CN104361593A - Color image quality evaluation method based on HVSs and quaternions - Google Patents

Abstract

The invention discloses a color image quality evaluation method based on HVS and quaternion, which belongs to the technical field of image processing and computer vision. The steps of the present invention are: 1. Construct the original reference image and the mathematical evaluation model of the distorted image to be evaluated by analyzing the visual characteristics of the human eye: the spatial position function Q _L of the image, the local variance Q _V , the texture edge complexity function Q _TE and the color Function Q _C ; 2. Construct the quaternion matrix of the original reference image and the distorted image to be evaluated, and perform singular value decomposition on the quaternion matrix to obtain the singular value eigenvector of the image; 3. Use the original reference image and the distorted image to be evaluated The Euclidean distance of the singular value eigenvectors measures the degree of image distortion. The invention combines the visual characteristics of the human eye with the quaternion, extracts the brightness and chromaticity information of the image, uses the visual characteristics of the human eye to construct the spatial position function, the texture edge complexity function and the local variance, and the evaluation results are consistent with the perception of the image by the human eye. The effect is more consistent.

Description

A Color Image Quality Evaluation Method Based on HVS and Quaternion

technical field

The present invention relates to the technical field of image processing and computer vision, and more specifically, relates to a mathematical model that uses the characteristics of the human visual system to construct a mathematical model that is consistent with the image observed by the human eye, and combines it with quaternion singular value decomposition to perform color image processing. method of quality assessment.

Background technique

Image quality is one of the important parameters in the field of image processing and computer vision. With the development of computer science and technology, the requirements for image quality in printing, ceramic tiles, images, and image retrieval are getting higher and higher. However, in image acquisition, Different degrees of image distortion and image degradation will occur during processing, compression, transmission, display, etc.

Human beings are the ultimate recipients of images, making their subjective quality evaluation of images (Difference Mean OpinionScore, DMOS) considered to be the most reliable. Subjective quality evaluation is to allow observers to evaluate and score the visual perception effect of the target image to be evaluated based on their own subjective perception experience or some pre-defined evaluation criteria, and then weight the scores of all observers. On average, the result is the subjective quality score of the image. However, subjective image quality evaluation is time-consuming and laborious, and is greatly affected by the observer, image type and surrounding environment, and its real-time performance is weak. Therefore, people have been devoting themselves to the research of an objective image quality evaluation method that can reflect people's subjective visual perception correctly, timely and effectively. Objective image quality evaluation is to use algorithms, mathematical models, etc. to provide timely and rapid feedback on image quality to obtain evaluation results that are consistent with people's subjective feelings. There are many kinds of methods, and the classification methods are also different due to different entry points and basic ideas. According to the reference to the original image, the objective quality evaluation methods are divided into three types: full reference type, partial reference type and no reference type. The full reference type is suitable for encoder design and performance comparison of different encoders, and the partial reference type and no reference type are suitable for multimedia applications with limited bandwidth. Since the full-reference type can use all the information of the original image, its image evaluation results are more in line with human subjective evaluation.

The peak signal-to-noise ratio (Peak Signal Noise Ratio, PSNR) and the mean square error (Mean Square Error, MSE) is the most classic full-reference objective image quality evaluation method. PSNR reflects the fidelity of the image to be evaluated (Fidelity), while MSE reflects the difference (Diversity) between the image to be evaluated and the original image. The theory of the above two methods is simple and clear, easy to understand, and convenient to calculate, but they only consider the comparison of each pixel of the image, and do not consider the possible structural relationship between each pixel of the image. There is a deviation.

In "Image quality assessment from error measurement to structural similarity" published by Z Wang et al. in "IEEE Transactions on Image Processing" in 2004, the SSIM algorithm was proposed to comprehensively compare the brightness, contrast and structural similarity of the original undistorted image and the image to be evaluated. The differences between the three different types of information take into account the structural relationship between pixels, but there are problems such as poor grasp of details in severe ambiguity, and difficulty in determining index parameters.

In "Gradient magnitude similarity deviation: A highly efficient perceptual image quality index" published by W. Xue et al. in "IEEE Transactions on Image Processing" in 2013, the similarity deviation algorithm GMSD based on the gradient magnitude is considered. Distortion is highly sensitive, but processing of color images must be converted to the grayscale domain. The evaluation of color images by the above methods must be converted into grayscale images, and the evaluation results deviate from what the human eye actually sees.

