CN100580700C - Implicit writing analysis method based on pivot characteristic in implicit writing analysis system - Google Patents

Abstract

This invention discloses a hidden-writing analysis algorithm based on the character of a master element in a hidden-writing analysis system, which captures tiny changes resulted in embedded information in capturing images and overcomes high error test rate in the traditional algorithm by introducing differentiate between image hidden-writing analysis and computation of adjacent pixels in channels and associated matrix of pixel brightness between channels to expand the application of the association matrix to high stage derivation and grads to describe the correlated character of data and space positions in the channels, computing one stage and second stage statistic matrixes of the derivation character function of the statistic volumes to get 136-D characters from an image and reduce it to 18-D by a primary-element analysis method finally supporting a vector machine to constitute a hidden-writing analysis algorithm for the sorting method.

Description

In the steganalysis system based on the steganalysis method of pivot characteristic

Technical field

The present invention relates in a kind of steganalysis system steganalysis method based on pivot characteristic.

Background technology

In recent years, concealed art and digital watermarking (corresponding with concealed art, as to refer in particular to invisible digital watermark) Study on Technology obtains large development.Many concealed arts and digital watermarking software can directly be downloaded from network, make the ordinary people utilize these technology to realize that " hidden " communication becomes possibility.This phenomenon objectively requires the steganalysis development of technology, so that detect and stop illegal Information hiding to be transmitted in seeming the generic media (image, Voice ﹠ Video etc.) that is as good as.

Concealed art is with " existence " that hide Info and be not that the mankind are perceived as purpose.Steganalysis is then broken through the limitation of human sense organ, by COMPUTER DETECTION, analyze even extract the algorithm details of hiding information or concealed art.The realization thought of steganalysis is based on the recognition: image exists before and after the embedding information difference and the such difference can be detected." passive " steganalysis algorithm only detects whether contain hiding information in the medium; " initiatively " steganalysis then will further obtain the length that hides Info, the title or the ins and outs of hidden algorithm, even extracts hiding information.Steganalysis also is divided into " blind " and " non-blind " two kinds: " non-blind " steganalysis designs at specific concealed art, and " blind " steganalysis algorithm can be handled multiple concealed art.The steganalysis that the present invention relates to belongs to " passive " " blind " steganalysis, promptly whether has the information of using multiple concealed art to hide in the detected image.Efficient steganalysis algorithm should improve the verification and measurement ratio to " secret " image under the prerequisite that reduces false drop rate as far as possible.False drop rate refers in the testing process " totally " image mistake is divided into the probability of " secret " image.

Summary of the invention

The purpose of this invention is to provide in a kind of steganalysis system steganalysis method based on pivot characteristic.

Steganalysis method based on pivot characteristic in the steganalysis system comprises the steps:

1) the steganalysis field is introduced in the higher differentiation computing

Differentiating has the effect of amplification " subtle change ", the variation naturally of using higher differentiation to catch the catastrophe point in the image and cause because embedding hides Info;

2) calculate the histogram of all pixel intensity, single order total differential and second order total differential distribution

The single order total differential of each location of pixels correspondence and second order total differential in the computed image; The single order total differential can be regarded two color of pixel values in right-hand and below of current pixel location and poor with 2 times of the current pixel location color value as; The second order total differential can regard as current pixel location two pixels in right-hand and below the single order total differential and with total differential 2 times poor of current pixel location single order; With the number of all pixel intensity, just obtain the histogram of pixel intensity according to the color value of numeral size statistics different pixels:

Formula (1) is used to calculate three channels (α ∈ { r, g, b}) frequency of middle brightness v (v ∈ [0,255]); Wherein, during s=t,

Otherwise

The frequency of all brightness is formed the histogram of pixel intensity; Similarly, can obtain the total differential histogram of single order total differential and second order; When calculating single order total differential histogram, with b ^α(i j) changes d into ₁ ^α(i j), and suitably changes the variation range of i and j; Calculating the histogrammic formula of second order total differential can similarly obtain;

3) histogram of calculating high-order partial differential

The high-order partial differential of each location of pixels correspondence in the computed image.The high-order partial differential at present corresponding single order, second order and three rank partial differentials; The right-hand pixel color value that the single order partial differential can be regarded current pixel location as is poor with the current pixel location color value, perhaps the color value of its lower pixel poor with the current pixel location color value; With the single order partial differential of all location of pixels number, just obtain the histogram of single order partial differential according to the single order partial differential of numeral size statistics different pixels position:

Formula (2) is used to calculate the frequency of single order partial differential v in the color channel α, and all frequency are formed the histogram of single order partial differential; It is similar to calculate second order partial differential and the histogrammic formula of three rank partial differentials; Similarly, can obtain the histogram of second order and three rank partial differentials respectively;

The single order total differential of right-hand pixel that the second order partial differential can be regarded the current pixel position as poor with the single order total differential of current pixel position, perhaps the single order total differential of its lower pixel poor with the single order total differential of current pixel position; The calculating of three rank partial differentials similarly;

