CN108510496B - A Blur Detection Method Based on SVD Decomposition in Image DCT Domain - Google Patents

Abstract

The invention proposes a blur detection method based on the SVD decomposition of the image DCT domain. First calculate the gradient map of the image to be tested, and the edge information of the image can be obtained from the gradient map, then divide the gradient map into blocks, and perform DCT transformation, because the AC coefficient of the DCT domain reflects the edge and clarity of the image, and then the difference The matrix is used to analyze the AC coefficient information in the DCT domain. By calculating the singular value of the difference matrix, and constructing the response function to represent the blur degree of the image of the block, the mean and variance are used to normalize the sum of the image block responses to eliminate the image content. Impact. Experiments show that the fuzzy score obtained by this method is highly consistent with the subjective evaluation score of the image by the human eye. The detection model of the present invention takes into account the characteristics of wider edges and weaker definition in the process of image blurring, and effectively eliminates the influence of image content, so the detection accuracy is high, the detection efficiency is fast, and the overall performance is better than the previous one. the way of man.

Description

A Blur Detection Method Based on SVD Decomposition in Image DCT Domain

technical field

The invention relates to the field of image blur detection, and proposes a blur detection method based on SVD decomposition in the image DCT domain, which can quickly and accurately detect blurred images.

Background technique

As one of the carriers of information transmission, digital images play an important role in daily life or work. For example, the popularity of mobile phones has made mobile phone photography one of people's daily entertainment items; satellite remote sensing images have brought convenience to agriculture, industry and the environment. But digital images inevitably introduce some distortions in the process of acquisition, compression, transmission and storage, which not only affects the visual experience, but also may bring huge losses. Image blur is the most common type of distortion, so the detection of image blur is getting more and more attention.

Although the human eye has the ability to distinguish blurry images from clear images, it has disadvantages such as time-consuming and heavy workload. Therefore, it is particularly important to use computers to detect blurry images. At present, there are many image blur detection methods, which are roughly divided into spatial domain method, frequency domain method and mixed domain method. In general, image blurring produces wider edges, so most spatial methods are based on the edge width of the image. For example, Marziliano et al. proposed an algorithm based on the Sobel operator. This method first detects the Sobel edge in the vertical direction of the image, and then obtains the width of the image edge through the local extreme points. Finally, the blur of the image is defined as the average edge width; as proposed by Ferzli and Karam A visually visible blur (Just Noticable Blur, JNB) model, the method first determines the edge blocks and sliders of the image, then calculates the block edge width of the edge blocks, and finally obtains the blur degree of the image through the JNB model. Considering the limitation of image feature representation in spatial domain, many methods transform the image into frequency domain, such as DWT domain or DCT domain. By analyzing the distribution of non-zero coefficients in the frequency domain of the image, Marichal et al. proposed a method based on the DCT domain of the image. This method first divides the image into blocks, then obtains the DCT coefficients of each 8x8 block, and finally passes the weighted histogram of the DCT non-zero coefficients. figure to estimate image blur. Tong et al. proposed a method based on the wavelet domain. The method first classifies the edges through multi-scale wavelet domain coefficients, and then judges whether the image is blurred according to the proposed rules. Finally, the blurriness of the image can be obtained by the number of blurred edges. At present, some scholars have proposed a hybrid domain algorithm that combines the spatial domain and the frequency domain. For example, Vu et al. also proposed a comprehensive evaluation algorithm based on the hybrid domain (S3). The frequency domain features are obtained by transforming the Sigmoid function, and the local variation is used to obtain Spatial domain features, the final fuzzy estimation is obtained by taking the weighted average of the first two items; such as an algorithm based on discrete orthogonal moments proposed by Li et al., the method first estimates the edge of the image through gradient information, and then uses the discrete orthogonal moments. The frequency domain information is obtained, and finally the sum of the discrete orthogonal moments of the image is calculated to represent the blurriness of the image. At the same time, it shows that the algorithm combining spatial domain and frequency domain has better effect.

There are many existing image blur detection methods, all of which utilize the characteristics of blurred images: as the blurring degree of the image increases, the edges of the image will become wider and the outline will become less and less obvious.

SUMMARY OF THE INVENTION

By comparing the characteristics of the above methods, a detection method based on SVD decomposition in the image DCT domain is proposed, which combines the image spatial domain and frequency domain information. First calculate the gradient map of the image, the edge information of the image can be obtained from the gradient map, then divide the gradient map into blocks, and perform DCT transformation, because the AC coefficient of the DCT domain reflects the edge and clarity of the image, and then use the difference matrix. To analyze the AC coefficient information of the DCT domain, calculate the singular value of the difference matrix, and construct the response function to represent the blur degree of the image of the block, and finally use the mean and variance to normalize to eliminate the influence of the image content.