After searching, the Chinese patent application number 200610027433.1, the application date is June 8, 2006, and the name of the invention is: an image quality evaluation method based on super-complex singular value decomposition; the application uses super-complex numbers (quaternions) to directly For the color image modeling, the inherent energy features of the color image are extracted by hyper-complex singular value decomposition, and the distortion mapping matrix is constructed by using the distance between the singular value of the original image and the distorted image, and the quality of the color image is evaluated using the distortion mapping matrix. Chinese patent application number 201210438606.4, the application date is November 6, 2012, and the name of the invention is: color image quality evaluation algorithm. The application uses the chroma, brightness and saturation of the image as the imaginary part of the quaternion, and construct The quaternion matrix of the reference image and the image to be evaluated, and perform singular value decomposition on them respectively to obtain the singular value eigenvector, and finally apply the gray correlation degree to calculate the singular value eigenvector of the reference image and the singular value eigenvector of each image to be evaluated The higher the degree of correlation, the better the quality of the image to be evaluated. However, there is still a large deviation between the evaluation results obtained in the above application and what the human eye actually sees, and the evaluation method of color image quality still needs to be further optimized.

Contents of the invention

1. The technical problem to be solved by the invention

In order to overcome the problem that the traditional evaluation method needs to convert the color image into a grayscale image for processing when constructing the evaluation model, resulting in a large deviation between the evaluation result and the situation actually seen by the human eye, the present invention provides a method based on HVS and The color image quality evaluation method of the quaternion; the present invention proposes to combine the visual characteristics of the human eye with the quaternion, extract the brightness and chromaticity information of the image, and use the visual characteristics of the human eye to construct a spatial position function, a texture edge complexity function and Local variance, in order to improve the traditional method of splitting the R, G, and B channels, the energy characteristics of the image are extracted by using the quaternion singular value decomposition, so that the evaluation result is more consistent with the effect of human perception of the image.

2. Technical solution

In order to achieve the above object, the technical scheme provided by the invention is:

A kind of color image quality evaluation method based on HVS and quaternion of the present invention, its steps are:

Step 1. Construct the mathematical evaluation model of the original reference image and the distorted image to be evaluated by analyzing the visual characteristics of the human eye. The mathematical evaluation model includes the spatial position function Q _L of the image, the local variance Q _V , and the texture edge complexity function Q _TE and color function Q _C ;

Step 2. Use Q _L , Q _V , and Q _TE as the imaginary part of the quaternion, and Q _C as the real part of the quaternion, respectively construct the quaternion matrix of the original reference image and the distorted image to be evaluated, and calculate the quaternion Singular value decomposition is carried out on the number matrix to obtain the singular value eigenvector of the image;

Step 3, using the Euclidean distance between the original reference image and the singular value eigenvectors of the distorted image to be evaluated to measure the degree of image distortion.

Furthermore, the specific process of building a mathematical evaluation model in Step 1 is as follows:

(1) Obtain the RGB tristimulus values of the original reference image and the distorted image to be evaluated;

(2) Extract the spatial position information of the original reference image and the distorted image to be evaluated, construct the spatial position function Q _L and the texture edge complexity function Q _TE ;

(3) Convert the original reference image and the distorted image to be evaluated from RGB space to YUV color space, extract image brightness information to construct local variance Q _V , extract image brightness and chrominance information to construct color function Q _C .

Furthermore, step 1 constructs a spatial position function Q _L using the central concave feature of the human visual system, and the spatial position function

${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}}$

In the formula, e _L is the distance and quotient; e _c is a constant.

Furthermore, step 1 uses the masking effect of the human visual system to construct the texture edge complexity function Q _TE , the texture edge complexity function

Q _TE = Q _T × Q _E

In the formula, Q _T is the texture complexity function of pixel point (i, j), and Q _z is the edge complexity function of pixel point (i, j).

Furthermore, step 1 uses the multi-channel characteristics of the human visual system to construct a local variance Q _V , the local variance

${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Wherein, according to the brightness component of the image, non-overlapping blocks are carried out to obtain I _i,j , L is the number of pixels η _p contained in the image block I _i,j , $\stackrel{\&OverBar;}{I_{i,j}}=\frac{1}{L}\underset{p=1}{\overset{L}{\mathrm{\&Sigma;}}}{\mathrm{\&eta;}}_p.$

Furthermore, the color function

Q _C ＝αQ _L +βQ _U

In the formula, Q _L is the luminance information of the image, Q _U is the chrominance information of the image, and α and β are the proportions of luminance and chrominance respectively.

