基于高斯偏导数的自适应JPEG隐藏术分析新方法

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本文主要探讨了"基于高斯偏导数滤波器组的内容自适应JPEG隐写术的隐写分析"这一主题，发表在《电子成像》(Journal of Electron Imaging)期刊上，2017年第26卷第1期，文章编号为013011，DOI为10.1117/1.JEI.26.1.013011。作者包括 Yi Zhang、Fenlin Liu、Chunfang Yang、Xiangyang Luo、Xiaofeng Song 和 Jicang Lu，他们在各自的机构——郑州数学工程与先进计算国家实验室（a）、郑州科技学院（b）和西安通信学院（c）进行了这项研究。内容自适应JPEG隐写术是一种利用JPEG编码特性进行信息隐藏的方法，它可以根据图像内容的变化来调整隐藏策略，使得痕迹更加难以检测。而高斯偏导数滤波器组则是一种在图像处理中常用的工具，通过应用高斯函数对图像进行滤波，可以有效地提取特征并分析嵌入的隐写信息。这种方法的优势在于，由于高斯函数具有平滑滤波性质，能有效地保留图像的边缘信息，同时抑制背景噪声，这对于隐写分析中的细节特征提取至关重要。论文摘要指出，作者提出了一种基于高斯偏导数滤波器组的新型隐写分析方法。该方法旨在通过提取由内容自适应JPEG隐写术隐藏的图像中的特征，提高隐写分析的准确性和鲁棒性。这种方法可能涉及以下几个步骤： 1. **图像预处理**：首先对图像进行高斯滤波，以减少噪声干扰，并突出图像的关键特征。 2. **高斯偏导数计算**：利用高斯函数对图像进行一阶或二阶偏导数计算，这有助于识别潜在的模式变化和边缘信息，这些都是隐写信息可能存在的地方。 3. **特征提取**：从滤波后的图像中提取与JPEG编码相关联的特征，如频率域特性、纹理特征或者边缘方向等。 4. **分析与模型建立**：通过统计分析和机器学习技术，构建一个能够区分真实图像和含有隐写信息图像的模型，例如支持向量机(SVM)或深度神经网络(DNN)。 5. **性能评估**：通过实验验证，对比不同方法和模型在隐写分析任务上的表现，优化算法以提高隐写分析的敏感性和特异性。这篇研究论文深入研究了如何利用高斯偏导数滤波器组优化内容自适应JPEG隐写术的隐写分析，为隐写检测技术的发展提供了新的思路和方法，对于信息安全和数字版权保护具有重要意义。

feature extraction sources. Fortunately, these redundancies

do not exist in the filtered images generated by basis filters,

which can also represent the texture and edge information in

any arbitrary orientation. Therefor e, it should be possible to

obtain low-complexity sensitive features using basis filters.

Considering that Gauss partial derivative filter bank can

be used as basis filters to construct steerable filter, a stega-

nalysis feature extraction method based on Gauss partial

derivative filter bank is proposed in this paper. In the pro-

posed method, the filter bank is first constructed with eight

scales and the first five-order Gauss partial derivatives. Then,

the filtered images comprising rich texture and edge infor-

mation are generated. Finally, 5000-dimensional histograms

are extracted for detection. Experimental results for UED,

JUNIWARD, and SIUNIWARD indicate that the proposed

feature set results in competitive performance with fewer fea-

ture dimension compared with DCTR, PHARM, and GFR.

The rest of this paper is organized as follows. Section 2

describes steerable filter using Gauss partial derivative filter

bank as basis filters. The property of filtered image coeffi-

cients is first analyzed in Sec. 3, and then the feature extrac-

tion steps of the proposed method are outlined. In Sec. 4, the

recommended parameters of feature extraction are obtained

according to the experimental results, and the validity of the

proposed feature set is verified by comparing it with other

three steganalysis feature sets. The paper is concluded

in Sec. 5.

2 Steerable Filter

Steerable filter

has the advantages of translational invari-

ance and directional operability. Its most remarkable charac-

teristic is that it can be constructed in any orientation by

taking a suitable linear combination of a small number of

basis filters,

resulting in the capture of texture and edge

information in multiple orientations conveniently. It has

been successfully used for edge detection,

texture analy-

sis,

and image denoising.

Researchers have also applied

it to the steganalysis of stego images in color domain.

this paper, Gauss partial derivative filter bank is used as basis

filters to construct steerable filter.

