CN102542539A - Strong-applicability image enhancement method based on power spectrum analysis - Google Patents

Abstract

The invention relates to a strong applicability image enhancement method based on power spectrum analysis, which belongs to the field of image enhancement. The method includes establishing a mathematical model of the image power spectrum, analyzing the model, deriving the features of the real image, and performing statistical proof on the features. The present invention solves and analyzes the average power spectrum curves of the fuzzy image and the clear image, and finds that the fuzzy image has a power loss phenomenon; a clear image that has nothing to do with the fuzzy image is used as a reference image, and the size of the reference image is the same as that of the fuzzy image. A clear image with rich details or taken from the same scene as the blurred source image; then perform image enhancement processing on the blurred image; first solve the average power spectrum curve of the two selected images, and use this curve to perform segmented data fitting, and then The spectrum adjustment parameters are calculated from the gap between the fitting data of the two images, and finally the purpose of enhancing the image is achieved by adjusting the spectrum of the fuzzy image.

Description

A Strong Applicability Image Enhancement Method Based on Power Spectrum Analysis

technical field

The invention relates to an image processing technology, in particular to a method for enhancing a power spectrum lossy blurred image with strong applicability, and belongs to the field of image enhancement.

Background technique

During image acquisition, defocus, motion, inaccurate parameter setting, weather, etc. are all reasons for image blur. The purpose of image enhancement is to improve the details of the image so that we can get more useful information from the image. When the hardware conditions of image acquisition have been determined, software post-processing is an effective method to enhance images. Although there are many existing image enhancement methods, most of them are aimed at pure image blur, such as motion blur or defocus blur. Considering their speed and applicability, not many can be widely used.

Image enhancement is a research topic with a long history. Image blurring can be viewed as a degradation process with a functional form of:

g(x)=h(x)*f(x)+n(x) (1)

In the above formula, f(x) can be regarded as the real scene, h(x) is various blur degradation factors in the process of acquiring images, and n(x) is noise, which is not considered here.

Histogram equalization is a widely used image enhancement method. This method has a certain enhancement effect on the blur caused by simple natural degradation factors such as uneven brightness of the image, but it has a certain effect on the elimination of blur caused by motion blur and inaccurate camera focus. not ideal. Many methods regard deblurring as a deconvolution process, resulting in blind restoration methods, but such methods require iteration and take a long time, and such algorithms rely on the estimation of the image blur kernel, so the blur type for Single, not very adaptable. For defocus blur, there are also methods to analyze from the perspective of optics or 3D imaging. Although the effect is good, it also has the defect of not being widely applicable. There are also many methods for motion blur. Gradient information is often used in image motion blur processing, but it is difficult to correctly restore the edge of large motion blur in real motion. This method is only for a single image with motion blur. Fog can be regarded as a special fuzzy factor. There are many algorithms for foggy image processing, He Kaiming (Single Image Haze Removal Using DarkChannel Prior[C]. CVPR2009: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Miami Beach, Florida , Jun.2009: 1956-1963), the bright color channel defogging method proposed has achieved good results for the enhancement of hazy images, but the effect is not good for dense fog images.

In 1987, David J. Field pointed out the shape of the power spectrum of natural images and used it in the study of cortical cell images (Relations between the statistics of natural images and the response properties of cortical cells[J], Optical Society of Amercia, vol. 4, no.12, 2379-2393, Dec.1987). In 1992, NormanB.Nill proposed to use image power spectrum to analyze image quality (Objective Image Quality Measure Derived from Digital Image Power Spectra[J], Optical Engineering, vol.31, no.4, 813-825, Apr.1992). In 1997, Daniel L. Ruderman analyzed the scale characteristics of images starting from the power spectrum power index (Origins of Scaling in Natural Images[J], Vision Research, vol 37, No23, 3385-3395, 1997). DavidJ.Field pointed out the source of the variability of the image power spectrum through the analysis of the power spectrum, and analyzed noise, blur, etc. (Visual Sensitivity, Blur and the Sources of Variability in the Amplitude Spectra of Natural Scenes[J], Vision Research, vol .37, no. 23. pp. 3367-3383, 1997). In 2003, Antonio made a statistical analysis of the average power spectrum of images in different scenes, and pointed out that the image power spectrum and the power spectrum radius have a power exponential relationship (Statistics of natural image categories[J]. NETWORK: COMPUTATION IN NEURAL SYSTEMS, vol.14, pp.391-412, May.2003).

Contents of the invention

The purpose of the present invention is to overcome the defects and deficiencies existing in the prior art, and to provide a processing method for image enhancement with strong applicability. The method includes the establishment of a mathematical model of the image power spectrum, the analysis of the model, the derivation of the characteristics of the real image, and the statistical proof of the characteristics; to solve the problem of fuzzy or unclear useful information in the process of obtaining the image, to achieve The purpose of image enhancement.