Furthermore, the Euclidean distance described in step 3

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span>\sqrt{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; )</span>}$

In the formula, _λi is the singular value eigenvector of the original reference image, is the singular value eigenvector of the distorted image to be evaluated, K is the minimum value of the number of eigenvalues of the two singular value eigenvectors, that is, the minimum value of the ranks of the two quaternion matrices:

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; rank</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; rank</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

3. Beneficial effect

Compared with the existing known technology, the technical solution provided by the invention has the following remarkable effects:

(1) A color image quality evaluation method based on HVS and quaternion of the present invention, which constructs the spatial position function Q _L , the local variance Q _V , the original reference image and the distorted image to be evaluated by analyzing the visual characteristics of the human eye Texture edge complexity function Q _TE and color function Q _C , and integrate the above four parts of image information through quaternions, and obtain the energy characteristics of the image through singular value decomposition, which improves the traditional method of splitting R, G, and B channels, The integrity of the color information is well guaranteed, and the extracted image information contains global and local information, so that the evaluation result can more completely represent all the information of the image;

(2) A kind of color image quality evaluation method based on HVS and quaternion of the present invention combines human visual characteristics and quaternion, and the evaluation result is more consistent with the effect of human eye perception image, which is better than traditional SSIM And several other typical image quality evaluation algorithms.

Description of drawings

Fig. 1 is the algorithm flowchart of a kind of color image quality evaluation method based on HVS and quaternion of the present invention;

Fig. 2 is the equivalent diagram of the central concave characteristic of the human visual system in the present invention;

Fig. 3 is the fitting result figure of quality evaluation method of the present invention, traditional method and image subjective quality; Wherein, (a) among Fig. 3 is the non-linear fitting curve figure of PSNR and DMOS value, (b among Fig. 3 ) is the nonlinear fitting curve of SSIM and DMOS value, (c) in Fig. 3 is the nonlinear fitting curve of MS-SSIM and DMOS value, (d) in Fig. 3 is the non-linear fitting curve of SVD and DMOS value Linear fitting curve, (e) in Fig. 3 is the nonlinear fitting curve of GMSD and DMOS value, (f) among Fig. 3 is the nonlinear fitting curve of quality evaluation method of the present invention and DMOS value ;

(a)-(e) in Fig. 4 are comparison charts of non-linear fitting curves of HVS-QSVD, GMSD, SSIM and DMOS values of five groups of images with different distortion types.

Detailed ways

In order to further understand the content of the present invention, the present invention will be described in detail in conjunction with the accompanying drawings and embodiments.

Example 1

Combining with Figure 1, this embodiment provides a method based on HVS and quaternion to solve the problem that the traditional evaluation method needs to convert the color image into a grayscale image for processing when constructing the evaluation model, which causes the evaluation result to be inconsistent with the perception of the human eye. Several color image quality assessment methods. In this embodiment, by combining the visual characteristics of the human eye with the quaternion, an image energy feature conforming to the perception of the human eye is obtained. Experiments show that this embodiment is better than other methods in evaluating color images, and the evaluation results are more consistent with the images perceived by human eyes. The image quality evaluation method of this embodiment will be described in detail below in combination with the experimental results:

Step 1. Construct the mathematical evaluation model of the original reference image and the distorted image to be evaluated by analyzing the visual characteristics of the human eye:

Based on the understanding of the physiological structure of the human visual system, the visual characteristics of the human eye are closely related to how the human eye observes the external environment and images. Because people are the ultimate recipients of the images, the evaluation results must be consistent with what the human eyes actually see. In this embodiment, a corresponding mathematical model is constructed by analyzing the visual characteristics of the human eyes.

The human eye is similar to a convex lens with variable focal length, but it is affected by the complex structure of the human brain, which is different from a general convex lens. Generally, human visual characteristics include fovea characteristics, visual multi-channel characteristics, visual nonlinearity, contrast sensitivity and masking effect. In this embodiment, a mathematical evaluation model is constructed starting from the concave characteristics, visual multi-channel characteristics, and masking effects.

(1) Spatial position function

The central concave characteristic of the human visual system means that when an image appears, the center position information of the image will be observed by the human eye first, especially the position change information of the texture edge near the center of the image, because the human eye is more likely to perceive the edge information of the image .

The human eye will first see the center of the image, and then spread to the surroundings, and the human eyes should treat the points with the same distance from the center as the same. As shown in Figure 2, assuming that the center of the circle O is the center of the image, the distances from the points on the circle to the center of the circle are equal, and the four points A, B, C, and D have the same probability of being observed by human eyes, and E and F are also the same.

