeat steps 2-3, calculate the feature vectors of all training samples for each type of texture, and use the feature vectors as column vectors to form a feature matrix M.

Step 5, calculate the correlation pair sequence of each type of image.

5a) Calculating the covariance matrix C of a certain type of characteristic matrix M, the coefficient c _ij in the matrix C is the correlation coefficient of subband i and subband j, and subband i and j form a subband pair;

5b) Arrange each subband pair in descending order according to the correlation coefficient ρ, select the correlation pair with significant correlation where ρ>T _α , and put it into the correlation pair sequence, and output the correlation pair sequence. Here, considering the requirements of speed and accuracy, Generally take T _α =0.4;

5c) Steps 5a) to 5b) are repeated to calculate the correlation pair sequence of each type of image.

Step 6: Find the classification parameter matrix X to form a classifier.

6a) Apply the unary linear regression model to calculate the classification model parameters of each relevant pair in the relevant pair sequence of each type of texture. Let the parameters of the i-th relevant pair be a _i , b _i , μ _i , σ _i , and the calculation formula is as follows :

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; m</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i\; h</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i\; h</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i\; h</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i\; h</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i\; h</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i\; h</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$ ${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}\underset{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i\; h</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}\underset{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i\; h</span>}}$

${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i\; h</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; i\; h</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}$ ${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i\; h</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; i\; h</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}$

是由线性回归方程 ${\hat{y}}_i=a_i\&times;x_i+b_i$ 得到的该相关对对应子带能量y_ih的估计值，m为样本大小，当两个子带相关性较高时，线性回归方程可以很好的拟合两个子带间的关系，图4是纹理图像D6的相关对28和29的能量分布图，其相关系数为0.9952，图4中直线是线性回归方程得到的，可以看到，该直线可以很好的拟合子带相关对间的关系；Among them, x _ih , y _ih respectively represent the energy of two subbands of the i-th correlation pair of the h-th sample of a certain type of image,

is given by the linear regression equation ${\widehat{\mathrm{the\; y}}}_i=a_i\&times;x_i+b_i$ The obtained correlation pair corresponds to the estimated value of sub-band energy y _ih , m is the sample size, when the correlation between the two sub-bands is high, the linear regression equation can well fit the relationship between the two sub-bands, Figure 4 is the texture The energy distribution diagram of the correlation pair 28 and 29 of the image D6 has a correlation coefficient of 0.9952. The straight line in Fig. 4 is obtained by a linear regression equation. It can be seen that the straight line can well fit the relationship between the sub-band correlation pairs;

6b) According to the descending order of the correlation coefficient, put the parameters a, b, μ, σ, correlation pair label and correlation coefficient ρ of each type of texture into the classification parameter matrix X as the classification features of each type of texture Parameters that make up the classifier.

Step 7, perform 2-dimensional fast Fourier transform on the given test sample image, and then calculate its frequency-domain direction feature vector V according to the frequency-domain direction feature extraction method described in steps 2-3 above;

Step 8: Compare the feature vector V of a given test sample with the fitting degree of all parameters in the classifier to obtain the class label of the test sample.

8a) Take the unary linear regression model classification parameters a _i , b _i , μ _i , σ _i of the i-th correlation pair of the j-th image type and the sub-band features (x _i , y _i ) corresponding to the correlation pair in the test sample features ;

8b) According to the linear regression equation of one variable $\widehat{\mathrm{the\; y}}=a\&times;x+b$ Find the estimated value of the subband feature y _i Calculation error

8c) According to the following formula, the probability p _ij of the test sample conforming to each relevant pair classification parameter model of the image of the jth class is obtained:

${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; if</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; if</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 3</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\right.<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; ,</span>$

Wherein L is the total number of correlation pairs in the jth type image correlation pair sequence;

8d) Calculate the probability P _j that the test sample belongs to the image of the jth category:

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; ;</span>$

8e) Repeat steps 8a) to 8d), calculate the probability that the test sample belongs to each type of image, and obtain the probability set P={P _j , j=1,...,S}, where S is the total number of categories in the image set ;

8f) Arrange the probability set P obtained in step 8e) in descending order, if the maximum probability value P _max is unique, then classify the test sample into the class corresponding to the maximum probability; if P _max is not unique, then classify the test sample into the rejection domain , indicating that the class label of the sample is uncertain.

Step 9, repeat step 8, find and output the class labels of all test sample images in the test sample image dataset.

The effects of the present invention can be further illustrated by the following simulation experiments.

1. Simulation content: the present invention and Brodatz texture image and SAR image classification experiments of wavelet, wavelet packet, and contourlet.

2. Simulation conditions: Intel(R) Pentium(R) 4CPU, 3.00GHz, Windows XP system, Matlab7.4.0 operating platform.

3. Simulation results:

In the experiment, the texture image and the SAR image are classified respectively.

