CN1897634A - Image-quality estimation based on supercomplex singular-value decomposition - Google Patents

Abstract

The method comprises: using super complex number (quaternion) to build a model for color image, which can save the whole information of the color image; using the singular value decomposition of the super complex number to extract the self energy feature of the color image; using the difference between the signaler values in the original image and the distortional image to build the distortion mapping matrix, which is used to evaluate the quality of the color image. The invention can measure the type and level of image distortion so as to accurately evaluate the quality of color image.

Description

A kind of image quality measure method based on the supercomplex singular value decomposition

Technical field

The invention belongs to technical field of image processing, be specifically related to a kind of assessment coloured image (comprising color video frequency image, colour picture) method for evaluating quality.

Background technology

The obtaining of image, compress, digital picture tends to produce a large amount of dissimilar and different stages in storage, transmission and the reproduction process distortion, these distortions will cause the serious decline of picture quality.How picture quality being assessed has accurately become in the image processing field one and has had challenging problem.

In in the past 30 years, a large amount of articles proposes many methods and attempts to address this problem [1].Some article is divided into two classes with the assessment of picture quality: subjective evaluation and objective evaluation [2].Subjective method is subjected to comprising influence of various factors such as environmental condition, motivation and mood, and takes time and effort, costs dearly.The objective evaluation method comprises the bivariate method, as least mean-square error (MSE) or Lp norm [3]-[5], imitate in addition in addition human visual system (HVS) estimate [4] [7]-[20] and draw estimate [19] [21] etc.Some articles have compared the above-mentioned appraisal procedure of mentioning at the compression [13-14] [16] [18] [21] [22] of image, the noise of image and the ambiguity [13] [23] of image, find that the most frequently used objective image quality evaluation MSE is very unreliable, can cause and the correlation of HVS very poor [24].In addition, very complicated based on the algorithm of HVS objective measurement, effect is but unlike MSE, Y-PSNR (PSNR), or RMSE method better [24].

Document [20] is called general image quality index (UQI) method for the objective measurement grayscale image quality has proposed a kind of numerical method.The dynamic range of UQI is [1,1], is to use yi=xi, and i=1,2 ..., optimal value during n is described (wherein xi, yi represents the value of original image picture element and distorted image pixel respectively).Its index model is described any distortion and is made up of correlation loss, three different factors of average distortion and variance distortion.This index is calculated by one 8 * 8 sliding window, obtains the quality figure of image.The quality index of the overall situation is represented with the average of all UQI values among its quality figure.When arbitrary denominator very approaching zero the time, the UQI index unsettled quality assessment result that will bear results.For fear of this problem, this is estimated and is generalized to the space structure similarity and estimates (SSIM) [26].The analysis showed that the UQI index is a kind of special circumstances that SSIM estimates, it is the situation of C1=C2=0 during SSIM estimates.The index of overall importance of similar UQI, its global image mass M SSIM be by calculate SSIM the mean value under fenestrate obtain.Recently document [24] is original image and image block to be assessed, and these pieces are carried out singular value decomposition.By the singular value and then the acquisition picture quality figure of original image and image block to be assessed, the method for a kind of part and global assessment picture quality has been proposed.But this method can only be applied to the gray scale picture, rather than video and coloured image.

At present, the objective evaluation method of color image quality all is the brightness layer information that extracts coloured image by certain conversion, on the basis that half-tone information is handled, thereby coloured image brightness layer information is handled the objective evaluation of realizing color image quality with the objective evaluation method of grayscale image quality.Obviously, this way has been ignored the color information of image, makes it can't make effective judgement for the little impaired coloured image of some distortion factors, can not tell the type of distortion of different impaired coloured images effectively.

