CN103208100B - Blurred kernel inversion method for blurred retouching images based on blurred deformation Riemann measure - Google Patents

Abstract

The invention discloses a blurred kernel inversion method for blurred retouching images based on blurred deformation Riemann measure and belongs to the technical field of digital image trusted authentication. Isometries before and after image blurring of logarithm Fourier domains are used, and blurred kernels are recovered from the blurred irrelevant amount before and after the image blurring through Riemann geodesic distance. According to the blurred kernel inversion method, Gaussian blur kernels can be recovered effectively and accurately from the blurred retouching images, the recovered Gaussian blur kernels can be used for manufacturing blurred images from source images and identifying whether the images are subjected to blurred retouching, and the method can be further used for recovering 'clean' images from the blurred images.

Description

The image blurring core inversion method of fuzzy retouching of estimating based on fuzzy indeformable Riemann

Technical field

The invention discloses the image blurring core inversion method of a kind of fuzzy retouching of estimating based on fuzzy indeformable Riemann, belong to digital picture authentic authentication technical field.

Background technology

Along with the fast development of Image Acquisition and picture editting's technology, digital picture has incorporated modern people's life, utilizes image editing software can be easily existing image such as to be retouched, synthesize at the editing operation, produces pleasing picture.These are edited exquisite image and are used for internet, Digital Media document, social media etc., are expressing individual character, are beautifying mediaspace and enrich the aspects such as people's spiritual exchange field and bringing into play irreplaceable effect.Meanwhile, be used to the aspects such as advertisement, media, internet through editor's image, gain public trust by cheating, reduced the public credibility of people to Digital Media, causing trust crisis.Therefore, it is very urgent that research digital picture is forged detection, studies especially quantitatively image forge detection and have more major and immediate significance.

Image blurring noise and editor's generation from obtaining equipment, or the display quality of imaged image, or in order to retouch editing trace, be the research emphasis of image processing and computer graphics always.Image blurring retouching is carried out convolution algorithm to eliminate noise, weaken details, to manufacture special efficacy etc. by image and fuzzy operator, is important inpainting operation.The types such as image blurring retouching comprises Gaussian Blur, average is fuzzy, boxlike is fuzzy, motion blur.The fuzzy part existing in image is in the passive generation of acquisition process, and also having part is initiatively to retouch generation in order to reach content consistency.The key of image deblurring is to recover fuzzy core from blurred picture.Classic method utilization has or prior imformation is carried out image deblurring and deconvoluted by methods such as energy minimization, partial differential equation, Markov fields, and the Given information entropy providing is provided deblurring effect.Image deblurring problem is not still outstanding issue.

Summary of the invention

Technical matters to be solved by this invention is to overcome the deficiencies in the prior art, provide a kind of fuzzy retouching of estimating based on fuzzy indeformable Riemann image blurring core inversion method, utilize the image blurring forward and backward isometry that meets of logarithm Fourier domain, adopt the image blurring forward and backward fuzzy invariant of Riemann's geodesic distance tolerance, can inverting obtain Gaussian Blur kernel function, thereby provide solid foundation for the qualification of image deblurring and image forge.

The present invention specifically solves the problems of the technologies described above by the following technical solutions:

The image blurring core inversion method of fuzzy retouching of estimating based on fuzzy indeformable Riemann, described fuzzy retouching image is obtained through Fuzzy Processing by source images, and the method comprises the following steps:

Steps A, by source images I and fuzzy retouching image I _blurbe converted into respectively logarithm Fourier, the source images after conversion and fuzzy retouching image be designated as respectively into with

Step B, calculate respectively and the Riemann's geodesic distance between vector of unit length v ; The expression formula of described vector of unit length v is as follows:

$v=-\frac{2\mathrm{\π}}{\sqrt{3}}{\mathrm{\ξ}}^2,$

In formula, ξ represents logarithm Fourier transform frequency;

Step C, calculate the Gaussian Blur core δ of described Fuzzy Processing according to following formula:

$\mathrm{\δ}=\frac{2}{\sqrt{3}}\left|\left(Q\right[\tilde{I}]-Q[{\tilde{I}}_{\mathrm{blur}}\left]\right)\right|.$

Described by source images I and fuzzy retouching image I _blurbe converted into respectively logarithm Fourier, specifically in accordance with the following methods:

First to source images I and fuzzy retouching image I _blurcarry out respectively Fourier transform, obtain respectively with ; For the image after Fourier transform with , first carry out following processing: if its real part is zero, its real part is replaced to one and be greater than zero infinitesimal real number; Then to after treatment with , ask for respectively the natural logarithm of its mould, obtain being converted into source images and the fuzzy retouching image of logarithm Fourier, be designated as respectively with .

The fuzzy core inversion method of fuzzy retouching image that the present invention proposes, utilizes the image blurring forward and backward isometry of logarithm Fourier domain, recovers fuzzy core by Riemann's geodesic distance from image blurring forward and backward fuzzy irrelevant amount.The inventive method can effectively and exactly recover Gaussian Blur core from fuzzy retouching image, and the Gaussian Blur core recovering can either be used for manufacturing blurred picture from source images, and whether qualification image is by fuzzy retouching; Can be used in again from blurred picture and recover " totally " image.