In order to achieve the above object, the present invention adopts the following technical solution to achieve.

A strong applicability image enhancement method based on power spectrum analysis proposed by the present invention comprises the following steps:

Step 1: Given an image to be enhanced, first select a reference image that satisfies two conditions: first, the size of the reference image is the same as the blurred image; Clear images of the same scene;

Step 2: Perform Fourier transform on the image to be enhanced given in step 1 and solve the image power spectrum. For the solution of the digital image power spectrum, it is to find the modulus after Fourier transform;

Step 3: Solve the average power spectrum curve of the image power spectrum obtained in step 2, and perform data fitting by the following fitting function formula (2):

z=Ar ^-β (2)

In formula (2), r is an independent variable, z is a dependent variable, and A and β are fitting parameters to be solved;

Step 4: divide the image frequency band by the fitting curve solved in step 3, here divide the image frequency band into four frequency bands of low frequency, intermediate frequency, high frequency and ultrahigh frequency;

Step 5: Simultaneously perform discrete cosine transform (DCT) on the image to be enhanced and the reference image, and perform local data fitting on the average spectral curve in the DCT domain;

Step 6: Solve the spectrum adjustment coefficient in each frequency band divided in step 4;

Step 7: Adjust the DCT domain spectrum of the fuzzy image in each frequency band divided in step 4;

Step 8: Perform DCT inverse transform on the adjusted DCT domain frequency spectrum in step 7 to obtain a clear image in time domain after enhanced processing;

The image to be enhanced is a square digital image, or a non-square digital image; the image to be enhanced is a grayscale image, or a color image.

In the above-mentioned technical scheme, the average power spectrum curve solution method described in step 3 is: the time domain function form of digital image is expressed as f(x, y), and its Fourier frequency domain form is F(u, v); The solution method of the digital image power spectrum curve is represented by the following formula (3):

$\stackrel{\‾}{{\left|f\left(r\right)\right|}^2}=\frac{\underset{u}{\mathrm{\Σ}}\underset{v}{\mathrm{\Σ}}{\left|f(u,v)\right|}^2}{N}$ (3)

是一个关于r的函数，变量r为点(u，v)到功率谱中心的距离，N为离中心点距离为r的频域点的总数。In the formula

is a function of r, the variable r is the distance from the point (u, v) to the center of the power spectrum, and N is the total number of frequency domain points whose distance from the center point is r.

In the above-mentioned technical solution, the image frequency band division described in step 4, wherein, the frequency band division method of the intermediate frequency and the ultrahigh frequency is as follows:

The "center of gravity point" of the intermediate frequency part is the point with the largest curvature of the overall fitting curve of the image average power spectrum curve solved in step 3;

When the image is a square digital image, its UHF part is the external data of the inscribed circle of the image power spectrum matrix data; when the image is a non-square digital image, its UHF part is the image power spectrum matrix data The outer data of the short side inscribed circle.

In the above-mentioned technical scheme, the average spectrum curve solution mode described in step 5: the time domain function form of the digital image is expressed as f (x, y), and its DCT domain spectrum form is G (u, v); The way to solve the curve is expressed by the following formula (4):

$G\left(r\right)=\frac{\underset{u}{\mathrm{\Σ}}\underset{v}{\mathrm{\Σ}}\left|G(u,v)\right|}{N}$ (4)

In the formula, G(r) is a function about r, the variable r is the distance from the point (u, v) to the center of the DCT domain spectrum, and N is the total number of frequency domain points whose distance from the spectrum center is r.

In the above-mentioned technical scheme, the solution of the average spectrum curve fitting curve described in step 5: it is to do local data fitting in the image frequency band divided in step 4, because the high-frequency band part is longer, the band needs to be segmented, specifically Fitting is performed in segments according to the size of the image, and the fitting function formula (2) becomes:

z＝Ar ^-β +γ (5)

In the above fitting formula, r is the independent variable, z is the dependent variable, and A, β and γ are the fitting parameters to be solved.

In the above technical solution, the solution to the adjustment coefficient described in step 6 is to obtain different fitting functions z _blur and z _ref of the two images through local data fitting, and the normalized ratio of these two functions is the adjustment coefficient function, Expressed by the following formula (6):

$z_{\mathrm{rate}}=\frac{z_{\mathrm{ref}}/z_{\mathrm{ref}\max }}{z_{\mathrm{blurred}}/z_{\mathrm{blurred}\max }}$ (6)

In the above technical solution, the fuzzy image DCT domain spectrum adjustment method described in step 7: take r as a variable, and perform spectrum adjustment with 1 as a unit, and the adjustment coefficient is the function z _rate about r solved in step 6. When r is taken The value z _rate (r _g ) when the integer r _g is fixed; the DCT domain spectrum of the blurred image is enhanced: specifically, the solved z _rate (r _g ) is used to enhance the frequency spectrum of the DCT domain r _g -1<r≤r _g , and Adjustments are made across the entire spectral domain.