Summary of the invention

The objective of the invention is to propose a kind of comparatively intuitive and accurate coloured image (comprising color video frequency image, colour picture etc.) method for evaluating quality,

The color image quality estimating method that the present invention proposes is a kind of color image quality estimating method based on supercomplex (hypercomplex number) singular value decomposition.This method is made up of following five steps: 1. with supercomplex to the coloured image modeling, 2. pair coloured image piecemeal, 3. pair chromatic image piece carries out the supercomplex singular value decomposition, 4. calculated distortion mapping collection of illustrative plates, the 5. description that quantizes of image fault.Each step specific implementation process is as follows:

With supercomplex to the coloured image modeling.

Coloured image is by R (red), G (green), and three components of B (indigo plant) are formed, and can utilize supercomplex to coloured image modeling [31] thus, [32]:

f _(q)(m，n)＝f _R(m，n)i+f _G(m，n)j+f _B(m，n)k (1)

F wherein _R(m, n), f _G(m, n), f _B(m n) represents the R of coloured image respectively, G, and the element of B component, m and n are represented the position of the matrix row and column at pixel place respectively.As seen, a width of cloth coloured image can be expressed as a supercomplex matrix.

2. to the coloured image piecemeal.

Coloured image is carried out piecemeal according to certain rule, for example image is divided into some 8 * 8 fritter.(note, be 8 * 8 fritter in the method with picture breakdown, because in JPEG compression and other image processing are used 8 * 8th, the standard units size, the sliding window size of using in the MSSIM algorithm in addition also is 8 * 8, can certainly be according to taked other piecemeal measure by the processing method of evaluation map picture.); Equally, also can represent each fritter coloured image with a supercomplex matrix.

3. the coloured image piece is carried out the supercomplex singular value decomposition.

Respectively original color image piece and distortion coloured image piece are done the supercomplex singular value decomposition, the singular value that obtains is represented the intrinsic energy feature of coloured image (proof as follows).

4. calculated distortion is shone upon collection of illustrative plates

Calculate each original color image piece singular value σ _iWith its corresponding distortion coloured image piece singular value Between Euclidean distance:

$D_i=\mathrm{sqrt}\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{({\mathrm{\σ}}_i-{\widehat{\mathrm{\σ}}}_i)}^2\right],$

Thereby produce a width of cloth by D _iThe distortion map collection of illustrative plates that constitutes.According to the different characteristics and the variation tendency of these distortion map collection of illustrative plates, can obviously distinguish different type of distortion of coloured image and distortion level.

5. the method that quantizes of image fault

Numerical method is based on a kind of method that graphic method proposes, and it obtains a numerical value of describing image fault at last according to the global error between different type of distortion calculating coloured image singular value difference root mean square:

$M-\mathrm{QSVD}=\frac{\underset{i=1}{\overset{(k/n)\×(k/n)}{\mathrm{\Σ}}}|D_i-D_{\mathrm{mid}}|}{(k/n)\×(k/n)}---\left(3\right)$

D in the formula (3) _MidExpression distortion distance D _iIntermediate value, k is the size of entire image, n is the size of image block.This value of M-QSVD is exactly a description to the image fault situation.

Based on this, this method become a kind of graphically with the method that quantizes and combine, can be accurate, reflect the quality of coloured image intuitively.

Singular value is represented the proof of the intrinsic energy feature of coloured image:

One width of cloth coloured image can be expressed as a supercomplex matrix, and is known again, and the ENERGY E of a matrix A can be with its L ₂Norm is represented.Promptly

E＝‖A‖ ₂ (4)

Then the ENERGY E of coloured image just can be used the L of supercomplex matrix A ₂Norm is represented.