Brief description of the drawings

Fig. 1 is logarithm fourier space function track and normal trajectories schematic diagram thereof;

Fig. 2 is the inventive method schematic flow sheet;

Fig. 3 is that the Gaussian Blur of actual use is retouched the difference between core and the Gaussian Blur core of the inventive method inverting.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is elaborated:

Image is as a kind of 2D signal, and it can represent at multiple transform domains, for example frequency domain (Fourier transform), Laplace domain etc.Gaussian Blur essence is image filtering, uses gaussian kernel function (normal distribution) to calculate fuzzy matrix, and uses fuzzy matrix and source images to carry out convolution algorithm, carries out fuzzy.Fuzzy operation can be expressed as the convolution of source images I (x, y) and Gaussian Blur kernel function G (x, y, δ) in time domain, be shown below.

$I_{\mathrm{blur}}(x,y)=I(x,y)*G(x,y,\mathrm{\δ})$

In formula δ is at the standard deviation of gaussian kernel normal distribution (referred to as Gaussian Blur core), I _blur(x, y) is fuzzy retouching image, and * is convolution algorithm.

If f is R → R function, R is real number field, K _δfor convolution kernel function k _δmeet normalization character, i.e. ∫ K _δ(x) d δ=1.If * is convolution operator, K _δto the convolution operation of f suc as formula shown in (1).

$(f,K_{\mathrm{\δ}})\left(x\right)={\∫}_{-\∞}^{\∞}f\left(y\right)K_{\mathrm{\δ}}(x-y)\mathrm{dy}---\left(1\right)$

From formula (1), thereby convolution kernel K _δform half group space R of an isomorphism ₊.R ₊in all convolution kernels produce a convolution track [f]={ (f, K after acting on f _δ) | δ ∈ R ₊.

If for the Fourier transform of f, K _δfourier transform be .

${\hat{K}}_{\mathrm{\δ}}\left(\mathrm{\ξ}\right)=\frac{1}{\mathrm{\δ}}{\∫}_{-\∞}^{\∞}{e}^{-\mathrm{\π}{x}^2/\mathrm{\δ}}{e}^{-\mathrm{ix\ξ}}\mathrm{dx}=\frac{1}{\mathrm{\δ}}{K}_{{\mathrm{\δ}}^{-1}}\left(\mathrm{\ξ}\right)$

Spatial domain convolution operation f*K _δbe converted at frequency domain with product .Convolution shows as the property taken advantage of operation at frequency domain, convolution can be converted to additivity operation by getting further logarithm operation.

$(\hat{f},{\hat{K}}_{\mathrm{\δ}})\left(\mathrm{\ξ}\right)=\hat{f}\·{\hat{K}}_{\mathrm{\δ}}---\left(2\right)$

If f ₁, f ₂for any two signals, with be respectively f ₁and f ₂with core convolution, in logarithm fourier space, with between Riemann's geodesic distance be calculated as follows shown in.

$\left|\right|{\tilde{f}}_1^{/}-{\tilde{f}}_2^{/}\left|\right|=\left|\right|({\tilde{f}}_1-{\mathrm{\δ}}_0\mathrm{\π}{\mathrm{\ξ}}^2)-({\tilde{f}}_2-{\mathrm{\δ}}_0\mathrm{\π}{\mathrm{\ξ}}^2)\left|\right|=\left|\right|{\tilde{f}}_1-{\tilde{f}}_2\left|\right|---\left(3\right)$

for the logarithm Fourier transform of signal f.After above formula explanation logarithm fourier space convolution, the forward and backward Riemann's geodesic distance of any two signal convolution equates, not affected by convolution; Show that logarithm fourier space Riemann geodesic distance can be used as the tolerance that measures convolution signal.

In logarithm fourier space, f and f _briemann's geodesic distance suc as formula shown in (4).

$\left|\right|\tilde{f}-{\tilde{f}}_b\left|\right|=\left|\right|\tilde{f}-(\tilde{f}-\mathrm{\π\δ}{\mathrm{\ξ}}^2)\left|\right|=\left|\right|\mathrm{\π\δ}{\mathrm{\ξ}}^2\left|\right|---\left(4\right)$

F refers to original signal, f _brefer to Gaussian Blur signal.Norm in formula adopts index Riemann metric to calculate.

Along side-play amount π ξ ²the vector of unit length of trajectory direction is:

$v=\frac{-\mathrm{\π}{\mathrm{\ξ}}^2}{\sqrt{\⟨\mathrm{\π}{\mathrm{\ξ}}^2,\mathrm{\π}{\mathrm{\ξ}}^2\⟩}}=\frac{-{\mathrm{\ξ}}^2}{\sqrt{\∫{\mathrm{\ξ}}^4{e}^{-\mathrm{\π}{\mathrm{\ξ}}^2}\mathrm{d\ξ}}}=-\frac{2\mathrm{\π}}{\sqrt{3}}{\mathrm{\ξ}}^2;$

True origin with the vector of upper any point .As shown in Figure 1, in logarithm fourier space, track and side-play amount π ξ ²track to meet isometry constraint, must make function vertically ; Whole on trace, $Q\left(\tilde{f}\right)=\⟨\⟨\tilde{f},v\⟩\⟩.$

In Fig. 1, trace-π ξ ²it is δ=1 o'clock convolution kernel represent trace corresponding to convolution kernel that δ is different.Correspondingly, each K _δcorresponding difference, there is unique definite solution.In the situation that δ is definite, edge motion, there will be be greater than, equal and be less than 03 kinds of situations. be greater than the minus cut off value of zero-sum and be required δ.