4) co-occurrence matrix of 6 high-order partial differentials of calculating adjacent pixel location object

According to 3) in method can calculate " OK " and " row " both direction totally 6 high-order partial differential objects; The number that the numerical value of adjacent two the pixel place higher differentiations in position occurs simultaneously on statistics " OK " direction; The number of all paired single order partial differentials is formed the co-occurrence matrix of single order partial differential; Similarly, can obtain the co-occurrence matrix of other objects;

5) the high-order partial differential co-occurrence matrix of two color interchannels of calculating

Colored RGB image has three color channels, calculate the high-order partial differential of all location of pixels in each color channel after, add up the number that same coordinate position place single order partial differential occurs simultaneously in two different channels, just obtain single order partial differential co-occurrence matrix; Similarly, can obtain other partial differential co-occurrence matrix;

6) compute gradient co-occurrence matrix

For the brightness of r, g and three color channels of b is taken all factors into consideration, introduced the notion of gradient; Gradient is counted as the image enhancement technique based on the single order partial differential in Flame Image Process; Briefly, the gradient of a pixel position be this pixel position single order partial differential in three color channels absolute value and.Gradient is divided into " the row gradient " of " OK " direction " row gradient " and " row " direction; Two adjacent states that Grad occurs simultaneously of statistics position just obtain the gradient co-occurrence matrix;

7) use the histogram feature function calculation as above the statistical moment of statistic as initial characteristics

A histogram is done the one-dimensional discrete Fourier transform and asked its amplitude, obtain its " differential characteristics function ", use the statistical moment formula to calculate a feature of this histogram correspondence; A co-occurrence matrix is done two dimensional discrete Fourier transform and asked its amplitude, obtain its " differential characteristics function ", use the statistical moment formula to calculate two features of this co-occurrence matrix correspondence; According to calculating, can obtain 136 initial dimensional feature vectors from all statistics from a width of cloth coloured image as upper type;

8) using the pivot analysis method is the method for the final proper vector of 18 dimensions with 136 initial dimensional feature vector dimensionality reductions

Use " pivot analysis method " dimensionality reduction, regard every width of cloth image as one " OK ", 136 dimensional features of piece image correspondence are regarded 136 " row " as, just obtain a matrix; Use the method for eig in the linear algebra, choose maximum several characteristic value and characteristic of correspondence vector thereof, and other eigenwert characteristic of correspondence vectors are changed to 0, just obtain the dimensionality reduction proper vector; With the computing between the dimensionality reduction proper vector, obtaining final dimensionality reduction is in the proper vector process of 18 dimensions by original feature vector, has used 18 proper vectors of 18 maximum eigenwert correspondences to form the dimensionality reduction eigenmatrix.

Described differentiating has the effect of amplification " subtle change ", the variation naturally of using higher differentiation to catch the catastrophe point in the image and cause because embedding hides Info:

Use b _α(then the single order partial differential at this place is defined as for m, the n) brightness at capable, the n row place of position m in the color channel α in the colored BMP image of expression $p_{\mathrm{\α}}^{(1,C)}(m,n)=b_{\mathrm{\α}}(m,n+1)-b_{\mathrm{\α}}(m,n)$ With $p_{\text{\α}}^{(1,R)}(m,n)=b_{\mathrm{\α}}(m+1,n)-b_{\mathrm{\α}}(m,n);$ Thereby single order total differential herein and second order total differential can be defined as formula (3) and (4) respectively:

$d_{\mathrm{\α}}^1(m,n)=\left|p_{\mathrm{\α}}^{(1,C)}(m,n)\right|+\left|p_{\mathrm{\α}}^{(1,R)}(m,n)\right|---\left(3\right)$

$d_{\mathrm{\α}}^2(m,n)=p_{\mathrm{\α}}^{(1,C)}(m,n)+p_{\mathrm{\α}}^{(1,R)}(m,n)-p_{\mathrm{\α}}^{(1,C)}(m,n-1)-p_{\mathrm{\α}}^{(1,R)}(m-1,n)---\left(4\right)$

Be defined as follows (shown in 5～8) respectively so obtain the second order and the three rank partial differentials of " row " and " OK " both direction:

$p_{\mathrm{\α}}^{(2,C)}(m,n)=d_{\mathrm{\α}}^1(m,n+1)-d_{\mathrm{\α}}^1(m,n)---\left(5\right)$

$p_{\mathrm{\α}}^{(2,R)}(m,n)=d_{\mathrm{\α}}^1(m+1,n)-d_{\mathrm{\α}}^1(m,n)---\left(6\right)$

$p_{\mathrm{\α}}^{(3,C)}(m,n)=d_{\mathrm{\α}}^2(m,n+1)-d_{\mathrm{\α}}^2(m,n)---\left(7\right)$

$p_{\mathrm{\α}}^{(3,R)}(m,n)=d_{\mathrm{\α}}^2(m+1,n)-d_{\mathrm{\α}}^2(m,n)---\left(8\right)$

For the brightness of r, g and three color channels of b is taken all factors into consideration, introduced the notion of gradient; Gradient is counted as the image enhancement technique based on the single order partial differential in Flame Image Process;