The technical solution steps of the present invention are as follows:

Step 1: Calculate the gradient map of the image to be detected, and divide the gradient image into blocks with a size of p×p.

Step 2: Perform DCT transformation on each gradient image block to obtain DCT coefficients and remove the DC coefficients.

Step 3: Calculate the difference matrix of the horizontal and vertical directions of the DCT coefficients.

Step 4: Calculate the singular values of the difference matrix and get the block response from the response function.

Step 5: Sum the responses of all blocks to get the response E of the whole image.

Step 6: Divide the image into blocks (the block size is the same as that of step 1), calculate the mean and variance of each image block, and sum the mean and variance of all blocks respectively to obtain the mean C and variance V of the entire image.

Step 7: Normalize E in step 5 with C and V obtained in step 6 to obtain the final fuzzy score S.

Step 8: By comparing the size of S and the selected threshold T, the image is divided into two categories: clear and blurred.

Beneficial effects of the present invention:

The invention combines the information of the image space domain and the frequency domain, effectively improves the accuracy of the blur detection, and makes up for the defect of only using the space domain or the frequency domain. The image edge information is obtained in the spatial domain, and the blur degree (response) of the image is obtained in the frequency domain, which not only retains the intuition of the image spatial domain information, but also retains the validity of the image frequency domain information. In addition, the present invention also performs normalization operation on the response obtained in the frequency domain of the image, thereby eliminating the influence of the image content.

Description of drawings

Figure 1 algorithm flow chart.

Figure 2. Clear image sample.

Figure 3 Blurred image sample.

Figure 4. Blur scores for 58 images in the LIVE image library.

Figure 5. Detection results of clear image samples and blurred image samples.

Detailed ways

The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings. The fuzzy detection method based on the SVD decomposition of the image DCT domain, and its specific steps are described in Figure 1:

Step 1: Calculate the gradient map of the image to be detected, and divide the gradient image into blocks with a size of p×p.

Step 2: Perform DCT transformation on each gradient image block to obtain DCT coefficients and remove the DC coefficients.

Step 3: Calculate the difference matrix of the horizontal and vertical directions of the DCT coefficients.

Step 4: Calculate the singular values of the difference matrix and get the block response from the response function.

Step 5: Sum the responses of all blocks to get the total response E of the whole image.

Step 6: Divide the image into blocks (the block size is the same as that of step 1), calculate the mean and variance of each image block, and sum the mean and variance of all blocks respectively to obtain the mean C and variance V of the entire image.

Step 7: Normalize E in step 5 with C and V obtained in step 6 to obtain the final fuzzy score S.

Step 8: By comparing the size of S and the selected threshold T, the image is divided into two categories: clear and blurred.

Step 1 is as follows: Calculate the gradient map G of the image I to be tested, and the formula is as follows:

I _x =I*[-101],I _y =I*[-101] ^T

Where * is the convolution operation, and then the gradient image G is divided into blocks, each block is set to B _k , k=(1,2,...,N), N is the total number of image blocks, and the block size is p ×p, p=6 in the experiment.

Step 2 is as follows: transform the image block B _k to the DCT domain D _k , and remove the DC coefficient, the formula is as follows:

D _k =DCT(B _k )

where i,j∈{1…p}.

Step 3 is as follows: Calculate the difference matrix in the horizontal direction and the vertical direction respectively, and the formula is as follows:

where i∈{1,…,p},j∈{1,…,p-1}.

where i∈{1,…,p-1},j∈{1,…,p}.

Step 4 is as follows: Calculate the singular value of the difference matrix, the formula is as follows:

(:) means to convert the matrix into a column vector, the size of F is p(p-1)×2, and then perform singular value decomposition on F to obtain singular values s ₁ , s ₂ , and obtain the energy of the image block from the response function e .

e _k =s ₁ ×s ₂ -α(s ₁ +s ₂ ) ²

where α is a constant, and α=0.01 in the experiment.

Step 5 is as follows: Calculate and sum up the responses of all blocks of the image to be tested to obtain the total response E of the entire image. The formula is as follows:

where N is the total number of image blocks.