This embodiment is based on the literature (CHEN T, WU H R. Space variant median filters for the restoration of impulse noise corrupted images [J]. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 2001, 48 (8): 784- 789.) Mentioned, according to the fovea characteristics of the human visual system, use the exact formula to express how the spatial resolution affects the human eye to observe the image. The specific process is as follows: firstly obtain the RGB tri-stimulus values of the original reference image and the distorted image to be evaluated, then extract the spatial position information of the original reference image and the distorted image to be evaluated, and construct the spatial position function Q of the original reference image and the distorted image to be evaluated respectively _L :

${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula, e _L is the distance from the pixel point (i, j) observed by the human eye to the pixel point (M/2, N/2) in the center of the image divided by the first pixel point (0, 0) of the image The distance from pixels to the center pixel of the image _ec is a constant determined according to test results, and _ec is set to 0.6 in this embodiment after testing.

(2) Texture edge complexity function

The masking effect of the human visual system refers to the phenomenon that can be noticed originally is ignored due to the existence of other phenomena. In different areas, the masking effect of the human visual system can be reflected by their respective weight ratios, which is more consistent with the characteristics of human eyes observing images.

This embodiment extracts the texture feature information and edge feature information of the image, and obtains the texture edge complexity function Q _TE of the image. The larger the Q _TE , the simpler the texture. Larger; on the contrary, the smaller the QTE, the more complex the texture, the easier it is for the human eye to ignore. The specific calculation process is as follows:

First calculate the gradient direction:

Among them, θ(i,j) represents the gradient direction of the pixel point (i,j), and Indicates the horizontal and vertical gradient values of the pixel point (i, j). Use the Sobel edge detection operator to calculate the corresponding image edge feature information, and normalize the edge information, denoted as E(i,j). In the [0,360°) range, the gradient direction is divided into the following areas, as shown in the following formula:

θ(i,j)∈{0°,180°,45°,225°,90°,270°,135°,315°} (3)

Among them, 0° and 180°, 45° and 225°, 90° and 270°, 135° and 315° are respectively symmetrical about the origin, that is, there are 4 different direction areas.

Calculate texture complexity:

Let a ₁ be the number of direction types, that is, the number of types of θ(i,j), and a ₂ be the number of edge points, that is, the number of pixels with E(i,j)=1, and calculate their values respectively. When a ₂ is smaller than the set threshold, a ₂ =0, otherwise a ₂ =1, and the threshold is set to 40 through experimental testing. Therefore, we define the texture complexity function Q _T of a certain pixel point (i, j) in the image as follows:

Borderline complexity:

First define three vectors P=(-1,0,2,0,1), L=(1,4,6,4,1), E=(-1,-2,0,2,1). Among them, P represents the "point" feature descriptor, L represents the "line" feature descriptor, and E represents the "edge" feature descriptor. Using these 3 operators, 6 masks can be obtained: L ^T × E, L ^T × P, E ^T × L, E ^T × P, P ^T × L, P ^T × E. Let the responses of these six masks at a certain pixel point (i,j) in the figure be f _i,j (L ^T ×E), f _i,j (L ^T ×P), f _i,j ( E ^T ×L), f _i,j (E ^T ×P), f _i,j (P ^T ×L), f _i,j (P ^T ×E), then the edge of the pixel (i,j) The complexity is:

${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; =</span>\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

The texture edge complexity function of pixel point (i, j):

Q _TE =Q _T ×Q _E (6)

The larger the calculation result, the weaker the masking effect, the weaker the masking effect, the simpler the texture, the easier it is for the human eye to see clearly, that is, the stronger the visual impact on the human eye.

(3) Local variance

The multi-channel characteristic of the human visual system means that the human eye observes images in different channels. When the resolution is low, only the general outline can be distinguished, while the high resolution can only distinguish the details. The detailed information of the image can be represented by the local variance of the image, so the local variance of the image is used as a means to describe and analyze the content information of the image, and some important structural information of the image can also be summarized by the local variance distribution of the image .

Use Q _V to represent the variance of the local area of the image I centered on the pixel point (i, j), that is, the local variance. In this embodiment, firstly, the original reference image and the distorted image to be evaluated need to be converted from the RGB space to the YUV color space, and the local variance is calculated by using Y (representing brightness) classification. The Y component of the image is divided into non-overlapping blocks by using a sliding window, and the variance of each block is obtained, which is the local variance of the image. For each image block I _i,j , which contains L pixels, use _ηp to represent each pixel inside it, then the local variance can be expressed as:

${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

in, is the mean value of block I _i,j .