In the above technical solution, the image enhancement method is a processing process for a grayscale image. If a color image is processed, the green component of the color image is processed according to the above steps 1-8, and then the red component of the color image is processed. The adjustment coefficients of the two color components of blue and blue are no longer calculated, but the adjustment coefficient of the green component obtained in step 6 is used to adjust the two color components of red and blue from step 7.

A strong applicability image enhancement method based on power spectrum analysis of the present invention, in step 4, after averaging the average power spectrum curves of a large number of square images in several different scenes, it is found that between the inscribed circles of the frequency domain data In addition, the curve has a relatively obvious depression; therefore, the outside of the inscribed circle of the spectrum matrix is defined as UHF, and if the image is a non-square image, the outside of the short side of the spectrum matrix inscribed in the ellipse is defined as UHF.

A strong applicability image enhancement method based on power spectrum analysis of the present invention, in the step 5, since the DCT domain also reflects the distribution of the image power spectrum, and the distribution forms are similar, in view of the simple calculation of DCT domain data, Therefore, the DCT domain transformation process is used, and because the modulus and the modulus of the value have the same fitting function, the absolute value of the value is taken in the DCT domain instead of the modulus, and simple global data fitting cannot be performed during the enhancement process. Because the error caused by global data fitting is too large. That is, when the image spectrum is segmented, the Fourier transform is used to solve the power spectrum and the spectrum is segmented, and the local data fitting is performed through the above segmented results during the real enhancement process.

A strong applicability image enhancement method based on power spectrum analysis of the present invention, in the step 7, the difference between the blurred image and the clear image is that the useful information of the blurred image is not rich enough, which is manifested in the frequency domain It is the loss of power spectrum energy. The present invention compares the average power spectrum curves of several different types of fuzzy images with the same clear image. Through the comparison, it is found that the fuzzy image has insufficient spectrum energy compared to the clear image, and adjustments are needed to achieve enhanced image quality. Purpose. The above-mentioned adjustment idea is to find the law of the power spectrum curve, and under the constraints of this law, adjust the image spectrum through a reasonable adjustment coefficient to achieve the purpose of enhancing the image.

The characteristics and technical effects of a powerful image enhancement processing method based on power spectrum analysis in the present invention: the processing method of the present invention can realize the enhancement of various blurred images, not only blurred images, but also some low-end cameras Images that do not come out with the desired clarity can also be enhanced. Although adopting the processing method of the present invention requires a clear image as a reference image, the degree of freedom in the selection of the reference image is relatively large. Many algorithms in the prior art need to adjust the image multiple times, but the present invention only needs to adjust the adjustment coefficient It is only necessary to adjust the image once, and the speed is fast, the effect is good, and the applicability is wide.

In the processing method of a kind of strong applicability image enhancement based on power spectrum analysis of the present invention, the fitting function described in its step 3 proves as follows:

Although Antonio made a statistical analysis of the average power spectrum of images in different scenes in 2003, and pointed out that the power spectrum of the image has a power exponential relationship with the radius of the power spectrum, calculated the shape of the average power spectrum, and described the characteristics of the power spectrum, but The power spectrum is not abstracted into a concrete functional form. The present invention abstracts the average power spectrum from a mathematical point of view into a more specific and applicable function and performs mathematical modeling. The modeling function is shown in formula (7):

z＝[(au) ^2/m +(bv) ^2/n ] ^-s (7)

In the formula, u and v represent the two directions of the function, z is the function value, a, b, m, n, s are the adjustment parameters, and the form of the power spectrum approximation function can be changed by adjusting these parameters.

The present invention is to analyze and process the above-mentioned function by combining the statistical data of the real image to obtain the solution method of the average power spectrum curve, and the statistical analysis process is as follows:

1. The cross-sectional form of the function in formula (7) is when z takes a fixed value greater than zero:

(au) ^2/m + (bv) ^2/n = z ₀ ^-1/s (8)

In the formula, z ₀ is the specific tangent value taken by z, the above function is a two-dimensional plane function, if a=b=1, and a specific one when 2/m=2/n=-1/s=2/3 is of the form:

(u) ^2/3 + (v) ^2/3 = z ₀ ^2/3 (9)

The above function is a star-shaped line, and the intersection point of the star-shaped line and the coordinate axis is z ₀ . The form of this function is similar to the shape of the top view of the average power spectrum of a large number of urban scene image sets proposed by Antonio in his article.