$G_C(m,n)=\left|p_r^{(1,C)}(m,n)\right|+\left|p_g^{(1,C)}(m,n)\right|+\left|p_b^{(1,C)}(m,n)\right|---\left(9\right)$

$G_R(m,n)=\left|p_r^{(1,R)}(m,n)\right|+\left|p_g^{(1,R)}(m,n)\right|+\left|p_b^{(1,R)}(m,n)\right|---\left(10\right).$

The co-occurrence matrix of 6 high-order partial differentials of described adjacent pixel location object is:

Formula (11) calculates two " frequency " that adjacent pixels brightness occurs simultaneously on " row " direction, and all such frequency are formed " co-occurrence matrix " of pixel brightness;

Other 5 co-occurrence matrix formula are similar; " OK " " co-occurrence matrix " of above-mentioned 6 objects of adjacent two pixel position can calculate equally on the direction.

The high-order partial differential co-occurrence matrix of described two color interchannels is:

In the formula, α β ∈ { rg, gb, br}, corresponding two color channels; The frequency that formula (12) is used for calculating α and two same location of pixels of color channel of β i is capable, two the brightness value s in j row place and t occur simultaneously, all frequency are formed " brightness " co-occurrence matrixs; Similarly, can obtain the co-occurrence matrix formula of these four objects of single order partial differential of single order total differential, second order total differential and " row " and " OK " both direction.

The computing formula of described gradient co-occurrence matrix is

The gradient G of RGB coloured image _C(m, n) and G _R(m, n) be respectively the single order partial differential of " row " direction and " OK " direction in three color channels of r, g and b absolute value with, they can add up the change that hides Info to three color channel same position places, have reflected that the integral body to coloured image changes; Co-occurrence matrix based on " gradient " is more responsive to embedding information; The gradient G that is divided into " row " direction according to gradient _C(m is n) with " OK " direction gradient G _R(m, n), and " symbiosis " can divide into " appearance simultaneously " of " row " adjacent position and " OK " adjacent position, can be divided into as above four formula.

Described use histogram feature function calculation formula is (17) and (18):

$M_1^l=\frac{{\mathrm{\Σ}}_{k=0}^{\mathrm{\γ}/2-1}{k}^l\·c\left(k\right)}{{\mathrm{\Σ}}_{k=0}^{\mathrm{\γ}/2-1}c\left(k\right)}---\left(17\right)$

L ∈ in the formula 1,2}, the amplitude of c (k) expression frequency k correspondence; γ is the frequency maximal value; Formula (17) is done the one-dimensional discrete Fourier transform and is asked its amplitude a histogram, obtains " differential characteristics function " c=|DFT (h) |, can calculate its single order statistical moment and second-order statistics square;

$M_2^l=\frac{{\mathrm{\Σ}}_{k_1=0}^{\mathrm{\ζ}/2-1}{\mathrm{\Σ}}_{k_2=0}^{\mathrm{\η}/2-1}(k_1^l,k_2^l)\·c_2(k_1,k_2)}{{\mathrm{\Σ}}_{k_1=0}^{\mathrm{\ζ}/2-1}{\mathrm{\Σ}}_{k_2=0}^{\mathrm{\η}/2-1}{c}_2(k_1,k_2)}---\left(18\right)$

A co-occurrence matrix is done two dimensional discrete Fourier transform and asked its amplitude, obtain corresponding differential characteristics function c ₂=| DFT ₂(h ₂) | after, use first-order statistics square and the second-order statistics square of formula (18) calculated characteristics function at k1 and k2 both direction, obtain 4 features;

Use as above formula, can obtain 136 initial dimensional feature vectors from a width of cloth coloured image.

The present invention is a kind of based on differential statistics moment characteristics vector, and adopting support vector machine is " blind " detection algorithm of sorting algorithm.Calculate differential statistics moment function in the digital picture, and use the dependence between " pivot analysis method " elimination feature, thereby express the otherness that image causes because of embedding information better.

The present invention has the high efficiency (false drop rate is low, verification and measurement ratio is high) of detection and to multiple performance robustness of coming source images; Algorithm complexity is low, computing cost is little.(1, the experimental result of the concealed art of two kinds of spread spectrums of Cox and Piva is shown false drop rate is that this algorithm verification and measurement ratio all reaches 100% under 0% the situation.2, the performance on CorelDraw and two kinds of image libraries of Washington has disclosed the universality and the robustness of algorithm.)

Description of drawings:

Fig. 1 (a) is employing Cox (α=0.05) and the concealed art of two kinds of spread spectrums of Piva (α=0.1) embed information in 1096 width of cloth CorelDraw " totally " images " latent close " image, and " the feature cloud atlas of corresponding " totally " image; Cox (α=0.05), Piva (α=0.1) and cover in the difference corresponding diagram.

Fig. 1 (b) is employing Cox (α=0.05) and the concealed art of two kinds of spread spectrums of Piva (α=0.1) embed information in 1324 width of cloth Washington " totally " images " latent close " image, and " the feature cloud atlas of corresponding " totally " image.