Since the size and mode of each sub-block will affect the structure of the image, for the pixel point η _p contained in the I _i,j sub-block, the literature (Z Wang, Z Bovik, et al. Image quality assessment from error measurement to Structural similarity[J].IEEE Transactions on Image Processing.2004,13(4):600-612.) The Gaussian weighting method mentioned to calculate the mean and variance is as follows:

Block mean: $\stackrel{\&OverBar;}{I_{i,j}}=\frac{\underset{p=1}{\overset{L}{\mathrm{\&Sigma;}}}{x}_p{\mathrm{\&eta;}}_p}{\underset{p=1}{\overset{L}{\mathrm{\&Sigma;}}}{\mathrm{\&eta;}}_p}---\left(8\right)$

Block local variance: $Q_V\left(I_{i,j}\right)=\frac{\underset{p=1}{\overset{L}{\mathrm{\&Sigma;}}}{x}_p{({\mathrm{\&eta;}}_p-\stackrel{\&OverBar;}{I_{i,j}})}^2}{\underset{p=1}{\overset{L}{\mathrm{\&Sigma;}}}{x}_p}---\left(9\right).$

In the formula, X _p is the number of pixel points η _p .

(4) Color information

Hue, saturation, and brightness are the three attributes of color, also known as the three elements of color. They are inherent properties of color and are different from each other. Hue and saturation can be represented by chroma. The only characteristic of grayscale images is brightness, while color images also have chrominance characteristics.

Brightness is a physical quantity, which is the human perception of the intensity of light, and reflects the intensity of light (reflection) on the surface of a luminous body (reflector). Hue refers to the overall tendency of the color of the picture in a painting, and it is the largest color effect. Saturation, also known as the purity of the color, refers to the vividness of the color, indicating the proportion of the color components contained in the color. The saturation of the color increases with the increase of the color ratio, which is directly related to the light exposure and the surface structure of the object being photographed. Since hue and saturation can be uniformly represented by chroma, this embodiment uses brightness and chroma to represent essential attributes of color.

The sensitivity of the human visual system to brightness is higher than that to chroma. This embodiment uses the weight method to represent the color information of the image, that is, for different color images, the weight ratios of brightness and chroma are different. The specific calculation The relationship is as follows:

Q _C ＝αQ _L +βQ _U (10)

Among them, Q _L is the brightness information of the image, Q _U is the chrominance information of the image, and α and β are the proportions of brightness and chrominance respectively. According to the experimental results, 1.063 and 0.937 are the best for α and β respectively.

Step 2. Construct the quaternion matrix of the original reference image and the distorted image to be evaluated respectively, and perform singular value decomposition on the quaternion matrix to obtain the singular value eigenvector of the image:

(a) Quaternions

In 1843, the British mathematician WR Hamilton created quaternions. a quaternion Contains 4 parts, 1 real part plus 3 imaginary parts, its basic form is:

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}$

Among them, q _r , q _i , q _j , q _k are four real numbers, the primitive satisfy:

${\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; j</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; j</span>}}\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; j</span>}}\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; j</span>}}\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; j</span>}}$

Quaternion Matrix In the field of real numbers, it can be decomposed into the following form:

$\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; =</span>\left(\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\end{array}\right)$

The singular value decomposition theorem of the quaternion matrix can be expressed as: for any quaternion matrix Q _e(q) = U _(q) Λ'V _(q) x, if rank(A) = r, then there is a quaternion unitary matrices U _(q) and V _(q) such that

Q _(q) = U _(q) ΛV _(q) λ

in,

${\mathrm{<span\; class="notranslate">\; u</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; I</span>}$

$\mathrm{<span\; class="notranslate">\; \&Lambda;</span>}<span\; class="notranslate">\; =</span>{\left(\begin{array}{cccccc}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& & & & & \\ & <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& & & & \\ & & {\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}& & & \\ & & & \mathrm{<span\; class="notranslate">\; 0</span>}& & \\ & & & & <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& \\ & & & & & \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right)}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{\left(\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; \&Lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}& & & \\ & \mathrm{<span\; class="notranslate">\; 0</span>}& & \\ & & <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& \\ & & & \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right)}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}$

And satisfy λ _i ∈ R,|λ ₁ |≥|λ ₂ |≥...≥|λ _r |＞0, λ _i is a non-zero singular value.