The edge longitudinal section form of the function is as follows:

z=(au) ^-2s/m or z=(bv) ^-2s/n (10)

The above functional form also satisfies the "power exponent" relationship proposed in the aforementioned article.

2. Simplify the modeling function formula (7) by analyzing the real image statistical data:

In Antonio's research, many images are counted, and each image is regarded as a set of sampling data. Antonio's statistical results show that when the number of sampled images is large enough, the horizontal, vertical and 45-degree angle directions of the power spectrum will be found. The curves basically coincide. The present invention further simplifies the model, assuming that the parameters m and n are the same in the model, the model is simplified as:

z＝[(au) ^2/t +(bv) ^2/t ] ^-s (11)

Transform the model to polar coordinates and simplify the form to get:

z=α(θ)r ^-β (12)

The above formula (12) β is no longer related to θ, indicating that when the amount of data is large enough, the probability of all directions of the image frequency domain energy spectrum is the same. From the perspective of probability, it means that when an image has not been collected, the frequency Domain energy angle orientations are equiprobable. From the nature of Fourier transform, it can be known that an edge of a time-domain image corresponds to a direction of frequency-domain energy. The closure of objects in the world we live in determines that the edge of the obtained image has multi-directionality, so even a single image It can also be regarded as a sampling set; the edges of the time domain in different directions correspond to multiple different directions of the power spectrum energy, and a set of data in each direction of these frequency domains can be regarded as a set of sampling values.

3. Process the function formula (12) obtained above:

$\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}$

$=\frac{{\&Integral;}_0^{2\mathrm{\&pi;}}\mathrm{\&alpha;}\left(\mathrm{\&theta;}\right)\mathrm{d\&theta;}}{2\mathrm{\&pi;}}{r}^{-\mathrm{\&beta;}}$ (13)

$<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Ar</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}}$

In the present invention, the above formula (12) still has the property of Ar ^-β form after integral, which is called the circular integral invariance of this function.

Here, the present invention puts forward a hypothesis: the image also has this discretized circular integral invariance, that is, the image can still be fitted with Ar ^-β after being processed by formula (3). Following the present invention proves the correctness of this assumption from two points:

(i) smoothness

The present invention adopts 2670 pictures, carries out statistical processing with images of 8 different scenes 64x64 in size, and proves that the horizontal, vertical and 45 degree of the power spectrum after discretizing the power spectrum of the real image is better than that of the power spectrum without circular integration. The data in the angular direction is smoother. Table 1 below shows the comparison between the image average power spectrum curve and the smoothness of the power spectrum curve in three directions: horizontal, vertical, and 45-degree angles. The cumulative value of the absolute value of the curve gradient is used as the smoothness evaluation standard.

Table 1 Comparison of image average power spectrum curve and its horizontal, vertical and 45-degree angle direction smoothness

It can be seen from Table 1 that the average power spectrum curves of 2260/2670≈84.6% of test images are smoother than those in both horizontal and vertical directions; there are 2026/2670≈75.9% of test image average power spectrum curves in three directions. are smooth, so it is reasonable to use the average power spectrum curve for fitting.

(ii) Fit

The present invention uses the square of the correlation coefficient, that is, the coefficient of determination d ² , to calculate the fitting degree of the function z=Ar ^-β and the image average power spectrum curve, see ["Calculation Method"People's Posts and Telecommunications Publishing House, edited by Xu Shiliang April 2009 first edition];

(14)

(14)

为被拟合数据的均值，式中d²越接近1说明拟合程度越好。下表2显示了公式(13)对2670幅图，64x64大小的8个不同场景图像的平均功率谱曲线拟合程度进行检测的结果。In the above formula is the fitting function, y _k is the fitted data,

is the mean value of the fitted data, and the closer d ² is to 1, the better the fitting degree. Table 2 below shows the result of the formula (13) testing the fitting degree of the average power spectrum curve of 8 different scene images of 2670 images and 64x64 in size.

Table 2 Fitting degree test results

Scene (frame) best fit worst fit Seaside(360) 99.998% 98.659% Woods(310) 99.996% 96.77% Highway(260) 99.997% 99.457% In the city(308) 99.982% 98.636% Mountain(374) 99.996% 91.336% Rural location(410) 99.995% 98.641% Street(292) 99.993% 97.946% Building(356) 99.989% 98.142%

The above proofs and statistics fully prove the rationality of step 3 for image processing.