Fig. 1 (c) is employing Cox (α=0.1) and the concealed art of two kinds of spread spectrums of Piva (α=0.2) embed information in 1096 width of cloth CorelDraw " totally " images " latent close " image, and " the feature cloud atlas of corresponding " totally " image.

Fig. 1 (d) is employing Cox (α=0.1) and the concealed art of two kinds of spread spectrums of Piva (α=0.2) embed information in 1324 width of cloth Washington " totally " images " latent close " image, and " the feature cloud atlas of corresponding " totally " image.

Embodiment

Steganalysis algorithm based on pivot characteristic in the steganalysis system is: will differentiate and introduce the image latent writing analysis field, and construct initial multidimensional feature.Extract 136 dimensional feature vectors to (eight) from every width of cloth the colored BMP image according to step (), dimensionality reduction to 18 dimension; Use the support vector machine training then; The dimensionality reduction eigenmatrix that uses the training stage is realized classification with the training template at last to 136 dimensional feature vector dimensionality reductions by the test pattern gained, obtains the experimental result in (nine):

(1) the steganalysis field is introduced in the higher differentiation computing

(m, n) (then the single order partial differential at this place is defined as for m, the brightness of n) locating in the position in the color channel α in the colored BMP image of expression with b α $p_{\mathrm{\α}}^{(1,C)}(m,n)=b_{\mathrm{\α}}(m,n+1)-b_{\mathrm{\α}}(m,n)$ With $p_{\mathrm{\α}}^{(1,R)}(m,n)=b_{\mathrm{\α}}(m+1,n)-b_{\mathrm{\α}}(m,n).$ Thereby single order total differential herein and second order total differential can be defined as formula (1) and (2) respectively:

$d_{\mathrm{\α}}^1(m,n)=\left|p_{\mathrm{\α}}^{(1,C)}(m,n)\right|+\left|p_{\mathrm{\α}}^{(1,R)}(m,n)\right|---\left(1\right)$

$d_{\mathrm{\α}}^2(m,n)=p_{\mathrm{\α}}^{(1,C)}(m,n)+p_{\mathrm{\α}}^{(1,R)}(m,n)-p_{\mathrm{\α}}^{(1,C)}(m,n-1)-p_{\mathrm{\α}}^{(1,R)}(m-1,n)---\left(2\right)$

Be defined as follows (shown in 3～6) respectively so obtain the second order and the three rank partial differentials of " row " and " OK " both direction:

$p_{\mathrm{\α}}^{(2,C)}(m,n)=d_{\mathrm{\α}}^1(m,n+1)-d_{\mathrm{\α}}^1(m,n)---\left(3\right)$

$p_{\mathrm{\α}}^{(2,R)}(m,n)=d_{\mathrm{\α}}^1(m+1,n)-d_{\mathrm{\α}}^1(m,n)---\left(4\right)$

$p_{\mathrm{\α}}^{(3,C)}(m,n)=d_{\mathrm{\α}}^2(m,n+1)-d_{\mathrm{\α}}^2(m,n)---\left(5\right)$

$p_{\mathrm{\α}}^{(3,R)}(m,n)=d_{\mathrm{\α}}^2(m+1,n)-d_{\mathrm{\α}}^2(m,n)---\left(6\right)$

For the brightness of r, g and three color channels of b is taken all factors into consideration, introduced the notion of gradient.Gradient is counted as the image enhancement technique based on the single order partial differential in Flame Image Process.

$G_C(m,n)=\left|p_r^{(1,C)}(m,n)\right|+\left|p_g^{(1,C)}(m,n)\right|+\left|p_b^{(1,C)}(m,n)\right|---\left(7\right)$

$G_R(m,n)=\left|p_r^{(1,R)}(m,n)\right|+\left|p_g^{(1,R)}(m,n)\right|+\left|p_b^{(1,R)}(m,n)\right|---\left(8\right)$

(2) add up the histogram of all pixel intensity, single order total differential and second order total differential distribution

Formula (9) is used to calculate three channels (α ∈ { r, g, b}) frequency of middle brightness v (v ∈ [0,255]).Wherein, during s=t,

Otherwise

The frequency of all brightness is formed the histogram of pixel intensity.When calculating single order total differential histogram, with b ^α(i j) changes d into ₁ ^α(i j), and suitably changes the variation range of i and j.Calculating the histogrammic formula of second order total differential can similarly obtain.

(3) histogram of high-order partial differential

Formula (10) is used to calculate the frequency of single order partial differential v in the color channel α, and all frequency are formed the histogram of single order partial differential.It is similar to calculate second order partial differential and the histogrammic formula of three rank partial differentials.

(4) co-occurrence matrix of 6 objects of adjacent pixel location

The co-occurrence matrix of pixel intensity, single order partial differential, second order partial differential, three rank partial differentials, single order total differential and 6 objects of second order total differential of adjacent two pixel position on statistics " row " direction is represented the statistical distribution state that two numerical value of each object correspondence occur simultaneously.Formula (11) calculates two " frequency " that adjacent pixels brightness occurs simultaneously on " row " direction, and all such frequency are formed " co-occurrence matrix " of pixel brightness.