A. Brodatz Texture Image Classification

The experimental parameter settings are shown in Table 3. Considering the robustness of wavelet and wavelet packet transform, the minimum sub-band size is 16×16, so the decomposition layers of database 128 and database 64 are different, and 3-layer and 2-layer transformations are used respectively. According to the experimental results, the number of directions and layers of contourlet decomposition is the optimal parameter. For the frequency-domain direction decomposition of the present invention, multiple experiments on multiple databases show that the classification results are relatively robust when the parameters α=1.5, D=16, and N=6 are set.

Table 3 Brodatz texture classification experiment parameter settings

Randomly select 10 groups of training and test samples for experiments, and find the average result of 10 classifications. The experimental results are as follows:

1) The Brodatz texture library 128 and the texture library 64 are classified by using the correlation classification method, and the experimental results shown in Tables 4 and 5 below are obtained.

Table 4 Correlation classification results of Brodatz texture library 128

features correct reject mistake standard deviation Wavelet 3-layer decomposition 85.82 5.95 8.23 1.74 3-layer decomposition of wavelet packet 87.64 0 12.36 2.00 Contour wave 2-layer decomposition, number of directions 4, 8 83.51 5.31 11.19 3.15 The present invention (α=1.5, D=16, N=6) 96.04 0 3.96 0.87

Table 5 Correlation classification results of Brodatz texture library 64

Features correct reject mistake standard deviation Wavelet 2-layer decomposition 23.95 73.79 2.26 5.04 2-layer decomposition of wavelet packet 52.72 38.72 8.56 1.26 Contour wave 2-layer decomposition, number of directions 4, 8 46.00 48.68 5.32 1.45 The present invention (α=1.5, D=16, N=6) 83.43 0 16.57 0.74

It can be seen from Table 4 and Table 5 that applying the frequency domain direction feature of the present invention to the correlation classification method can obtain a good classification effect. Compared with the widely used classification method based on wavelet transform and the multi-scale geometric analysis method contourlet, the classification accuracy rate obtained by the present invention is significantly improved. For the texture library 128, the classification accuracy rate of the present invention is at least increased by nearly 9 percentage points. For texture Library 64, the advantages are more obvious, and the correct rate is increased by at least 24%. This result fully verifies that the features of the present invention are divided more carefully in frequency and direction, and the advantages of better classification performance.

By comparing the classification results of Texture Library 128 and Texture Library 64, we found that as the size of the submap decreases, the classification performance of the present invention drops much lower than that of other transformations. The reason is that the frequency domain direction feature extraction method operates directly in the frequency domain, and the parameters are adjustable, and the subband size is variable, so the change of the image size has little effect on the method, while other transformations are affected by the transformation framework. Influence, considering the robustness, the sub-band size is generally required higher, so there is a limit to the minimum size of the image. The experimental results fully demonstrate that the classification performance of the present invention is superior to several other methods, and it has better robustness to image size.

2) Feature extraction time, the frequency domain direction feature extraction time of the present invention is obviously lower than other transformations, and its computational complexity is low. The table below shows the time taken to transform a 1024×1024 texture image and extract its energy features.

Table 6 Feature extraction time of various transformations, image size is 1024*1024

transform Wavelet 3-layer decomposition 3-layer decomposition of wavelet packet Contour wave 2-layer decomposition, number of directions 4, 8 The present invention (α=1.5, D=16, N=6) Feature extraction time 1.07s 4.38s 5.76s 0.73s

Table 5 shows the feature extraction time of several transformations. The experimental results fully demonstrate that since the present invention is realized by fast Fourier transform, the feature extraction time is significantly lower than other transformations, and the computational complexity is greatly reduced.

B. SAR image classification

The experimental parameter settings are shown in Table 7. The parameter setting of the SAR image classification experiment is similar to that of the Brodatz texture image.

Table 7 SAR classification experiment parameter settings

Classify the two databases SAR128 and SAR64 of SAR images, and get the classification results of 10 averages as shown in Table 8 and Table 9.

Table 8 Correlation classification results of database SAR128

features correct reject mistake standard deviation Wavelet 3-layer decomposition 95.3 2.94 1.76 0.41 3-layer decomposition of wavelet packet 79.18 8.32 12.5 4.50 Contour wave 2-layer decomposition, number of directions 4, 8 84.00 12.66 3.34 8.60 The present invention (α=1.5, D=16, N=6) 96.43 0 3.57 0.34

Table 9 Correlation classification results of database SAR64

features correct reject mistake standard deviation Wavelet 2-layer decomposition 58.87 38.20 2.93 7.81 2-layer decomposition of wavelet packet 55.48 39.57 4.95 1.24 Contour wave 2-layer decomposition, number of directions 4, 8 58.02 36.64 5.34 1.50 The present invention (α=1.5, D=16, N=6) 92.49 0 7.51 0.70

The results shown in Table 8 and Table 9 show that the classification effect of the frequency domain direction decomposition of the present invention is the best. For the database SAR128, the classification accuracy rate of the present invention is 1.13% higher than the wavelet transform, 12.43% higher than the contourlet transform, and 17.25% higher than the wavelet packet transform; the database SAR64, the classification result advantage of the present invention is more significant, higher than the other three transforms Out of more than 30 percentage points, fully verified the effectiveness of the present invention.