Document ^[30]Verified supercomplex matrix can be made singular value decomposition, according to the definition of supercomplex singular value decomposition ^[27]: for any order is that (order of supercomplex matrix A is r to r, and if only if its complex matrix x _AOrder be 2r) supercomplex matrix A ∈ H ^{N * M}, have two unit supercomplex matrix U, V, (supercomplex unit matrix W ∈ H ^{N * N}Has following character: WW ^T=W ^TW=I _N, I _N∈ R ^{N * N}Be unit matrix.) make:

Wherein subscript "  " is represented conjugate transpose, ∑ _rBe real diagonal matrix, and the value (being the singular value of A) of r non-NULL is arranged.U∈H ^N×N，V∈H ^M×M。

By formula (4) and (5), the ENERGY E of coloured image can be expressed as:

$E={\left|\right|A\left|\right|}_2={\left|\right|U\left(\begin{array}{cc}{\mathrm{\&Sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="A20061002743300192.png,A20061002743300201.png"\; state="\{\{state\}\}">r</figure-callout>}}& 0\\ 0& 0\end{array}\right)V^H\left|\right|}_2={\left|\right|U\left|\right|}_2{\left|\right|\left(\begin{array}{cc}{\mathrm{\&Sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="A20061002743300192.png,A20061002743300201.png"\; state="\{\{state\}\}">r</figure-callout>}}& 0\\ 0& 0\end{array}\right)\left|\right|}_2{\left|\right|V^H\left|\right|}_2=\left|\right|{\left(\begin{array}{cc}{\mathrm{\&Sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="A20061002743300192.png,A20061002743300201.png"\; state="\{\{state\}\}">r</figure-callout>}}& 0\\ 0& 0\end{array}\right)\left|\right|}_2---\left(6\right)$

Because U, V is a unit supercomplex matrix, so its L ₂Norm is 1, from (6) formula as can be seen, the energy of coloured image can be fully by the singular value L of supercomplex matrix ₂Norm represents that in other words, the singular value of supercomplex matrix has been represented the energy feature of coloured image, can be used as the standard of weighing color image quality, and this provides theoretical foundation for the color image quality estimating algorithm that we propose.

Hypercomplex singular value decomposition (QSVD):

Known QSVD can also be written as except the form of being write as (5) formula

Wherein Represent supercomplex to shift adjoint operator, u _nBe the column vector of left singular matrix, v _nColumn vector for right singular matrix.σ _nBe real singular value.Can be according to the supercomplex matrix H ^N*MWith complex matrix C ^{2N * 2M}. relation to extrapolate the algorithm of QSVD as follows:

The singular value of supercomplex matrix A can be by the supercomplex adjoint matrix) x _ASingular value (SVD) decompose and to obtain.Complex matrix x _ASVD be decomposed into: $x_A=U^{x_A}\left(\begin{array}{cc}{\mathrm{\&Sigma;}}_{2\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="A20061002743300192.png,A20061002743300201.png"\; state="\{\{state\}\}">r</figure-callout>}}& 0\\ 0& 0\end{array}\right){\left(V^{x_A}\right)}^H=\underset{n^{\&prime;}=1}{\overset{2r}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_{n^{\&prime;}}{u_{n^{\&prime;}}}^{x_A}{\left({v_{n^{\&prime;}}}^{x_A}\right)}^H,$ U wherein ^XA∈ C ^2N, V ^XA∈ C ^2M, u _{N '}Be the column vector of left singular matrix, v _{N '}Column vector for right singular matrix.σ _{N '}Be real singular value.And

${u_{n^{\&prime;}}}^{x_A}=\left[\begin{array}{c}{u_{n^{\&prime;}}}^{x_A\&prime;}\\ -{\left({u_{n^{\&prime;}}}^{x_A\&prime;\&prime;}\right)}^{*}\end{array}\right],{v_{n^{\&prime;}}}^{x_A}=\left[\begin{array}{c}{v_{n^{\&prime;}}}^{x_A\&prime;}\\ -{\left({v_{n^{\&prime;}}}^{x_A\&prime;\&prime;}\right)}^{*}\end{array}\right],$ ${u_{n^{\&prime;}}}^{x_A}\&Element;C^{2N}({u_{n^{\&prime;}}}^{x_A\&prime;}\&Element;C^N,{u_{n^{\&prime;}}}^{x_A\&prime;\&prime;}\&Element;C^N),$