The expression for Gaussian function with scale factor σ

is as follows:

EQ-TARGET;temp:intralink-;e001;63;289Gðx; yÞ¼

2πσ



−

þy

2σ



; (1)

where x; y ∈ R and its m-order partial derivative set is G

m;i

g;i ¼ 0;:::;m.ForG

m;i

, the orders of partial deriva-

tive with respect to x and y are m − i and i respectively:

EQ-TARGET;temp:intralink-;e002;63;215G

m;i

∂

m−i

∂x

m−i

∂

∂y

Gðx; yÞ; (2)

exactly signify m -order Gauss partial derivative filter

bank, and steerable filter f

m;θ

constructed on G

can be

expressed as

EQ-TARGET;temp:intralink-;e003;63;137f

m;θ

i¼0

m;i

ðθÞG

m;i

; (3)

where θ is the orientation of steerable filter and k

m;i

ðθÞ is the

weighting coefficient for G

m;i

EQ-TARGET;temp:intralink-;e004;326;752k

m;i

ðθÞ¼ð−1Þ





cos

m−i

ðθÞ sin

ðθÞ;i¼ 0;1;:::;m:

(4)

From the above, it can be seen that f

m;θ

is obtained by accu-

mulating the product of each G

m;i

and k

m;i

ðθÞ. Figure 1 gives

m-order Gauss partial derivative filter bank and correspond-

ing steerable filter f

m;π∕3

with scale parameter σ ¼ 0.8. It can

be seen that f

m;π∕3

is G

m;0

rotated by π∕3 along the positive

x-axis countercloc kwise. From Eqs. (3) and (4 ), it is clear

that if θ ¼ 0 deg, then f

m;0 deg

¼ G

m;0

. In fact, f

m;θ

can

be obtained by rotating f

m;0 deg

(or G

m;0

)byθ along the pos-

itive x-axis counte rclockwise.

The process of generating filtered image Z

m;θ

from spatial

image X and steerable filter f

m;θ

can be summarized as fol-

lows. First, construct basis filter G

m;i

and calculate weighting

coefficient k

m;i

ðθÞ according to parameters m, σ, and θ. Next,

generate basis filtered images Y

m;i

by convolving X with

m;i

. Last, filtered image Z

m;θ

can be generated by accumu-

lating the product of each Y

m;i

and k

m;i

ðθÞ. The process can

be expressed as follows:

EQ-TARGET;temp:intralink-;e005;326;516

m;θ

¼ X  f

m;θ

¼ X 

i¼0

m;i

ðθÞG

m;i

i¼0

m;i

ðθÞ

X  G

m;i

|ﬄﬄﬄﬄ{zﬄﬄﬄﬄ}

m;i

;

(5)

where “*” denotes the convolution without padding. Figure 2

shows the schematic of filtered image Z

3;π∕3

generated using

steerable filter. The input image is “70.pgm” in the Boss-base

1.01 image databa se. From Fig. 2, it can be seen that filtered

image Z

3;π∕3

is a linear combination of basis filtered

images Y

3;0

;:::;Y

3;3

Textures and edges appear in arbitrary orientations in

natural images. One approach to capture texture and edge

information in many orientations is to apply many versions

of the same filter (such as Gabor filter), each different from

the others by some rotation in orientation. The number of

convolution operations needed is equal to the number of ori-

entations. Another more efficient approach is to apply steer-

able filters as described above, in which case the number of

convolution operations needed is independent of the number

of orientations but is equal to the number of basis filters. The

number of orientations is usually greater than that of basis

filters. Although the second approach is more efficient

than the first, both approac hes have shortcomings in stega-

nalysis. For example, there may be redundancies in filtered

images generated by filters with different orientations, which

would result in increased feature complexity and reduced

sensitivity. Such as, the dimension and extraction time of fea-

tures are directly propor tional to the number of Gabor filter

orientations in GFR. When the number is less than 32, the

detection performance of features improves with increases in

the orientation number. Conversely, when the number is

greater than 32, the detection performance of features

reduces with increases in the orientation number. For steer-

able filter, the linear relationship with the basis filters results

in the filtered images generated in different orientations hav-

ing a certain association, e.g., Z

2;θ

having a linear relation-

ship with Z

2;0

and Z

2;π∕2

, which is not conducive to the

Journal of Electronic Imaging 013011-2 Jan∕Feb 2017

•

Vol. 26(1)

Zhang et al.: Steganalysis of content-adaptive JPEG steganography based on Gauss partial derivative filter bank

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