Other 5 co-occurrence matrix formula are similar." OK " " co-occurrence matrix " of above-mentioned 6 objects of adjacent two pixel position can calculate equally on the direction.

The co-occurrence matrix of (five) two color interchannels

In the formula, α β ∈ { rg, gb, br}, corresponding two color channels.Formula (12) is used for calculating α and two same location of pixels of color channel of β, and (i j) locates the frequency that two brightness value s and t occur simultaneously, and all frequency are formed " brightness " co-occurrence matrixs.Similarly, can obtain the co-occurrence matrix formula of these four objects of single order partial differential of single order total differential, second order total differential and " row " and " OK " both direction.

(6) gradient co-occurrence matrix

The gradient G of RGB coloured image _C(m, n) and G _R(m n) is the combination of single order partial differential in three color channels, and they can add up the change that hides Info to three color channel same position places, has reflected that the integral body to coloured image changes.Co-occurrence matrix based on " gradient " is more responsive to embedding information.The gradient G that is divided into " row " direction according to gradient _C(m is n) with " OK " direction gradient G _R(m, n), and " symbiosis " can divide into " appearance simultaneously " of " row " adjacent position and " OK " adjacent position, can obtain four co-occurrence matrixs (shown in the formula 13～16):

(7) use the histogram feature function calculation as above the statistical moment of statistic as initial characteristics

A histogram is done the one-dimensional discrete Fourier transform and is asked its amplitude, obtain " differential characteristics function " c=|DFT (h) |, can calculate its single order statistical moment and second-order statistics square.

$M_1^l=\frac{{\mathrm{\Σ}}_{k=0}^{\mathrm{\γ}/2-1}{k}^l\·c\left(k\right)}{{\mathrm{\Σ}}_{k=0}^{\mathrm{\γ}/2-1}c\left(k\right)}---\left(17\right)$

L ∈ in the formula 1,2}, the amplitude of c (k) expression frequency k correspondence; γ is the frequency maximal value.

A co-occurrence matrix is done two dimensional discrete Fourier transform and asked its amplitude, obtain corresponding differential characteristics function c ₂=| DFT ₂(h ₂) |, use first-order statistics square and the second-order statistics square of formula (18) calculated characteristics function at k1 and k2 both direction, obtain 4 features.

$M_2^l=\frac{{\mathrm{\Σ}}_{k_1=0}^{\mathrm{\ζ}/2-1}{\mathrm{\Σ}}_{k_2=0}^{\mathrm{\η}/2-1}(k_1^l,k_2^l)\·c_2(k_1,k_2)}{{\mathrm{\Σ}}_{k_1=0}^{\mathrm{\ζ}/2-1}{\mathrm{\Σ}}_{k_2=0}^{\mathrm{\η}/2-1}{c}_2(k_1,k_2)}---\left(18\right)$

(8) using the pivot analysis method is the final proper vectors of 18 dimensions with 136 initial dimensional feature vector dimensionality reductions

At first use " pivot analysis method " 136 dimensional feature vector dimensionality reductions to 18 dimension with some training samples, and " pivot characteristic matrix " when preserving training " sample to " dimensionality reduction, 136 dimensional features that then it are used for " test sample book collection " drop to the processes of 18 dimensions.

(9) application example

100 width of cloth images are training sample in table 1. image library, the detection performance when other is test sample book

When using Cox algorithm and Piva algorithm to embed information in colored RGB image, at first image being converted into the representation of YIQ, then data being embedded in Y part wherein, is the RGB image with the YIQ image transitions at last again.To each width of cloth image in as above three kinds of " totally " image libraries, use the Cox algorithm to embed 1000 random numbers, produce " the concealed image library of Cox "; Use the Piva algorithm to embed 16000 random numbers and obtain " the concealed image library of Piva ".In the original Cox algorithm, embedment strength α=0.1, for

The test embedment strength is to detecting Effect on Performance, and we have tested the situation of α=0.05.To the Piva algorithm, tested the situation of α=0.1 and α=0.2 respectively.

1) training and the testing result on two image libraries

From " totally " image library, get 100 width of cloth images, from " secret " image library, take out corresponding " latent close " image, the two composition " training sample to " storehouse." totally " image that is left and " secret " version thereof are as the open to the outside world test set.For making algorithm have practicality, " the pivot characteristic matrix " when preserving 100 couple of being used to train " sample to " dimensionality reduction, and will 136 dimensional features in " test sample book collection " drop to 18 with it and tie up.For increasing the contrast of experiment, we (get 100 pairs of sample trainings equally on same image library, other sample is used for test) tested " expansion Shi Yun Q algorithm " that first segment is mentioned, promptly use 234 dimensional feature vectors to represent the algorithm of a width of cloth coloured image.Contrast experiment's sorting algorithm adopts LibSvm equally.The test result on image library 1 and 2 of this paper algorithm (being called for short " pivot algorithm ") and " expansion Shi Yun Q algorithm " (being called for short " Shi algorithm ") sees Table 1.The detection performance provides with the form of " verification and measurement ratio/false drop rate ".