${v_{n^{\&prime;}}}^{x_A}\&Element;C^{2N}({v_{n^{\&prime;}}}^{x_A\&prime;}\&Element;C^N,{v_{n^{\&prime;}}}^{x_A\&prime;\&prime;}\&Element;C^N),$ ${\mathrm{\&Sigma;}}_{2r}=\mathrm{diag}({\mathrm{\&sigma;}}_1;{\mathrm{\&sigma;}}_1;{\mathrm{\&sigma;}}_2;{\mathrm{\&sigma;}}_2;\&CenterDot;\&CenterDot;\&CenterDot;{\mathrm{\&sigma;}}_r;{\mathrm{\&sigma;}}_r).$

So can be from complex matrix x _A∈ C ^{2N * 2M}The SVD decomposition amount in recover supercomplex matrix A ∈ H ^{N * M}Singular value.But its QSVD algorithm brief summary is as follows:

(1) calculated complex matrix x _ASingular value decomposition (SVD);

(2) supercomplex singular value diagonal matrix sigma _rValue and plural singular value diagonal matrix sigma _2rThe pass of value is: n '=2n-1:

(3) supercomplex matrix A n is listed as right singular vector (left singular vector) and complex matrix x _AIt is n '=2n-1 that right singular vector (left singular vector) closes, and

$u_n={u_{n^{\&prime;}}}^{x_A\&prime;}+{u_{n^{\&prime;}}}^{x_A\&prime;\&prime;}j$

$v_n={v_{n^{\&prime;}}}^{x_A\&prime;}+{v_{n^{\&prime;}}}^{x_A\&prime;\&prime;}j$

The SVD that this shows N * M supercomplex matrix decomposes with the SVD decomposition of 2N * 2M complex matrix equivalent.

This method not only can be judged the image fault grade, can also judge different type of distortion, thereby color image quality is made objective and accurate assessment.This is a kind ofly brand-new will be graphical to combine, predict evaluation measure and method by the color image quality problem of various noises introducing distortions with quantizing.This method not only can be judged the image fault grade, can also judge different type of distortion, thereby color image quality is made objective and accurate assessment.

Description of drawings

Fig. 1 is Lena, Baboon, Peppers, Girl, Airplane and six original images of Goldhill.

Fig. 2 is the Lena distorted image set of different type of distortion (JPEG, G..blur, G..noise, Sharpening and DC-shifting), different stage (I level, II level, III level, IV level, V level).

Fig. 3 is the distortion map collection of illustrative plates of Lena distorted image with respect to original image.

Fig. 4 is different distortion type JPEG, G..blur, G..noise, Sharpening and DC-shifting), the set of the Baboon distorted image of different stage (I level, II level, III level, IV level, V level).

Fig. 5 is the distortion map collection of illustrative plates of Baboon distorted image with respect to original image.

Fig. 6 is the distortion map collection of illustrative plates after SVD method and QSVD method are handled through DC-shifting respectively.

Fig. 7 is the distortion map collection of illustrative plates after SVD method and QSVD method are handled through G.noise respectively.

Fig. 8 is the distortion map collection of illustrative plates after SVD method and QSVD method are handled through dissimilar distortions.

Fig. 9 is applied to comparative result in the Lena image for utilizing " average comparison method " with various appraisal procedures.

Figure 10 is applied to comparative result in the Baboon image for utilizing " brightness layer comparison method " with various appraisal procedures.

Embodiment

Utilize the inventive method respectively to six test patterns (Lena (Li Na), Baboon (baboon Buddha), Peppers (capsicum), Girl (girl), Airplane (aircraft), and Goldhill (Kingsoft) image is as shown in Figure 1) handle, produce five kinds of different type of distortion: JPEG compressions, Gaussian blur (Gaussian Blur), Gaussian noise (Gaussian noise), Sharpening (sharpening), and DC-shifting (pixel translation), and every kind of type of distortion has comprised five different specified distortion level.Test result shows, (as MSE, PSNR and MSSIM etc.) compares with the objective evaluation method of at present known color image quality, and this method performance is more excellent.

