CN103208100A - 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

Based on bluring the image blurring nuclear inversion method of fuzzy retouching that indeformable Riemann estimates

Technical field

The invention discloses a kind of image blurring nuclear inversion method of estimating based on fuzzy indeformable Riemann of fuzzy retouching, 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 editing operation, produces pleasing picture.The exquisite images of these editors are used for internet, Digital Media document, social medium etc. more, are bringing into play irreplaceable effect at the aspects such as spiritual exchange field of having expressed individual character, beautify mediaspace and having enriched people.Meanwhile, be used to aspects such as advertisement, medium, internet through the image of editing, gain public trust by cheating, reduced the public credibility of people to Digital Media, causing trust crisis.Therefore, it is very urgent that the research digital picture is forged detection, studies the image forge detection especially quantitatively and have more major and immediate significance.

Image blurring from the noise that obtains equipment and editor's generation, 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, reduction details, to make special efficacy etc. by image and fuzzy operator, is important images retouching operation.Types such as image blurring retouching comprises Gaussian Blur, average is fuzzy, boxlike is fuzzy, motion blur.The fuzzy part that exists in the image is in the passive generation of acquisition process, and it is initiatively to retouch generation in order to reach content consistency that part is also arranged.The key of image deblurring is to recover fuzzy core from blurred picture.The classic method utilization has or prior imformation is carried out image deblurring by methods such as energy minimization, partial differential equation, Markov fields and deconvoluted the Given information entropy that the dependence of deblurring effect provides.The 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, a kind of image blurring nuclear inversion method of estimating based on fuzzy indeformable Riemann of fuzzy retouching is provided, utilize the image blurring forward and backward isometry that satisfies of logarithm Fourier domain, adopt Riemann's geodesic distance to measure image blurring forward and backward fuzzy invariant, can inverting obtain the Gaussian Blur kernel function, thereby identify for image deblurring and image forge solid foundation is provided.

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

Based on the image blurring nuclear inversion method of fuzzy retouching that fuzzy indeformable Riemann estimates, described fuzzy retouching image is obtained through Fuzzy Processing by source images, and this method may further comprise the steps:

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

With

Step B, calculate respectively

And the Riemann's geodesic distance between the 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 the formula, ξ represents logarithm Fourier transform frequency;

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

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

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

At first to source images I and fuzzy retouching image I _BlurCarry out Fourier transform respectively, obtain respectively

With For the image after the Fourier transform

With

Carry out following processing earlier: be zero as its real part, then its real part replaced to one greater than zero infinitesimal real number; Then to after handling

With Ask for the natural logarithm of its mould respectively, namely 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 the 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 nuclear from fuzzy retouching image, the Gaussian Blur that recovers nuclear can either be used for making blurred picture from source images, identifies that whether image is by fuzzy retouching; Can be used in again from blurred picture and recover " totally " image.

Description of drawings

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

Fig. 2 is the inventive method schematic flow sheet;

Fig. 3 is the difference between the Gaussian Blur nuclear of the Gaussian Blur retouching nuclear of actual use and 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 a plurality of transform domains, frequency domain (Fourier transform) for example, 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, blurs.Fuzzy operation can be expressed as source images I in time domain, and (x, y) (convolution δ) is shown below for x, y with Gaussian Blur kernel function G.

I _blur(x,y)=I(x,y)*G(x,y,δ)

In the formula

δ is at the standard deviation of gaussian kernel normal distribution (abbreviating Gaussian Blur nuclear as), I _Blur(x y) is fuzzy retouching image, and * is convolution algorithm.

If f is R → R function, R is real number field, K _δBe the convolution kernel function

K _δSatisfy normalization character, i.e. ∫ K _δ(x) d δ=1.If * is convolution operator, K _δTo the convolution operation of f as the formula (1).

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

As seen from formula (1),

Thereby convolution kernel K _δConstitute the semigroup space R of an isomorphism ₊R ₊In all convolution kernels act on and produce a convolution track [f]={ (f, K behind the f _δ) | δ ∈ R ₊.

If

Be 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, can be converted to the additivity operation to convolution 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 ₂Be any two signals,

With

Be respectively f ₁And f ₂With nuclear Convolution, namely

In the logarithm fourier space,

With

Between Riemann's geodesic distance be calculated as follows shown in.

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

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

In the logarithm fourier space, f and f _bRiemann's geodesic distance as the formula (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 the Gaussian Blur signal.Norm in the formula adopts the index Riemann metric to calculate.