In addition, since the texture information contained in the 64×64 submap is not as rich as that of the 128×128 submap, it is relatively more difficult to distinguish the texture category, so the classification accuracy will decrease. But the present invention only decreased by 4%, while other methods decreased significantly, at least 24%. This experimental result further verifies that the present invention has better robustness to image size changes.

Claims (4)

1. An image classification method based on frequency domain direction feature correlation, the specific implementation process is as follows: (1) Select sample images of various textures, and divide these sample images into two data sets of training sample images and test sample images; (2) Carry out 2-dimensional fast Fourier transform respectively to the training sample image data set, divide the Fourier plane into different frequency domain direction subbands according to the frequency and direction of the Fourier plane; (3) Calculate the energy characteristics of each subband to obtain the frequency domain direction feature matrix M of the image; (4) Calculate the correlation coefficient between each sub-band feature of the frequency-domain direction feature matrix M, and arrange in descending order according to the correlation coefficient of each sub-band pair to obtain a correlation pair sequence; (5) Apply the linear regression model of one element to obtain the classification feature parameters of each feature correlation pair in the correlation pair sequence to form a classifier; (6) Compare the frequency-domain direction feature of the test sample image with the fitting degree of all parameters in the classifier, calculate the probability that the test sample belongs to each type of image, and take the class label corresponding to the maximum probability as the class of the sample mark; (7) Step (6) is repeated to obtain the class labels of all sample images in the test sample image dataset. 2, the image classification method according to claim 1, wherein according to the frequency and direction of Fourier plane described in step (2) Fourier plane is divided into different frequency domain direction sub-bands, carry out as follows: 2a) Taking the DC component of the Fourier plane as the center, divide the upper half of the Fourier plane into N frequency bands and D directions according to the radius and direction of polar coordinates, and obtain K=N×D+2 sectors, and each sector represents Different frequency bands and direction information from low frequency to high frequency constitute different subbands; 2b) Use the following formula to calculate the position of each subband center point (r _n , θ _d ): $r_{\mathrm{no}}={\left(\frac{\mathrm{no}}{N}\right)}^{\mathrm{\&alpha;}}(R-1)+1,$ n=1,...,N ${\mathrm{\&theta;}}_d=\frac{\mathrm{\&pi;}}{\mathrm{D.}}\&Center\; Dot;d,$ d=1,...,D Among them, n represents the frequency band, N is the total number of frequency bands, d represents the polar coordinate direction of the upper half plane of Fourier, D is the total number of directions, R represents the maximum radius of the Fourier plane, α is an adjustable parameter, and D generally takes 16 , N generally takes 6, α generally takes 1.5; 2c) Calculate the subband size Δr _n on each frequency band according to the following formula: Δr _n =r _n -r _n-1 , n=1,...,N, Wherein, the subbands in different directions of the same frequency band have the same size; 2d) Taking (r _n , θ _d ) as the center of the subband, and Δr _n as the size of the subband, windowing is performed to obtain K subbands in the frequency domain direction. 3. The image classification method according to claim 1, wherein the calculation of the test sample belonging to the probability of each type of image in the step (6) is carried out as follows: 3a) Take the unary linear regression model classification parameters a _i , b _i , μ _i , σ _i of the i-th correlation pair of a certain type of image and the subband features (xi _, y _i ) corresponding to the correlation pair in the test sample features; 3b) According to the linear regression equation of one variable $\widehat{\mathrm{the\; y}}=a\&times;x+b$ Find the estimated value of the subband feature y _i Calculation error

3c) According to the following formula, the probability P _i that the test sample conforms to the classification parameter model of each relevant pair of the class is obtained: $P_i=\left\{\begin{array}{c}1,\mathrm{if}|{\mathrm{the\; y}}_i-{\widehat{\mathrm{the\; y}}}_i-{\mathrm{\&mu;}}_i|<{3\mathrm{\&sigma;}}_i\\ 0,\mathrm{if}|{\mathrm{the\; y}}_i-{\widehat{\mathrm{the\; y}}}_i-{\mathrm{\&mu;}}_i|>{3\mathrm{\&sigma;}}_i\end{array}\right.,$ i=1,...,L, Wherein L is the total number of correlation pairs in the jth type image correlation pair sequence; 3d) Calculate the probability P that the test sample belongs to this type of image: $\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ;</span>$ 3e) Steps 3a) to 3d) are repeated to calculate the probability that the test sample belongs to each type of image. 4. The image classification method according to claim 1, wherein the class label corresponding to the maximum probability value in step (6) is used as the class label of the sample, and all obtained probabilities are arranged in descending order, if the maximum probability value P _max is unique, the test sample is classified into the class corresponding to P _max ; if P _max is not unique, the test sample is classified into the rejection domain.

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