With Lena and Baboon image is example, at first Lena and baboon image is carried out dissimilarly, and the distortion of different stage is handled, and is as shown in table 1.

JPEG represents the image through the compression of JPEG method in the table 1, and image (add respectively on R, G and B component and have mutually homoscedastic Gaussian noise), DC-shifting that G.noise has represented to add Gaussian noise are illustrated in the numerical value that adds equivalent on R, G, each picture element of B component.They are all handled by MATLAB and obtain, and G.blur represents the image after the image through the Gaussian Blur processing, Sharpening are represented the process sharpening, and these two kinds of type of distortion are finished dealing with at AdobePhotoshop7.0.The parametric representation image compression rate that JPEG is capable in the table 1; The parametric representation Gaussian noise variance that G.noise is capable; The value that each picture element of parametric representation that DC-shifting is capable is added; The parameter that G.blur and Sharpening are capable then is that the parameter adjustment according to Adobe Photoshop7.0 gets, the radius of the fuzzy or sharpening of representative, and unit is a pixel.

Table 1 image fault type and level of distortion

The type of distortion rank	The I level	The II level	The III level	The IV level	The V level
						JPEG	10∶1	30∶1	50∶1	70∶1	90∶1
G.blur	0.3	0.6	0.9	1.2	1.5
						G.noise	3	6	9	12	15
Sharpening	0.3	0.6	0.9	1.2	1.5
						DC-shifting	2	4	6	8	10

Now original color image and the coloured image of introducing various distortions are carried out piecemeal respectively and handle, every width of cloth image is divided into 64 * 64 fritters by 8 * 8 size.Utilize the supercomplex matrix that each piece image is carried out modeling, calculate the singular value of every block of image, and obtain the singular value difference root mean square on original color image piece and the distortion chromatic image piece correspondence position, i.e. D in the formula (2) with the method for QSVD _iProduce a secondary size thus and be 64 * 64 distortion map collection of illustrative plates.

According to the different characteristics and the variation tendency of these distortion map collection of illustrative plates, can obviously distinguish different type of distortion of coloured image and distortion level.Its result such as Fig. 2～shown in Figure 5, wherein Fig. 2 is the distorted image set of the dissimilar different stages of Lena image, Fig. 3 is the distortion map collection of illustrative plates of every width of cloth distortion lena image with respect to original image; Fig. 4 is the distorted image set of Baboon image at dissimilar different stages, and Fig. 5 is the distortion map collection of illustrative plates of every width of cloth distortion baboon image with respect to original image.

From the corresponding relation of Fig. 2 to Fig. 5 two picture group image distortions mappings collection of illustrative plates and the image of different type of distortion and level of distortion as can be seen,

JPEG: along with the increase of level of distortion, image pane shape degree is more and more serious.It is apparent in view that this phenomenon is from compression ratio that 30:1 just begins.

G.blur: such distortion obviously shows edge and high-frequency region, can produce comparatively serious blooming.Along with the intensification of fog-level, the distortion profile of edge and high frequency can be more and more obvious.

G.noise: such distortion is that visible noise is uniformly distributed on the entire image, and at high frequency, the zone of low frequency and texture obviously as seen.

Sharpening: such distortion makes veined part of image and high-frequency region sharp-pointed more and obvious, and does not have obvious noise at low frequency region.

DC-shifting: if a definite value is added on each picture element, image can evenly brighten so, on the contrary then evenly deepening.

Like this, just can from the distortion map collection of illustrative plates, distinguish type of distortion, and then distinguish that in the middle of same type of distortion different level of distortion is just relatively easy according to the different characteristics of different type of distortion.