Step 6 is as follows: the image to be tested is divided into blocks, the process is the same as step 1, and the mean value _ck and variance _vk of each block are calculated, and then the sum of the mean values C and the sum of variances V of all blocks are calculated, and the formula is as follows:

Step 7 is as follows: normalize E with V and C to obtain the final fuzzy score S, the formula is as follows:

Step 8 is as follows: First, determine the threshold value T between the clear image and the blurred image. Through step 7, the blur score S of the clear image (see Figure 2) and the blurred image (see Figure 3) can be obtained. After analyzing the data S obtained from these two types of images, it can be seen that the clear image is much higher than the blurred image. (See Figure 5). In order to ensure sufficient experimental data, a large number of samples (half the number of blurred and clear images) are selected from the LIVE image library for testing, and the final threshold T is determined (see Figure 4). The final selected threshold is T=15 (the black line in FIG. 4 ). When T>15, the image is clear, and when T≤15, the image is blurred.

Claims (5)

1. The blur detection method based on the SVD decomposition of the image DCT domain, first calculate the gradient image of the image to be tested, the edge information of the image can be obtained from the gradient map, and then divide the gradient map into blocks and perform DCT transformation, because the DCT domain The AC coefficient reflects the edge and sharpness of the image. Then, the difference matrix is used to analyze the AC coefficient information in the DCT domain, and the singular value of the difference matrix is calculated. The response function is constructed by the singular value to represent the blur degree of the image of the block. Finally, use The mean and variance are normalized to eliminate the influence of image content; the specific steps are as follows: Step 1: Calculate the gradient map of the image to be detected, and divide the gradient image into blocks, and the size of the block is p×p; Step 2: Perform DCT transformation on each gradient image block to obtain DCT coefficients and remove the DC coefficients; Step 3: Calculate the difference matrix of the horizontal and vertical directions of the DCT coefficients; Step 4: Calculate the singular values of the difference matrix, and get the block response from the response function; Step 5: Sum the responses of all blocks to obtain the response E of the entire image; Step 6: Divide the image into blocks (the block size is the same as that in step 1), calculate the mean and variance of each image block, and sum the mean and variance of all blocks respectively to obtain the mean C and variance V of the entire image; Step 7: Normalize E in step 5 with C and V obtained in step 6 to obtain the final fuzzy score S; Step 8: By comparing the size of S and the selected threshold T, the image is divided into two categories: clear and blurred; The specific process of step 1 is as follows: Calculate the gradient map G of the image I to be tested, the formula is as follows:

I _x =I*[-1 0 1],I _y =I*[-1 0 1] ^T Where * is the convolution operation, and then the gradient image G is divided into blocks, each block is set to B _k , k=(1,2,...,N), N is the total number of image blocks, block size is p×p, p=6 in the experiment; The specific process of step 2 is as follows: Transform the image block B _k to the DCT domain D _k , and remove the DC coefficients, the formula is as follows: D _k =DCT(B _k )

where i,j∈{1...p}; The specific process of step 3 is as follows: Calculate the difference matrix in the horizontal and vertical directions respectively, the formula is as follows:

where i∈{1,...,p},j∈{1,...,p-1};

where i∈{1,...,p-1},j∈{1,...,p}; The specific process of step 4 is as follows: Calculate the singular values of the difference matrix, the formula is as follows:

(:) means to convert the matrix into a column vector, the size of F is p(p-1)×2, and then perform singular value decomposition on F to obtain singular values s ₁ , s ₂ ; obtain the response of the image block from the response function e ; e _k =s ₁ ×s ₂ -α(s ₁ +s ₂ ) ² where α is a constant, and α=0.01 in the experiment. 2. the fuzzy detection method based on the SVD decomposition of image DCT domain according to claim 1, is characterized in that step 5 concrete process is as follows: Calculate and sum the responses of all blocks of the image to be tested to obtain the total response E of the entire image. The formula is as follows:

where N is the total number of image blocks. 3. the fuzzy detection method based on the SVD decomposition of the image DCT domain according to claim 2, is characterized in that the concrete process of step 6 is as follows: The image to be tested is divided into blocks, the process is the same as step 1, and the mean value _ck and variance _vk of each block are calculated, and then the sum of the mean value C and the sum of variance V of all blocks is calculated, and the formula is as follows:

4. the fuzzy detection method based on the SVD decomposition of image DCT domain according to claim 3, is characterized in that step 7 concrete process is as follows: Normalize E with C and V to get the final fuzzy score S, the formula is as follows:

5. the fuzzy detection method based on the SVD decomposition of image DCT domain according to claim 4, is characterized in that step 8 concrete process is as follows: First determine the threshold value T between the clear image and the blurred image; through step 8, the blur score S of the clear image and the blurred image can be obtained, and by analyzing the data S obtained from these two types of images, it can be seen that the clear image is much higher than the blurred image. ; In order to ensure sufficient experimental data, a large number of samples are selected in the LIVE image library for testing, and the final threshold T is determined; the final threshold selected is T=15, when T>15 means the image is clear, when T≤15 means the image is fuzzy.

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