(b) Quaternion representation

In this embodiment, the four feature information of the color image obtained from the above analysis are integrated into a quaternion form, as shown below:

Q＝Q _C +Q _L i+Q _TE j+Q _V k (11)

Among them, Q _C is the color information of the image, Q _L is the spatial position information of the image, Q _TE is the texture edge information of the image, and Q _V is the local variance of the image.

In this way, an M×N color image can be regarded as a quaternion matrix, and the singular value eigenvector of the quaternion matrix represents the energy characteristics of the quaternion, so the quaternion matrix obtained from the color image can also be used To represent the energy characteristics of the corresponding color image.

Because a quaternion matrix q=q _r +q _i i+q _j j+q _k k can be represented by its real matrix, so this embodiment transforms Q into its corresponding real matrix form to perform its Singular value decomposition (SVD). Each quaternion matrix can obtain a singular value eigenvector through singular value decomposition, and each element of the eigenvector is a real number greater than 0. It is worth noting that, in view of the fact that the theoretical research on singular value decomposition of quaternion matrix is relatively mature, this embodiment is considered from the perspective of reducing space, and will not be repeated here.

Step 3, using the Euclidean distance between the original reference image and the singular value eigenvector of the distorted image to be evaluated to measure the degree of image distortion:

In this embodiment, the Euclidean distance (EuclideanDistance) of the singular value eigenvectors of the original reference image and the distorted image to be evaluated is used to measure the corresponding image distortion, namely

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span>\sqrt{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

Among them, λ _i and In order to calculate the singular value eigenvector corresponding to the obtained original reference image and the distorted image to be evaluated, K is the minimum value of the number of eigenvalues of the two singular value eigenvectors, that is, the minimum value of the rank of the two quaternion matrices:

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; rank</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; rank</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

The color image quality evaluation method based on HVS and quaternion in this embodiment combines the visual characteristics of the human eye with the quaternion, the evaluation result is more consistent with the effect of the human eye perceiving the image, and improves the traditional split R, G, B The three-channel method ensures the integrity of the color information well, and the extracted image information contains global and local information, so that the evaluation result can more completely represent all the information of the image. Its evaluation result is better than traditional SSIM and several other typical image quality evaluation algorithms. The following will analyze the experimental results of this embodiment from two aspects:

1) the nonlinear fitting of quality evaluation method of the present invention, PSNR, SSIM, MS-SSIM, Y-SVD, GMSD and DMOS value; 2) quality evaluation method of the present invention and PSNR, SSIM, MS-SSIM, Y- SVD, GMSD performance evaluation comparison.

The quality evaluation pictures are the image quality evaluation database Database Release 2 image library provided by the Image and Video Engineering Laboratory (Library for Image and Video Engineering, LIVE) of Texas State University in Austin (TEXAS), a total of 982 images. There are five distortion types: JPEG2000, JPEG, Gaussian white noise, Gaussian blur, and Fast Fading Rayleigh channel distortion. When comparing algorithms, there will be differences in the dimensions and units of each algorithm. Therefore, the objective image quality score obtained by the algorithm to be evaluated is subjected to nonlinear regression. Utilize the Logistic function as the non-linear mapping function to carry out the non-linear regression to the objective image quality original rating that the evaluation algorithm proposed by the present invention draws:

$\mathrm{<span\; class="notranslate">\; QQ</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

Among them, x is the original quality score obtained by the algorithm to be evaluated proposed by the present invention, and α ₁ , α ₂ , α ₃ , α ₄ are parameters for adaptive adjustment in the nonlinear regression process. The indicators of quantitative test evaluation results are MAE/RMSE/CC/SROCC/OR with higher recognition and citations.

1) The mean absolute error (Mean Absolute Error, MAE) between the scores after the subjective and objective nonlinear regression reflects the average error level between the objective quality evaluation results and the subjective evaluation results. The smaller the image quality evaluation results, the higher the accuracy. Define The formula is as follows:

$\mathrm{<span\; class="notranslate">\; MAE</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

2) The root mean square error (Root Mean Square Error, RMSE) between the scores after the subjective and objective nonlinear regression reflects the accuracy of the objective evaluation results. The smaller the value, the higher the accuracy of the image quality evaluation results. The definition formula is as follows:

$\mathrm{<span\; class="notranslate">\; RMSE</span>}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

3) The Pearson linear correlation coefficient (Correlation Coe cient, CC) between the scores after the subjective and objective nonlinear regression reflects the consistency and accuracy of the objective evaluation results. The range of values is [-1,1]. The closer to 1, the better the correlation between subjective and objective evaluation methods. The definition formula is as follows:

$\mathrm{<span\; class="notranslate">\; CC</span>}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</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">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</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">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