Document is mentioned in [24], the monochrome information of coloured image can be extracted, and directly image brightness is carried out SVD then and decomposes, and so also can obtain the distortion map collection of illustrative plates corresponding to the standard coloured image.Here be that 512 * 512 Lena and Baboon coloured image are example with size equally: at first, we use document respectively ^[24]In method and the QSVD method mentioned the coloured image of certain distortion type is handled.Fig. 6 has provided lena and the distortion map contrast collection of illustrative plates of baboon image after handling through DC-shifting with two kinds of methods respectively, and Fig. 7 has then provided lena and the distortion map contrast collection of illustrative plates of baboon image after handling through G.noise with two kinds of methods respectively.

From Fig. 6, Fig. 7, can obviously find out, adopt the SVD method that the monochrome information that extracts from coloured image is handled, can't show the image fault degree intuitively and accurately to such an extent as to lost a lot of information, and adopt after the QSVD method, the distortion map collection of illustrative plates has obtained obvious improvement, can the same type of distortion of clear resolution in different specified distortion level.

Below, we select width of cloth distorted image a: JPEG (70:1), G.blur (0.3), G.noise (9), Sharpening (0.2), DC-shifting (6) more respectively in every kind of type of distortion; Calculate the distortion map collection of illustrative plates of distorted image with QSVD method and SVD method respectively then corresponding to standard picture, as shown in Figure 8:

From Fig. 8, can obviously find out, for the lower image of specified distortion level, the distortion map collection of illustrative plates that utilizes QSVD to make can reflect the distortion information that gray scale SVD method can't be reacted, this shows that the amount of information that QSVD method result carries is more complete, so its judgement that picture quality is made is more reliable.

The method that quantizes test result

Now, we are with basis $M-\mathrm{QSVD}=\frac{\underset{i=1}{\overset{(k/n)\&times;(k/n)}{\mathrm{\&Sigma;}}}|D_i-D_{\mathrm{mid}}|}{(k/n)\&times;(k/n)}$ Obtain the method that quantizes of coloured image distortion situation description and traditional MSE, PSNR and MSSIM method compare.

We test comparison from two angles to these methods: one, consider to calculate respectively R, G, MSE on three monochromatic component of B, PSNR, and MSSIM, do the numerical value that on average obtains final numerical value and record then and compare (in following test process, being called " three look average comparison methods ") with the M-QSVD method; They are two years old, adopt traditional color image quality estimating method, the brightness layer information that is about to coloured image extracts, the MSE that handles with gray level image then, PSNR, and the MSSIM method handles this brightness layer information, and the numerical value that obtains compares with the numerical value that records with the M-QSVD method again.(in following test process, being called " brightness layer comparison method ")

At first, we use the thinking of " three look average comparison methods " respectively to four kinds of method MSE, PSNR, the image quality measure numerical value that the M-QSVD of MSSIM and proposition calculates is made comparative analysis, Fig. 9 has provided the distorted image of the dissimilar different stages of Lena image, reaches the numerical value that calculated in various ways obtains.INF among Fig. 9 a represents infinitely-great value:

According to the definition of distinct methods, we can know: for the MSE method, its numerical value is more little, shows that the image fault degree is low more, and picture quality is good more; For the PSNR method, numerical value is big more, and picture quality is good more; Also be that numerical value is big more for the MSSIM method, picture quality is good more; And for M-QSVD, numerical value is more little, and picture quality is good more.

From Fig. 9, we are not difficult to find by subjective judgement: Fig. 9 (b) plot quality is obviously poor than Fig. 9 (c) figure, but can find that from the result of calculation of MS (E) its MSE numerical value is 11.25 among Fig. 9 (b), and in Fig. 9 (c), be 146, conclusion according to MSE is that Fig. 9 (b) plot quality is better than Fig. 9 (c) figure far away, obviously with the subjective judgement that is not inconsistent us.And the numerical value that is obtained by M-QSVD calculating chart 9 (b) and Fig. 9 (c) is respectively 91.68 and 4.07, shows it is that the quality of Fig. 9 (c) is much better than Fig. 9 (b) according to the conclusion of M-QSVD, and this conclusion conforms to our subjective assessment result.