Description of drawings

Fig. 1 is a schematic block diagram of an image enhancement process flow in the present invention;

Fig. 2 is the effect diagram of the defocused image enhancement experiment to be enhanced in the present invention; (a) is a defocused image, (b) is an enhanced image, and (c) is a reference image;

Fig. 3 is the non-square defocused image enhancement experimental effect to be enhanced in the present invention; (a) is a defocused image, (b) is an enhanced image, and (c) is a reference image;

Fig. 4 is a segmented schematic diagram of the UHF part of the image of the present invention;

Fig. 5 is the experimental rendering of the motion blur image enhancement processing of the present invention; (a) is the motion blur source image, (b) is the enhanced image, and (c) is the reference image;

Fig. 6 is the experimental effect diagram of dense fog blurred image enhancement processing of the present invention; (a) is the dense fog blurred source image, (b) (d) is the enhanced image, (c) (e) is respectively (b) and (d) the reference image of

Fig. 7 is the fuzzy rock image enhancement experimental effect diagram scanned by the scanner in the present invention; (a) is a fuzzy source image, (b) is an enhanced image, and (c) is a reference image;

Fig. 8 is a schematic diagram of solving the average power spectrum curve of the enhanced processing image in the present invention;

Fig. 9 is the three-dimensional model of the image average power spectrum enhanced by the present invention; (a) is the power spectrum three-dimensional graph of the green component in Fig. 2 (a), (b) is the three-dimensional shape graph of different image average power spectra in 300 cities , (c) is the three-dimensional shape graph of the modeling function;

The section shape figure of Fig. 10 modeling function of the present invention; (a)-(g) is a=b=1 in the cross-section formula (8) of modeling function, z ₀ =3, parameter 2/m=2/n =-1/s is from 1 to 4, and its step size is the shape graph (h) of 0.5 is the longitudinal section shape graph of modeling function;

Fig. 11 is a schematic diagram of the image frequency domain frequency band division method of the present invention; (a) is a schematic diagram of the frequency domain low frequency, intermediate frequency, high frequency, and ultrahigh frequency band division; (b) is a schematic diagram of the determination of the intermediate frequency band, and the curvature of the overall fitting curve is the largest Point as the "center of gravity" of the intermediate frequency, (c) is a schematic diagram for determining the UHF band;

The average power spectrum curve of (a) green component in Fig. 12 of the present invention Fig. 2;

Fig. 13 is the top view of the three-dimensional figure after the average value of different image power spectra in the city using 308 pieces of the present invention; from this figure, it can be illustrated that the shape of a large amount of clear image power spectra after average is similar to the star-shaped line, that is, the invention is described. Equation (9) star line function shape is similar to the top view shape of the average power spectrum of the large urban scene image set proposed by Antonio in his article.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and examples. The example is only a specific illustration of the method of the present invention, and should not be construed as any limitation to the protection content of the present invention.

Example 1

Figure 1 is a schematic diagram of the entire algorithm flow. Here, an example of a color image with a small degree of defocus blur is shown in Figure 2 (a) to illustrate the entire processing process. At this time, the processed image is a square image. The specific operation steps are as follows :

Step 1: Use MATLAB software to read in the fuzzy digital image to be enhanced in the computer, as shown in Figure 2 (a), take out the green component of its RGB three components, and after the green component is taken out, it becomes a two-dimensional matrix . If the green component is displayed in the form of a 256 grayscale image, it is visually a grayscale image. Here, the color RGB image is processed. If it is a grayscale image, the grayscale image can be processed as the green component of the color image;

Step 2: Discrete Fourier transform (FFT) is performed on the green component of the fuzzy image and then the power spectrum of the image is solved, that is, the modulus of each matrix data is obtained after the FFT transformation. The power spectrum of the green component of this image is shown in Figure 9(a). For a single image, the data is complex and irregular, but the form of the average power spectrum of a large number of images is as shown in Figure 9 (b), and the three-dimensional shape of the modeling function formula (6) proposed by the present invention As shown in (c) figure among Fig. 9, Fig. 10 has shown some horizontal and vertical section diagrams of this function respectively;

求解示意图如图8所示，功率谱曲线的求解结果如图12所示；The third step: solve the average power spectrum curve of the green component of the image, the specific way is to use the formula (3) to solve the power spectrum matrix solved in the second step

The solution schematic diagram is shown in Figure 8, and the solution result of the power spectrum curve is shown in Figure 12;

Step 4: Fit the overall data to the average power spectrum curve of the fuzzy image through the function z=Ar ^-β ; the specific fitting method is the function about the variable r solved in the third step Through the data fitting toolbox in MATLAB, use the least square method to perform curve fitting, and solve the parameters A and β;