4) The Spearman Rank Correlation Coecient (SROCC) between scores after subjective and objective nonlinear regression is a widely used non-parametric statistical analysis method, which reflects the monotonicity of objective quality evaluation results and subjective evaluation results. The value range is [-1,1]. The closer the absolute value of the result is to 1, the better the consistency of the subjective and objective evaluation methods. The definition formula is as follows:

$\mathrm{<span\; class="notranslate">\; SROCC</span>}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\sqrt{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

5) The Outlier Rate (OR) between scores after subjective and objective nonlinear regression reflects the stability and predictability of the objective evaluation model. The value range is [0,1]. The smaller the value, the better the subjective and objective evaluation. The better the consistency, the better the predictability of the evaluation model. The definition formula is as follows:

$\mathrm{<span\; class="notranslate">\; OR</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; out</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

Among them, N is the total number of image databases, that is, 982, x _i and y _i respectively represent the subjective and objective evaluation values of the i-th image after nonlinear regression, u _i and v _i respectively represent the subjective and objective evaluation values of the i-th image in The ranking of all evaluation values in the entire image database, N _out indicates the number of images whose objective evaluation value is greater than twice the standard deviation of the subjective evaluation value.

Figure 3 shows the scatter diagrams of various algorithms and subjective evaluation values DMOS, each point in the figure represents an image, the abscissa of the point is the objective quality evaluation score of the image by the algorithm, and the ordinate is the subjective The DMOS values were evaluated, and the solid line indicates the fitted curve. The closer the scatter points are distributed near the fitting curve, the better the consistency between the algorithm and the subjective evaluation results, and the better the algorithm. It can be seen that the 982 scatter plots of the method provided by the present invention are closest to the fitting curve, indicating that the method proposed by the present invention is better than the other four methods after nonlinear fitting.

Table 1 Performance comparison of image quality evaluation methods in LIVE image database

From the experimental data in Table 1, we found that the quality evaluation method of the present invention is the best among the six evaluation indicators, with the smallest mean absolute error and root mean square error, the highest correlation with subjective visual perception, and the lowest outlier rate. Because the PSNR algorithm does not consider the correlation between each pixel and treats each pixel equally, the overall performance is the worst among the six comparison algorithms. The SSIM algorithm uses the structural information of the image to evaluate the image quality, which is related to the human visual perception mode. Based on the SSIM algorithm, the MS-SSIM algorithm uses multi-resolution analysis technology for multi-scale image quality evaluation, so its performance is better than PSNR and SSIM. The performance of the SVD algorithm that only performs singular value decomposition on the brightness component is significantly better than PSNR, which shows that the algorithm that performs singular value decomposition on images has certain advantages. Visually, the curve fitted by the GMSD algorithm and the DMOS value is the closest to a straight line, but it can be seen that some scattered points are scattered and far away from the curve. It can be seen from the last line of Table 1 that the quality evaluation method of the present invention is significantly better than traditional PSNR algorithm, structural similarity SSIM algorithm, multi-scale structural similarity MS-SSIM algorithm, singular value decomposition algorithm SVD, gradient amplitude similarity The deviation GMSD algorithm shows that the image quality evaluation algorithm based on quaternions and human visual characteristics of the present invention can better reflect the subjective visual experience of human eyes on images.

Since the 982 images are composed of image sub-databases of 5 different distortion types, in order to further prove the superiority of the quality evaluation method of the present invention, this embodiment performs HVS-QSVD algorithm and GMSD algorithm, SSIM respectively for 5 kinds of image sub-databases. Algorithm performance comparison. As shown in Figure 4, each of the three in the figure is a group, which are the nonlinear fitting curves of the HVS-QSVD algorithm, the GMSD algorithm, and the SSIM algorithm, and there are five groups in total. (a) in the first group of Figure 4 to (e) in the fifth group of Figure 4 are the five distortion types of JPEG2000, JPEG, Gaussian white noise, Gaussian blur, and Fast Fading Rayleigh channel distortion. It can be seen that the fitting effect of the HVS-QSVD algorithm provided by the present invention to the subjective evaluation value under different distortion types is better than that of the GMSD and SSIM algorithms.

A color image quality evaluation method based on HVS and quaternion described in Example 1, in order to make the evaluation result more consistent with the perception of the human eye, a mathematical model is constructed using the visual characteristics of the human eye, in order to improve the traditional split R, G, B The three-channel method uses the quaternion singular value decomposition to extract the feature information of the image. Experimental results show that the evaluation results are more consistent with the effect of human eyes perceiving images.