The numerical value of the PSNR of Fig. 9 (c) and Fig. 9 (e) does not almost have difference, and promptly the conclusion of differentiating according to the numerical value of PSNR is that this two width of cloth picture quality should be consistent; And being Fig. 9 (c) picture quality, our subjective conclusion is better than Fig. 9 (e).The numerical value of the M-QSVD of this two width of cloth image that shows in the comparison diagram 9, the numerical value of M-QSVD that can find Fig. 9 (c) is much smaller than the numerical value of the M-QSVD of Fig. 9 (e).This conclusion key diagram 9 (c) picture quality is better than Fig. 9 (e) picture quality, meets the subjective assessment result.

The MSSIM numerical value that Fig. 9 (d) calculating shows is less than the numerical value of Fig. 9 (e), according to conclusion key diagram 9 (d) picture quality of MSSIM than Fig. 9 (e) poor image quality, obviously with the subjective judgement that is not inconsistent us, then key diagram 9 (d) picture quality is better than Fig. 9 (e) image for the M-QSVD numerical value that Fig. 9 (d) and Fig. 9 (e) calculating show, the result conforms to subjective assessment.

Equally according to the thinking of this " three look average comparison methods ", we handle at the distorted image of dissimilar different stages the Baboon image with four kinds of methods respectively, analysis by numerical value that four kinds of methods are obtained, we also can obtain similar result, promptly under " thinkings of three look average comparison methods ", the M-QSVD method that proposes compares to MSE, and PSNR and MSSIM method meet the human eye subjective visual evaluation more.

Next, we use the thinking of " brightness layer comparison method " respectively to four kinds of method MSE, PSNR, the image quality measure numerical value that the M-QSVD of MSSIM and proposition calculates is made comparative analysis, Figure 10 has provided the distorted image of the dissimilar different stages of Baboon image, reaches the numerical value that calculated in various ways obtains.INF among Figure 10 (a) represents infinitely-great value:

From Figure 10, we are not difficult to find by subjective judgement: the quality of Figure 10 (c) is obviously good than Figure 10 (e) figure, but can find that from the result of calculation of MSE its MSE numerical value is 675.86 among Figure 10 (c), and in Figure 10 (e), be 661.54, according to the conclusion of MSE is that the quality of Figure 10 (e) is better than Figure 10 (c), obviously and our subjective judgement be not inconsistent.And calculate the numerical value that Figure 10 (c) and Figure 10 (e) obtain by M-QSVD is respectively 7.89 and 97.26, shows it is that the quality of Figure 10 (c) is much better than Figure 10 (e) according to the conclusion of M-QSVD, and this conclusion conforms to the subjective assessment result.

The numerical value of the PSNR of Figure 10 (d) and Figure 10 (f) does not almost have difference, and promptly the conclusion of differentiating according to the numerical value of PSNR is that this two width of cloth picture quality should be consistent; And being Figure 10 (d) picture quality, our subjective conclusion is better than Figure 10 (f).The numerical value of the M-QSVD of this two width of cloth image that shows among Figure 10 relatively, the numerical value of M-QSVD that can find Figure 10 (d) is much smaller than the numerical value of the M-QSVD of Figure 10 (f).This conclusion explanation Figure 10 (d) picture quality is better than Figure 10 (f) picture quality, meets the subjective assessment result.