The fifth step: image frequency band division, divide the image frequency domain into 4 frequency bands of low frequency, intermediate frequency, high frequency and ultra high frequency: the specific frequency division method is, use the fitting curve z solved in the fourth step to calculate the maximum curvature As a mark point, this point is referred to as the "center of gravity" of the intermediate frequency in the present invention, and a numerical value can be manually selected for the boundary between the intermediate frequency and the low frequency. Here, the center of the intermediate frequency "center of gravity" and zero frequency is taken as the boundary, and the "center of gravity" of the intermediate frequency The distance between this point and the high-frequency boundary point is 2 to 3 times the length from this point to the low-frequency boundary point. In addition, after averaging the average power spectrum curves of a large number of images in several different scenes, it is found that between the inscribed circle of the frequency domain data In addition, the curve has a relatively obvious depression, so the outside of the inscribed circle of the spectrum matrix is defined as the ultra-high frequency, and the ultra-high frequency is the area outside the inscribed circle of the square matrix in the frequency domain. The frequency division diagram is shown in Figure 11;

Step 6: read in the reference image (c) in Figure 2, and take out the green component of the reference image;

Step 7: Carry out DCT transformation on the green components of (a) in Fig. 2 of the blurred image and (c) of the reference image Fig. 2 respectively, and divide the two images in the DCT domain according to the frequency band division boundary solved in the fourth step For low frequency, intermediate frequency, high frequency, and ultrahigh frequency, solve the average spectral curve in the DCT domain. The solution method uses formula (4), and use z=Ar ^-β +γ for the average spectral curve of the green component of the two images in each frequency band. Segmented data fitting. The image size here is 512x512. The amount of low-frequency and intermediate-frequency data is not large. Segmentation is not required. Since the high-frequency data segment is too long, it needs to be segmented. Here, the high-frequency part data is divided into four segments for fitting. ;

Step 8: Adjust the spectrum of the green component by fitting the data;

那么当r取一个图像范围内的定值r₀时，两个函数求解出固定的函数值z₁₀和z₂₀；① Assume that the two fitting functions are solved according to the local data of the average power spectrum curve of the color component of the two images as and

Then when r takes a fixed value r ₀ in the image range, the two functions solve the fixed function values z ₁₀ and z ₂₀ ;

② Calculate the adjustment parameter z ₁₀ /z ₂₀ ;

③Amplify the spectrum with the adjustment parameter z ₁₀ /z ₂₀ within the DCT spectrum range from r ₀ -1 to r ₀ of the color component of the blurred image;

④ Change r so that it traverses the DCT frequency domain range of the entire image, and use the adjustment parameters solved by ① and ② to adjust the DCT domain spectrum of the image by means of ③;

Step 9: DCT inverse transform output enhances the green component of the processed image;

Step 10: Carry out DCT transformation for the red and blue color components of the color image, go to the eighth step, and adjust the frequency spectrum of these two components by obtaining the adjustment coefficient through the green component;

Step 11: The red and blue components are inversely transformed by DCT to obtain the component matrix values in the time domain;

Step 12: Synthesize the obtained three color components into a color image output, that is, obtain the processed enhanced image (b) in FIG. 2 .

With the same processing steps of embodiment 1, the motion blur image is enhanced, and its experimental effect figure is as shown in (b) in Figure 5, wherein (c) in Figure 5 is a reference figure; it can be compared to the motion blur source figure in Figure 5 ( a) and renderings of the enhanced image (b).

Similarly, the experimental effect of image enhancement processing on dense fog and blur is shown in Figure 6 (b) and (d), where (c) and (e) in Figure 6 are the reference images of (b) and (d) respectively; You can compare the renderings of the dense fog blurred source image (a) and the enhanced images (b) and (d) in Figure 6.

Similarly, the fuzzy rock image is enhanced, and the enhanced image after processing is scanned by a scanner, as shown in (b) in Figure 7, where (c) in Figure 7 is a reference image, which can be compared with the blurred source image before enhancement ( a) and renderings of the enhanced image (b).