As can be seen from Table 1, " Shi algorithm " is fine to the detection effect of the Piva algorithm of the Cox algorithm of embedment strength factor-alpha=0.05 and α=0.1; Yet, relatively poor on the contrary to the Piva algorithm of the Cox algorithm of α=0.1 and α=0.2.This is very abnormal phenomenon.The dimension that reason is the proper vector that " Shi algorithm " produces is big (234) too, according to the rule of pattern-recognition, need 2340 pairs of test samples (CorelDraw sample storehouse has only 1096 pairs altogether) at least, and resulting result is only actual believable.Sample number more after a little while, test result is higher with respect to legitimate reading, but the performance of algorithm also can be described." Shi algorithm " experimental result on image library 2 is relatively poor, exposes the extremely unsettled performance of this algorithm.On the contrary, " pivot algorithm " all shows perfect detection performance on two kinds of image libraries.

2) the part sample is a training set in image library, and another image library all images is the experimental result of test set

100 pairs of samples of table 2. a class image are done training sample, and another kind of all images is done the detection performance of test sample book

Be to improve the practicality of steganalysis system, need research to use which image library can train the equal classification model efficiently of the image in most other sources.To each concealed art, we use 100 pairs of CorelDraw sample image dimensionality reductions and train classification model; " the pivot characteristic matrix " of using these 100 pairs of CorelDraw proper vectors then drops to 18 dimensions with 136 dimensional features of all 1324 pairs of Washington images; With training gained classification model 1324 pairs of proper vectors are tested at last.Test result sees Table row of 2 intermediate hurdles " CorelDraw " by name.

To each concealed art, we use 100 pairs of Washington images to do training sample equally, have tested " pivot algorithm " and all 1096 pairs of CorelDraw images are test sample book.Test result sees Table row of 2 intermediate hurdles " Washington " by name.

3) macroscopical classifying quality of " pivot algorithm "

From table 1 and 2 as can be seen, " pivot algorithm " has very high detection performance and robustness.3.4 Fig. 1 of joint has provided partly answer from the angle of microcosmic to the reason that " pivot algorithm " possesses excellent properties like this; The performance of algorithm also needs to be illustrated with the feature that it extracts from great amount of images.For this reason, we reuse " pivot analysis method " 18 dimensional feature vectors are dropped to 3 dimensions, with the three-dimensional feature of a width of cloth coloured image correspondence respectively as the coordinate of x, y in the space coordinates and z axle, thereby piece image is exactly a unique point in the three dimensions.The feature " cloud atlas " of " latent close " image of 1096 width of cloth CorelDraw " totally " images and they is seen (a) and (c) among Fig. 1, and the feature " cloud atlas " of 1324 width of cloth Washington " totally " images and their " concealing close " image is seen (b) and (d).From the macro-effect figure of Fig. 2 as can be seen, " totally " image is distinguished in three dimensions obviously with the two " feature cloud atlas " of " latent close " image.

The beneficial effect that technical solution of the present invention is brought

The present invention differentiates by introducing and principle component analysis is realized dimensionality reduction to characteristic vector, greatly reduces False drop rate when detecting hidden close image has improved verification and measurement ratio. The present invention has following characteristics: false drop rate is low, The verification and measurement ratio height; Algorithm complexity is low, computing cost is little.

Claims (3)

1. In the steganalysis system based on the steganalysis method of pivot characteristic, it is characterized in that, comprise the steps:

   1) the steganalysis field is introduced in the higher differentiation computing

   Differentiating has the effect of amplification " subtle change ", the variation naturally of using higher differentiation to catch the catastrophe point in the image and cause because embedding hides Info;

   2) calculate the histogram of all pixel intensity, single order total differential and second order total differential distribution

   The single order total differential of each location of pixels correspondence and second order total differential in the computed image; The single order total differential is defined as two color of pixel values in right-hand and below of current pixel location and poor with 2 times of the current pixel location color value; The second order total differential be defined as current pixel location two pixels in right-hand and below the single order total differential and with total differential 2 times poor of current pixel location single order; With the number of all pixel intensity, just obtain the histogram of pixel intensity according to the color value of numeral size statistics different pixels:

   

   Formula (1) is used to calculate three channel α ∈ { r, g, the frequency of brightness v ∈ [0,255] among the b}; Wherein, r, g, b ∈ [0,255],

   

   General type be During s=t,

   

   Otherwise

   

   The frequency of all brightness is formed the histogram of pixel intensity; Obtain single order total differential and the total differential histogram of second order according to the principle identical with the pixel intensity histogram; When calculating single order total differential histogram, with b _α(i j) changes d into _a ¹(i j), and correspondingly changes the span of i and j; When calculating second order total differential histogram, with b _α(i j) changes d into _a ²(i j), and correspondingly changes the span of i and j;