The MSSIM numerical value that Figure 10 b calculating shows is less than the numerical value of Figure 10 (f), conclusion according to MSSIM illustrates that Figure 10 (b) picture quality is than Figure 10 ((f)) poor image quality, obviously with the subjective judgement that is not inconsistent us, Figure 10 (b) and Figure 10 (f) calculate the M-QSVD numerical value that shows and illustrate that then Figure 10 (b) picture quality is better than Figure 10 (f) image, and the result conforms to subjective assessment.

Equally according to the thinking of this " brightness layer comparison method ", we handle at the distorted image of dissimilar different stages the lena image with four kinds of methods respectively, analysis by numerical value that four kinds of methods are obtained, we also can obtain similar result, promptly under " thinking of brightness layer comparison method ", the M-QSVD method that proposes compares to MSE, and PSNR and MSSIM method meet the human eye subjective visual evaluation more.

We have carried out a large amount of tests according to the image of Fig. 1 under various distortion situations, its result and The above results are similar.Because be subjected to the restriction of article length, we do not list whole results.Our conclusion is: no matter under which kind of situation, the M-QSVD method of proposition compares to MSE, and PSNR and MSSIM method all meet the human eye subjective visual evaluation more.The QSVD method is applied to the height that color image quality estimating can reflect picture quality more objective, exactly, and its patterned method makes the evaluation process simple, intuitive more that becomes, and its assessment result that quantizes is also more identical with human subjective assessment result.

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Claims (3)

1, a kind of color image quality estimating method based on the supercomplex singular value decomposition is characterized in that concrete steps are as follows:

(1) with supercomplex to the coloured image modeling:

Coloured image is made up of R, G, three components of B, utilizes supercomplex that coloured image is expressed as a supercomplex matrix:

f _(q)(m，n)＝f _R(m，n)i+f _G(m，n)j+f _B(m，n)k (1)

F wherein _R(m, n), f _G(m, n), f _B(m n) represents the R of coloured image respectively, G, and the element of B component, m and n are represented the position of the matrix row and column at pixel place respectively, and R is red here, and G is green, and B is blue;

(2) with the coloured image piecemeal:

Coloured image is carried out piecemeal according to certain rule, each fritter coloured image is also represented with a supercomplex matrix;

(3) the coloured image piece is carried out the supercomplex singular value decomposition:

Respectively original color image piece and distortion coloured image piece are done the supercomplex singular value decomposition, the singular value that obtains is represented the intrinsic energy feature of coloured image;

(4) calculated distortion mapping collection of illustrative plates:

Calculate each original color image piece singular value σ _iWith its corresponding distortion coloured image piece singular value Between Euclidean distance:

$D_i=\mathrm{sqrt}\left[\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{({\mathrm{\&sigma;}}_i-{\widehat{\mathrm{\&sigma;}}}_i)}^2\right]---\left(2\right)$

Thereby produce a width of cloth by D _iThe distortion map collection of illustrative plates that constitutes according to the different characteristics and the variation tendency of these distortion map collection of illustrative plates, is distinguished different type of distortion of coloured image and distortion level;

(5) description that quantizes of image fault:

Global error according between different type of distortion calculating coloured image singular value difference root mean square obtains a numerical value of describing image fault at last:

$M-\mathrm{QSVD}=\frac{\underset{i=1}{\overset{(k/n)\&times;(k/n)}{\mathrm{\&Sigma;}}}|D_i-D_{\mathrm{mid}}|}{(k/n)\&times;(k/n)}---\left(3\right)$

D in the formula (3) _MidExpression distortion distance D _iIntermediate value, k is the size of entire image, n is the size of image block.

2, the appraisal procedure based on the supercomplex singular value decomposition according to claim 1 is characterized in that describedly to the coloured image piecemeal, is to be divided into 8 * 8 fritter.

3, the appraisal procedure based on the supercomplex singular value decomposition according to claim 2 is characterized in that the type of distortion of described image is divided into JPEG compression, Gaussian Blur, Gaussian noise, five kinds of sharpening and pixel translations.

Images