Example 2

Shown in Fig. 3 (a) with the non-square color digital image of a 512x300 size here, adopt processing method of the present invention to process:

The first step: read in the fuzzy digital image to be enhanced with MATLAB software in the computer, as shown in Figure 3 (a), take out the green component of its RGB three components;

Step 2: Discrete Fourier Transform (FFT) is performed on the green component of the fuzzy image and the power spectrum of the image is solved. Specifically, the FFT transformation is performed on it first, and then the power spectrum is solved;

The third step: solve the average power spectrum curve of the green component of the image, the specific way is to use the formula (3) to solve the power spectrum matrix solved in the second step

通过MATLAB中数据拟合工具箱利用最小二乘法进行曲线拟合，求解参数A和β；Step 4: Fit the overall data to the average power spectrum curve of the fuzzy image through the function z=Ar ^-β ; the specific fitting method is the function about the variable r solved in the third step

Through the data fitting toolbox in MATLAB, use the least square method to perform curve fitting, and solve the parameters A and β;

The fifth step: image frequency band division, the image frequency domain is divided into 4 frequency bands of low frequency, intermediate frequency, high frequency and ultra high frequency. The specific frequency division method is to use the fitting curve z solved in the fourth step to calculate the maximum curvature As a mark point, this point is called the "center of gravity" of the intermediate frequency in this implementation. A value can be manually selected for the boundary between the intermediate frequency and the low frequency. The distance between this point and the high-frequency boundary point is 2 to 3 times the length from this point to the low-frequency boundary point, and the ultra-high frequency is the outer area of the short-side inscribed circle of the rectangular matrix data in the frequency domain;

The sixth step: read in the reference image (c) in Figure 3, and take out the green component of the reference image;

Step 7: Carry out DCT transformation on the green components of (a) in Fig. 3 of the blurred image and (c) of the reference image in Fig. 3 respectively, and divide the two images in the DCT domain according to the frequency band division boundary solved in the fourth step For low frequency, intermediate frequency, high frequency, and ultrahigh frequency, solve the average spectral curve in the DCT domain. The solution method uses formula (4), and use z=Ar ^-β +γ for the average spectral curve of the green component of the two images in each frequency band. Segmented data fitting, the image size here is 300x512 pixels, the amount of low-frequency and intermediate-frequency data is not large, and segmentation is not required. Since the high-frequency data segment is too long, it needs to be segmented. Here, the high-frequency part of the data is divided into four segments. Fitting, in addition, due to the particularity of the non-square image, the UHF is divided into two sections, one section from the inscribed circle on the short side to the inscribed circle on the long side, and one section outside the inscribed circle on the long side, as shown in Figure 4;

Step 8: Adjust the spectrum of the green component by fitting the data;

和

那么当r取一个图像范围内的定值r₀时，两个函数求解出固定的函数值z₁₀和z₂₀；① Assume that the two fitting functions are solved according to the local data of the average power spectrum curve of the color component of the two images as

and

Then when r takes a fixed value r ₀ in the image range, the two functions solve the fixed function values z ₁₀ and z ₂₀ ;

② Calculate the adjustment parameter z ₁₀ /z ₂₀ ;

③Amplify the spectrum with the adjustment parameter z ₁₀ /z ₂₀ within the DCT spectrum range from r ₀ -1 to r ₀ of the color component of the blurred image;

④ Change r so that it traverses the DCT frequency domain range of the entire image, and use the adjustment parameters solved by ① and ② to adjust the DCT domain spectrum of the image by means of ③;

Step 9: Carry out DCT inverse transformation output enhancement processing image green component;

Step 10: Carry out DCT transformation to the red and blue color components of the color image, go to the eighth step, and adjust the frequency spectrum of these two components by obtaining the adjustment coefficient through the green component;

Step 11: The red and blue components are inversely transformed by DCT to obtain the component matrix values in the time domain;

Step 12: Synthesize the obtained three color components into a color image output, that is, obtain the processed enhanced image (b) in FIG. 3 .

A method for image enhancement with strong applicability of the present invention, in the segmental data fitting in the seventh step, the data length of the high-frequency part of Example 1 is 500, and the average is 4 in consideration of the computational complexity and fitting accuracy The data size of each segment is about 100, and the data length of the high-frequency part in Example 2 is 250. Also considering the computational complexity and fitting accuracy, it is divided into 3 segments on average, and the data amount of each segment is also about 100. Therefore, when fitting high-frequency segments, about 100 data are used as the segment length.

Claims (8)