   3) histogram of calculating high-order partial differential

   The high-order partial differential of each location of pixels correspondence in the computed image; The corresponding single order of high-order partial differential, second order and three rank partial differentials; The right-hand pixel color value that the single order partial differential is defined as current pixel location is poor with the current pixel location color value, perhaps the color value of its lower pixel poor with the current pixel location color value; With the single order partial differential of all location of pixels number, just obtain the histogram of single order partial differential according to the single order partial differential of numeral size statistics different pixels position:

   Formula (2) is used to calculate the frequency of single order partial differential v in the color channel α, uses b _α(then the single order partial differential at this place is defined as for i, the j) brightness at capable, the j row place of position i in the color channel α in the colored BMP image of expression $p_{\mathrm{\α}}^{(1,C)}(i,j)=b_{\mathrm{\α}}(i,j+1)-b_{\mathrm{\α}}(i,j)$ With $p_{\mathrm{\α}}^{(1,R)}(i,j)=b_{\mathrm{\α}}(i+1,j)-b_{\mathrm{\α}}(i,j);$ All frequency are formed the histogram of single order partial differential; Calculate second order partial differential and three rank partial differential histograms according to the principle of calculating the single order partial differential;

   The single order total differential of right-hand pixel that the second order partial differential is defined as the current pixel position poor with the single order total differential of current pixel position, perhaps the single order total differential of its lower pixel poor with the single order total differential of current pixel position;

   4) co-occurrence matrix of 6 high-order partial differentials of calculating adjacent pixel location object

   The number that the numerical value of adjacent two the pixel place higher differentiations in position occurs simultaneously on statistics " OK " direction; The number of all paired single order partial differentials is formed the co-occurrence matrix of single order partial differential; According to the principle of calculating single order partial differential co-occurrence matrix, calculate the co-occurrence matrix of other high-order partial differential objects;

   5) the high-order partial differential co-occurrence matrix of two color interchannels of calculating

   Colored RGB image has three color channels, calculate the high-order partial differential of all location of pixels in each color channel after, add up the number that same coordinate position place single order partial differential occurs simultaneously in two different channels, just obtain single order partial differential co-occurrence matrix; According to the principle of single order partial differential co-occurrence matrix between the calculating channel, calculate other partial differential co-occurrence matrix;

   6) compute gradient co-occurrence matrix

   For the brightness of r, g and three color channels of b is taken all factors into consideration, introduced the notion of gradient; Gradient is a kind of image enhancement technique based on the single order partial differential in Flame Image Process; Briefly, the gradient of a pixel position be this pixel position single order partial differential in three color channels absolute value and; Gradient is divided into " the row gradient " of " OK " direction " row gradient " and " row " direction; Two adjacent states that Grad occurs simultaneously of statistics position just obtain the gradient co-occurrence matrix;

   7) use the histogram feature function calculation as above the statistical moment of statistic as initial characteristics

   A histogram is done the one-dimensional discrete Fourier transform and asked its amplitude, obtain its " differential characteristics function ", use the statistical moment formula to calculate 1 feature of this histogram correspondence; A co-occurrence matrix is done two dimensional discrete Fourier transform and asked its amplitude, obtain its " differential characteristics function ", use the statistical moment formula to calculate 2 features of this co-occurrence matrix correspondence; All statistics by calculating as upper type, are obtained 136 initial dimensional feature vectors by 1 width of cloth coloured image;

   8) using the pivot analysis method is the method for final 18 dimensional feature vectors with 136 initial dimensional feature vector dimensionality reductions

   Use " pivot analysis method " dimensionality reduction, regard every width of cloth image as 1 " OK ", 136 dimensional features of piece image correspondence are regarded 136 " row " as and are obtained 1 matrix; Use the method for eig in the linear algebra, choose maximum several characteristic value and characteristic of correspondence vector thereof, and other eigenwert characteristic of correspondence vectors are changed to 0 obtain the dimensionality reduction proper vector; Use 18 dimensions " dimensionality reduction proper vector " " original feature vector " dimensionality reduction to be obtained the proper vector of 18 final dimensions;

   Described differentiating has the effect of amplification " subtle change ", the variation naturally of using higher differentiation to catch the catastrophe point in the image and cause because embedding hides Info:

   Single order total differential herein and second order total differential are defined as formula (3) and (4) respectively:

   $d_{\mathrm{\α}}^1(i,j)=p_{\mathrm{\α}}^{(1,C)}(i,j)+p_{\mathrm{\α}}^{(1,R)}(i,j)---\left(3\right)$

   $d_{\mathrm{\α}}^2(i,j)=p_{\mathrm{\α}}^{(1,C)}(i,j)+p_{\mathrm{\α}}^{(1,R)}(i,j)-p_{\mathrm{\α}}^{(1,C)}(i,j-1)-p_{\mathrm{\α}}^{(1,R)}(i-1,j)---\left(4\right)$

   So obtaining the second order and the three rank partial differentials of " row " and " OK " both direction defines respectively shown in formula (5)～(8):