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

$v=\frac{-\mathrm{\&pi;}{\mathrm{\&xi;}}^2}{\sqrt{<\mathrm{\&pi;}{\mathrm{\&xi;}}^2,\mathrm{\&pi;}{\mathrm{\&xi;}}^2>}}=\frac{-{\mathrm{\&xi;}}^2}{\sqrt{{\&Integral;\mathrm{\&xi;}}^4{e}^{-\mathrm{\&pi;}{\mathrm{\&xi;}}^2}\mathrm{d\&xi;}}}=-\frac{2\mathrm{\&pi;}}{\sqrt{3}}{\mathrm{\&xi;}}^2;$

True origin with

Go up the vector of any arbitrarily

As shown in Figure 1, in the logarithm fourier space,

Track and side-play amount π ξ ²Track to satisfy isometry constraint, must make function

Vertically

Whole

On the trace, $Q\left(\tilde{f}\right)=<<\tilde{f},v>>.$

Among Fig. 1, trace-π ξ ²It is δ=1 o'clock convolution kernel

Expression, the corresponding different trace of convolution kernel that δ is different.Correspondingly, each K _δCorresponding Difference,

There is unique definite solution.Under the situation that δ determines, the edge

Motion can occur

Greater than, equal and less than 03 kinds of situations.

Be the δ that asks greater than the minus cut off value of zero-sum.

The edge

Motion f and K _δDependence can be with unified formula

Express, wherein

Because function

Be the integral form function, so $Q(\tilde{f}-\widetilde{\mathrm{\&delta;}}\mathrm{\&pi;}{\mathrm{\&xi;}}^2)=Q\left(\tilde{f}\right)+\widetilde{\mathrm{\&delta;}}Q\left(\mathrm{\&pi;}{\mathrm{\&xi;}}^2\right)=C.$ Q (π ξ ²) in the integrated value in R territory be $\&Integral;\mathrm{vd\&xi;}=\frac{2{\mathrm{\&pi;}}^2}{\sqrt{3}}\frac{3}{4{\mathrm{\&pi;}}^2}=\frac{\sqrt{3}}{2},$ Therefore formula (5) is set up.

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

Get 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 nuclear inversion method of estimating based on fuzzy indeformable Riemann of fuzzy retouching of the present invention, specific as follows:

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

At first to source images I and fuzzy retouching image I _BlurCarry out Fourier transform respectively, obtain respectively

With

For the image after the Fourier transform With

Carry out following processing earlier: be zero as its real part, then its real part replaced to one greater than zero infinitesimal real number; Then to after handling

With

Ask for the natural logarithm of its mould (being square root sum square of real part and imaginary part) respectively, namely 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 the vector of unit length v

The expression formula of described vector of unit length v is as follows:

$v=-\frac{2\mathrm{\&pi;}}{\sqrt{3}}{\mathrm{\&xi;}}^2,$

In the formula, ξ represents logarithm Fourier transform frequency;

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

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

In order to verify effect of the present invention, utilize the fuzzy retouching of the inventive method inversion chart picture to examine and then image is forged in fuzzy retouching detected.Under the MATLAB2010 environment, realized fuzzy retouching inversion algorithm of the present invention.The experiment hardware platform is: four nuclear I7 processors, 8G internal memory.The image source data are from the CASIA image set, and picture size is 384 * 256.

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

Concrete experimental technique is as follows:

Use the different source images of 4 width of cloth, under Gaussian Blur nuclear δ=0.4, δ=0.6, δ=0.8 and δ=1.0 situations, source images is carried out the Gaussian Blur retouching respectively, and adopt the inventive method that Gaussian Blur nuclear is carried out inverting.Fig. 3 has shown the difference between the Gaussian Blur nuclear of the Gaussian Blur retouching nuclear of actual use and the inventive method inverting.As can be seen from the figure, increase along with Gaussian Blur nuclear, image blurring degree aggravation, the Gaussian Blur nuclear that algorithm recovers and the error that actual used Gauss retouches nuclear remain on about 0.1, illustrate that the inventive method can recover Gaussian Blur nuclear more exactly from fuzzy retouching image.

Claims (2)

1. based on bluring the image blurring nuclear inversion method of fuzzy retouching that indeformable Riemann estimates, described fuzzy retouching image is obtained through Fuzzy Processing by source images, it is characterized in that this method may further comprise the steps:

Steps A, with source images

With fuzzy retouching image

Be converted into the logarithm Fourier respectively, the source images after the conversion and fuzzy retouching image be designated as respectively into 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 the formula,

Expression logarithm Fourier transform frequency;

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

:

。

2. the image blurring nuclear inversion method of estimating based on fuzzy indeformable Riemann according to claim 1 of fuzzy retouching is characterized in that, and is described with source images

With fuzzy retouching image

Be converted into the logarithm Fourier respectively, specifically in accordance with the following methods:

At first to source images

With fuzzy retouching image

Carry out Fourier transform respectively, obtain respectively

With

For the image after the Fourier transform

With

, carry out following processing earlier: be zero as its real part, then its real part replaced to one greater than zero infinitesimal real number; Then to after handling

With

, ask for the natural logarithm of its mould respectively, namely obtain being converted into source images and the fuzzy retouching image of logarithm Fourier, be designated as respectively With

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