The above schematically describes the present invention and its implementations, but the description is not restrictive. What is shown in the drawings is only one of the implementations of the present invention, and is not actually limited thereto. Therefore, if a person of ordinary skill in the art is inspired by it, without departing from the inventive concept of the present invention, without creatively designing a structural mode and embodiment similar to the technical solution, it shall all belong to the protection scope of the present invention .

Claims (7)

1. A color image quality evaluation method based on HVS and quaternion comprises the following steps:

step one, constructing a mathematical evaluation model of an original reference image and a distorted image to be evaluated by analyzing human visual characteristics, wherein the mathematical evaluation model comprises a spatial position function Q of the image_LLocal variance Q_VTexture edge complexity function Q_TEAnd a color function Q_C；

Step two, Q is added_L、Q_V、Q_TEAs the imaginary part of a quaternion, Q_CAsRespectively constructing quaternion matrixes of an original reference image and a distorted image to be evaluated, and performing singular value decomposition on the quaternion matrixes to obtain singular value eigenvectors of the image;

and step three, measuring the image distortion degree by utilizing Euclidean distances of singular value feature vectors of the original reference image and the distorted image to be evaluated.

2. A HVS and quaternion based color image quality assessment method according to claim 1, characterized by: the specific process of constructing the mathematical evaluation model comprises the following steps:

(1) acquiring RGB tristimulus values of an original reference image and a distorted image to be evaluated;

(2) extracting the spatial position information of the original reference image and the distorted image to be evaluated, and constructing a spatial position function Q_LAnd texture edge complexity function Q_TE；

(3) Converting an original reference image and a distorted image to be evaluated from an RGB space into a YUV color space, extracting image brightness information and constructing a local variance Q_VExtracting image brightness and chroma information to construct color function Q_C。

3. The HVS and quaternion based color image quality assessment method according to claim 2, characterized in that: step one, constructing a spatial position function Q by utilizing the foveal characteristic of the human visual system_LSaid spatial position function

$Q_L(i,j)=\frac{e_c}{e_c+e_L}$

In the formula, e_LThe distance from the pixel point (i, j) for human visual observation to the image center pixel point (M/2, N/2) andquotient of (d); e.g. of the type_cIs a constant.

4. An HVS and quaternion based color image quality assessment method according to claim 2 or 3, characterized in that: step one, constructing a texture edge complexity function Q by utilizing the covering effect of a human visual system_TESaid texture edge complexity function

Q_TE＝Q_T×Q_E

In the formula, Q_TIs the texture complexity function, Q, of the pixel point (i, j)_EIs the edge complexity function of pixel point (i, j).

5. The HVS and quaternion-based color image quality evaluation method according to claim 4, wherein: step one, constructing a local variance Q by using the multichannel characteristics of the human visual system_VThe local variance of

<math> <mrow> <msub> <mi>Q</mi> <mi>V</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>L</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>L</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>&eta;</mi> <mi>p</mi> </msub> <mo>-</mo> <mover> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </math>

Wherein, non-overlapping blocks are divided according to the brightness component of the image to obtain I_i,jL is an image partition I_i,jContains the pixel point eta_pThe number of the (c) is, <math> <mrow> <mover> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mi>L</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>L</mi> </munderover> <msub> <mi>&eta;</mi> <mi>p</mi> </msub> <mo>.</mo> </mrow> </math>

6. the HVS and quaternion based color image quality assessment method according to claim 5, characterized in that: said color function

Q_C＝αQ_L+βQ_U

In the formula, Q_LAs luminance information of the image, Q_UAlpha and beta are the proportion of brightness and chroma respectively, which are the chroma information of the image.

7. The HVS and quaternion based color image quality assessment method according to claim 6, characterized in that: euclidean distance in step three

<math> <mrow> <mi>D</mi> <mo>=</mo> <msqrt> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>&lambda;</mi> <mi>i</mi> </msub> <mo>-</mo> <mover> <msub> <mi>&lambda;</mi> <mi>i</mi> </msub> <mo>^</mo> </mover> <mo>)</mo> </mrow> </msqrt> </mrow> </math>

In the formula, λ_iIs a singular value feature vector of an original reference image,and K is the singular value eigenvector of the distorted image to be evaluated, and is the minimum value of the eigenvalues of the two singular value eigenvectors, namely the minimum value of the two quaternion matrix ranks:

$K=\min (\mathrm{rank}\left(I\right),\mathrm{rank}\left(\hat{I}\right)).$