   $p_{\mathrm{\α}}^{(2,C)}(i,j)=d_{\mathrm{\α}}^1(i,j+1)-d_{\mathrm{\α}}^1(i,j)---\left(5\right)$

   $p_{\mathrm{\α}}^{(2,R)}(i,j)=d_{\mathrm{\α}}^1(i+1,j)-d_{\mathrm{\α}}^1(i,j)---\left(6\right)$

   $p_{\mathrm{\α}}^{(3,C)}(i,j)=d_{\mathrm{\α}}^2(i,j+1)-d_{\mathrm{\α}}^2(i,j)---\left(7\right)$

   $p_{\mathrm{\α}}^{(3,R)}(i,j)=d_{\mathrm{\α}}^2(i+1,j)-d_{\mathrm{\α}}^2(i,j)---\left(8\right)$

   For the brightness of r, g and three color channels of b is taken all factors into consideration, introduced the notion of gradient; Gradient is a kind of image enhancement technique based on the single order partial differential in Flame Image Process; The gradient G of RGB coloured image ^C(i, j) and G ^R(i, j) be respectively the single order partial differential of " row " direction and " OK " direction in three color channels of r, g and b absolute value with, they can add up the change that hides Info to three color channel same position places, have reflected that the integral body to coloured image changes;

   $G^C(i,j)=\left|p_r^{(1,C)}(i,j)\right|+\left|p_g^{(1,C)}(i,j)\right|+\left|p_b^{(1,C)}(i,j)\right|---\left(9\right)$

   $G^R(i,j)=\left|p_r^{(1,R)}(i,j)\right|+\left|p_g^{(1,R)}(i,j)\right|+\left|p_b^{(1,R)}(i,j)\right|---\left(10\right);$

   The co-occurrence matrix of 6 high-order partial differentials of described adjacent pixel location object is:

   Formula (11) calculates two " frequency " that adjacent pixels brightness occurs simultaneously on " row " direction, and all such frequency are formed " co-occurrence matrix " of pixel intensity;

   Principle according to calculating the co-occurrence matrix of two neighbor brightness on " row " direction obtains other 5 co-occurrence matrix formula; According to this principle, calculate " co-occurrence matrix " of above-mentioned 6 objects of adjacent two pixel position on " OK " direction.

   The pixel intensity co-occurrence matrix of described two color interchannels is:

   

   In the formula, α β ∈ { rg, gb, br}, corresponding two color channels; It is the frequency that capable, two the brightness value s in j row place of i and t occur simultaneously in the image that formula (12) is used for calculating α and two same location of pixels of color channel of β, and all frequency are formed " brightness " co-occurrence matrixs; According to and calculate two identical principles of color interchannel brightness co-occurrence matrix, obtain the co-occurrence matrix formula of these four objects of single order partial differential of single order total differential, second order total differential and " row " and " OK " both direction.
2. 2. based on the steganalysis method of pivot characteristic, it is characterized in that the computing formula of described gradient co-occurrence matrix is in a kind of steganalysis according to claim 1 system

   

   

   

   Co-occurrence matrix based on " gradient " is more responsive to embedding information; The gradient G that is divided into " row " direction according to gradient ^C(m is n) with " OK " direction gradient G ^R(m, n), and " symbiosis " be divided into " appearance simultaneously " such 2 kinds of situations of " row " adjacent position and " OK " adjacent position, obtains as above four formula.
3. 3. based on the steganalysis method of pivot characteristic, it is characterized in that described use histogram feature function calculation formula is (17) and (18) in a kind of steganalysis according to claim 1 system:

   $M_1^l=\frac{{\mathrm{\Σ}}_{k=0}^{\mathrm{\γ}/2-1}{k}^l\·c\left(k\right)}{{\mathrm{\Σ}}_{k=0}^{\mathrm{\γ}/2-1}c\left(k\right)}---\left(17\right)$

   L ∈ in the formula 1,2}, the amplitude of c (k) expression frequency k correspondence; γ is the frequency maximal value; Formula (17) is done the one-dimensional discrete Fourier transform and is asked its amplitude a histogram, obtains " differential characteristics function " c=|DFT (h) |, can calculate its single order statistical moment and second-order statistics square;

   $M_2^l=\frac{{\mathrm{\Σ}}_{k_1=0}^{\mathrm{\ζ}/2-1}{\mathrm{\Σ}}_{k_2=0}^{\mathrm{\η}/2-1}(k_1^l,k_2^l)\·c_2(k_1,k_2)}{{\mathrm{\Σ}}_{k_1=0}^{\mathrm{\ζ}/2-1}{\mathrm{\Σ}}_{k_2=0}^{\mathrm{\η}/2-1}{c}_2(k_1,k_2)}---\left(18\right)$

   A co-occurrence matrix is done two dimensional discrete Fourier transform and asked its amplitude, obtain corresponding differential characteristics function c ₂=| DFT ₂(h ₂) | after, use formula (18) calculated characteristics function at k ₁And k ₂The first-order statistics square of both direction and second-order statistics square obtain 4 features;

   Use as above formula, obtain 136 initial dimensional feature vectors from a width of cloth coloured image.