1. a strong applicability image enhancement method based on power spectrum analysis, is characterized in that comprising the following steps: Step 1: Given an image to be enhanced, first select a reference image that satisfies two conditions: first, the size of the reference image is the same as the blurred image; Clear images of the same scene; Step 2: Perform Fourier transform on the image to be enhanced given in step 1 and solve the image power spectrum. For the solution of the digital image power spectrum, it is to find the modulus of each matrix data after Fourier transform; Step 3: Solve the average power spectrum curve of the image power spectrum obtained in step 2, and perform data fitting by the following fitting function formula (2): z=Ar ^-β (2) In formula (2), r is an independent variable, z is a dependent variable, and A and β are fitting parameters to be solved; Step 4: divide the image frequency band by the fitting curve solved in step 3, here divide the image frequency band into four frequency bands of low frequency, intermediate frequency, high frequency and ultrahigh frequency; Step 5: Simultaneously perform discrete cosine transform (DCT) on the image to be enhanced and the reference image, and perform local data fitting on the average spectral curve in the DCT domain; Step 6: Solve the spectrum adjustment coefficient in each frequency band divided in step 4; Step 7: Adjust the DCT domain spectrum of the fuzzy image in each frequency band divided in step 4; Step 8: Perform DCT inverse transform on the adjusted DCT domain frequency spectrum in step 7, and the enhanced time domain clear image can be obtained; The image to be enhanced is a square digital image, or a non-square digital image; the image to be enhanced is a grayscale image, or a color image. 2. the strong applicability image enhancement method based on power spectrum analysis according to claim 1, it is characterized in that the power spectrum curve solution mode described in step 3 is: the time domain function form of digital image is expressed as f(x, y ), its Fourier frequency domain form is F(u, v); the way to solve the digital image power spectrum curve is expressed by the following formula (3): $\stackrel{\&OverBar;}{{\left|f\left(r\right)\right|}^2}=\frac{\underset{u}{\mathrm{\&Sigma;}}\underset{v}{\mathrm{\&Sigma;}}{\left|f(u,v)\right|}^2}{N}$ (3) In the formula

is a function of r, the variable r is the distance from the point (u, v) to the center of the power spectrum, and N is the total number of frequency domain points whose distance from the center point is r. 3. the strong applicability image enhancement method based on power spectrum analysis according to claim 1, is characterized in that the image frequency band division described in step 4, wherein, the frequency band division method of intermediate frequency and ultrahigh frequency is as follows: The "centroid point" of the intermediate frequency part is the point with the largest curvature of the overall fitting curve of the image average power spectrum curve solved in step 3; When the image is a square digital image, its UHF part is the external data of the inscribed circle of the image power spectrum matrix data; when the image is a non-square digital image, its UHF part is the image power spectrum matrix data The outer data of the short side inscribed circle. 4. the strong applicability image enhancement method based on power spectrum analysis according to claim 1, is characterized in that the average spectrum curve solution mode described in step 5: the time domain function form of digital image is represented as f(x, y ), its DCT domain spectrum form is G(u, v); the solution to the image average spectrum curve is represented by the following formula (4): $G\left(r\right)=\frac{\underset{u}{\mathrm{\&Sigma;}}\underset{v}{\mathrm{\&Sigma;}}\left|G(u,v)\right|}{N}$ (4) In the formula, G(r) is a function about r, the variable r is the distance from the point (u, v) to the center of the DCT domain spectrum, and N is the total number of frequency domain points whose distance from the spectrum center is r. 5. the strong applicability image enhancement method based on power spectrum analysis according to claim 1, is characterized in that the solution of the average spectrum curve fitting curve described in step 5: be to make local data in the image frequency band that step 4 divides Fitting, since the high-frequency band part is long, the band needs to be segmented, and the fitting is performed in segments according to the size of the image, and the fitting function formula (2) becomes: z＝Ar ^-β +γ (5) In the above fitting formula, r is the independent variable, z is the dependent variable, and A, β and γ are the fitting parameters to be solved. 6. The strong applicability image enhancement method based on power spectrum analysis according to claim 1, characterized in that the adjustment coefficient solution described in step 6: obtain the different fitting functions z _blur of two images through local data fitting and z _ref , the normalized ratio of these two functions is the adjustment coefficient function, expressed by the following formula (6): $z_{\mathrm{rate}}=\frac{z_{\mathrm{ref}}/z_{\mathrm{ref}\max }}{z_{\mathrm{blurred}}/z_{\mathrm{blurred}\max }}$ (6) 7. The strong applicability image enhancement method based on power spectrum analysis according to claim 1, characterized in that the fuzzy image DCT domain spectrum adjustment method described in step 7: take r as a variable, and take 1 as a unit to carry out spectrum adjustment, The adjustment coefficient is the value z _rate (r _g ) of the function z _rate about r solved in step 6 when r takes a fixed integer r _g ; to enhance the DCT domain spectrum of the fuzzy image: specifically use the solved z _rate ( r _g ) Enhance the frequency spectrum of the DCT domain r _g -1<r≤r _g , and adjust in the entire frequency spectrum domain. 8. according to the strong applicability image enhancement method based on power spectrum analysis described in any one of claim 1-7, it is characterized in that it is the processing procedure to grayscale image, if color image is processed, then the color image The green component is processed according to the above-mentioned steps 1-8, and then the red and blue color components of the color image are no longer solved for the adjustment coefficient, but the green component adjustment coefficient solved in step 6 is used to adjust the red color component from step 7. , blue two color components can be adjusted.

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