Edge motion f and K _δdependence can be by unified formula express, wherein due to function integral form function, so $Q(\tilde{f}-\widetilde{\mathrm{\δ}}\mathrm{\π}{\mathrm{\ξ}}^2)=Q\left(\tilde{f}\right)+\widetilde{\mathrm{\δ}}Q\left(\mathrm{\π}{\mathrm{\ξ}}^2\right)=C.$ Q (π ξ ²) in the integrated value in R territory be , therefore formula (5) is set up.

$Q\left(\tilde{f}\right)+\widetilde{\mathrm{\δ}}\frac{\sqrt{3}}{2}=C---\left(5\right)$

Obtain from formula (5) .The C of formula (5) can use the convolution f of f _bquantization function replace.

According to above analysis, can obtain the image blurring core inversion method of the fuzzy retouching of estimating based on fuzzy indeformable Riemann of the present invention, specific as follows:

Steps A, in accordance with the following methods by source images I and fuzzy retouching image I _blurbe converted into respectively logarithm Fourier:

First to source images I and fuzzy retouching image I _blurcarry out respectively Fourier transform, obtain respectively with ; For the image after Fourier transform with , first carry out following processing: if its real part is zero, its real part is replaced to one and be greater than zero infinitesimal real number; Then to after treatment with , ask for respectively the natural logarithm of its mould (being square root sum square of real part and imaginary part), obtain being converted into source images and the fuzzy retouching image of logarithm Fourier, be designated as respectively with ;

Step B, calculate respectively and the Riemann's geodesic distance between vector of unit length v ; The expression formula of described vector of unit length v is as follows:

$v=-\frac{2\mathrm{\π}}{\sqrt{3}}{\mathrm{\ξ}}^2,$

In formula, ξ represents logarithm Fourier transform frequency;

Step C, calculate the Gaussian Blur core δ of described Fuzzy Processing according to following formula:

$\mathrm{\δ}=\frac{2}{\sqrt{3}}\left|(Q\[\tilde{I}\]-Q\[{\tilde{I}}_{\mathrm{blur}}\])\right|.$

In order to verify effect of the present invention, utilize the fuzzy retouching core of the inventive method inversion chart picture and then fuzzy retouching forged to image and detect.Under MATLAB2010 environment, realize fuzzy retouching inversion algorithm of the present invention.Experimental Hardware platform is: four core I7 processors, 8G internal memory.Image source data are from CASIA image set, and picture size is 384 × 256.

The fuzzy retouching image using in experiment is edited generation by convolution function function and the image editing software PHOTOSHOP of MATLAB.

Specific experiment method is as follows:

Use the different source images of 4 width, in Gaussian Blur core δ=0.4, δ=0.6, δ=0.8 and δ=1.0 situation, source images is carried out to Gaussian Blur retouching respectively, and adopt the inventive method to carry out inverting to Gaussian Blur core.Fig. 3 has shown the difference between Gaussian Blur retouching core and the Gaussian Blur core of the inventive method inverting of actual use.As can be seen from the figure, along with the increase of Gaussian Blur core, image blurring degree aggravation, the error that the Gaussian Blur core that algorithm recovers and actual Gauss used retouch core remains on 0.1 left and right, illustrates that the inventive method can recover more exactly Gaussian Blur core from fuzzy retouching image.

Claims (1)

1. the image blurring core inversion method of fuzzy retouching of estimating based on fuzzy indeformable Riemann, described fuzzy retouching image

Obtained through Fuzzy Processing by source images, it is characterized in that, the method comprises the following steps:

Steps A, by source images with fuzzy retouching image be converted into respectively logarithm Fourier, the source images after conversion and fuzzy retouching image are designated as respectively with ; Described by source images with fuzzy retouching image be converted into respectively logarithm Fourier, specifically in accordance with the following methods:

First to source images with fuzzy retouching image carry out respectively Fourier transform, obtain respectively with ; For the image after Fourier transform with , first carry out following processing: if its real part is zero, its real part is replaced to one and be greater than zero infinitesimal real number; Then to after treatment with , ask for respectively the natural logarithm of its mould, obtain being converted into source images and the fuzzy retouching image of logarithm Fourier, be designated as respectively with ;

Step B, calculate respectively , with vector of unit length between Riemann's geodesic distance , ; Described vector of unit length expression formula as follows:

，

In formula, represent logarithm Fourier transform frequency;

Step C, calculate the Gaussian Blur core of described Fuzzy Processing according to following formula :

。