A Novel Approach for Detecting Forged Image

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A Novel Approach for Detecting Forged Image

Zhen Zhang#!, PeiYing Zhang*2, Zhou Yu #3

# School of Electrical Engineering,

Zhengzhou 450001, China

3

Zhengzhou University

subaina@http://wendang.chazidian.com

*

Zhengzhou College of Animal Husbandry Engineeringy

Zhengzhou 450001, China

2

15936220686@http://wendang.chazidian.com

Abstract-The advent of digital technology has not only brought about benefits but also some problems, such as the ease of creating image fogery. In this paper, we present a novel approach for tamper localization, which is based on the edge detection. We first process the input image with a smoothing filter, and then we use the LOG (Laplace-Gaussian Operator) edge detector for edge detection. By the evidence from the above steps, we can finally make judgement on missed edge: if the forged region is connected and its size is not less than 0.85% of the whole image size, we can judge that this forgery is significative. The results of our experiments illustrate that the novel approach can accurately detect the trace of blur operation when composite forgery happens. Besides, this approach can precisely locate the forged region. extracting, smoothing filter

Keywords-tamper detection, tamper localization, LOG, edge

image is created by taking an region from one image and

pasting it into another one. In actual process of regional copy, the copied region usually needs to be preprocessed, such as being rotated, resized and so on. Before pasting, operations like blur, adding noise and others are used for modification, in order to ensure the visual authenticity. Therefore, it is valuable to research the detection of image compostion and image retouch. In this paper, we propose an approach based on Gauss filtering and edge detecting algorithm, this approach is effective for tamper localization. The experiment results illustrate that this approach can accurately detect the blur operation traces, and can precisely locate the boundary in the composite image. II.

FEATURES OF SYNTHESIS IMAGE AND THE INFLUENCE THEY

BRING To THE STANDARD DEVIATION

I.

INTRODUCTION

With the development of image processing technology and multimedia technology, digital image has gradually taken the place of original analog photograph, and many image editing and processing software are used to deal with images, therefore, the forgery of digital image has become increasingly easy and indiscoverable. Some images are forged only for artistic use, some are only for personal use, which doesn't bring about trouble. However, some other forged images have great impact on our society, and bring serious threat to the security of image content. For those reasons, before using digital image, people may frequently doubt about the completeness and the authenticity of the image. Therefore, it is valuable to develop credible methods to detect whether a digital image is forged.

Digital image forensics can be divided into active forensics and passive forensics. The active forensic technology includes watermark technique and digital signature technique. Usually, digital images are not embedded with fragile watermark, and there is no supplementary information that can be used. Hence, the passive forensic is more realistic for image forensics.

In recent years, the passive forensic of digital image has been concerned by scholars both at home and abroad, and some preliminary research has been done. Hany farid classified forged images into six categories: composite images, morphed images, retouched images, enhanced images, computer graphics and painted images [1]. In practice, the most commonly used one is composite images. Composite

A. Features of Synthesis Image

In order to reduce visual distortion, people who tamper images usually blur the edge of forged region when they composite images, this blur operation will smooth the edge's gray mutation, in other words, the edge's contrast will decrease. The basic principle of blur operation is to average the pixel values within the local neighborhood, its purpose is to dilute the composite edge caused by forgery. In the blurred image, the contrast between target edge and the background pixels around it decreases, resulting in the mix of the edge and non-edge, so there will be many pixels to respond to the edge, which means we can not locate targets accurately. In 1980s, lCanny proposed three optimal criteria of edge detection operator: great detection performance (missed rate and error rate are low), localization precision and single-edge response [2]. Therefore, the blur operation goes against the optimal criteria for edge detection, and influences the accuracy of target detection. To a large extent, the standard deviation of gray can be used to characterize the contrast between the target and background. Set g(i,j) for the pixel grayscale of the (i,j) in the image, where the size of the image is M x N, i=1,2,3, ..., M, j=1,2,3, ..., N, 11 and (J are respectively the average grayscale and the standard deviation, then

11-

MXN??g(i,j)

1

M

N

(1)

978-1-4244-6439-5/1 0/$26.00 ©2010 IEEE

958

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a=

The mean and standard deviation reflect the brightness and contrast of the image, the greater the mean is, the higher the brightness is; the greater the standard deviation is, the higher the contrast is.

a1[0'= ---_b (r (n()) ) r

r 2 2' r 2 aE[1,r-1], then f(a) is a

Set f(a)= 2(a-"2) +

There:

i?1

(5)

The blur operation on the edge will smooth the edge's gray mutation. The following data is an example that shows how the blur operation influences the standard deviation of gray. The function for one-dimensional square-ware data (solid line) is defined as

quadratic parabola about a, the minimum can be obtained at a=r/2, the maximum can be obtained at a=1 or a=r-l, Therefore

(7)

E[ 0, nj]U[n2, n] Take (7) into (6), we can get (3) b tE(npn2) 2(r-1) (b-a)2 0"2O'2 (8) _n() The mean and variance of the function are defined as 2 r222

?=((n-n' )a+ n' b)/n,a=[(n-n' )(a_?)+ n' (b-?)]/n ,where That means 0" 0' ,namely, the blur operation decreases , =n-nn 2l the contrast of data, this may bring difficulty for the target

r2 r2

>

> °

<

t

detection and decrease the accuracy of target identification.

III. LINEAR SCALE SPACE

Commonly used scale spaces includes linear scale space, nonlinear scale space, mathematical morphology scale space and shape scale space. These four basic scale-space make up the main research for computer visual scale-space. At present, the international visual multi-scale analysis basically belongs to these four categories. In image processing, the introduction a

of scale space has aroused great interest. The scale space theory has played an irreplaceable role in many fields, such as

o image compression, image smoothing, image denoising, edge 01 02 n

detection and the localization of invariant feature points.

In the four categories of scale space mentioned above, this paper adopts the most common one, linear scale space. Linear Fig. 1. one-dimensional square wave and the data of slow blurring

scale space is known as Gaussian scale space, it was firstly

Set the spread radius of blurred edge of the data (dotted line proposed by Witkin[3], and then was further improved by in the figure) is r, and then the blur function can be given by Koenderink and other scholars[4]. Under a series of

reasonable assumptions, Koenderink and Lindeberg proved the only kernel of scale space is the Gaussian equation, namely the Gaussian kernel is the only transform kernel to achieve scale transform. Besides, Gaussian function is a

(4) f'(t) smooth function that will not increases new extreme points

when the scale rises. Therefore, the linear scale space can be defined as the equation L(X), which is the convolution of a variable-scale Gaussian equation g(X) and the input image I (X):

(9) L(X, ) =g(X, )* I(X) The mean and standard deviation are

where I:RD -) R, L: RD X R+ -) R, Gaussian function It is easy to prove that = , and the variance can be

g(X, ) is given by:

given by

b

atE [0, nl-r] U[n2, n] -i)a+ (r ib = ia+(r-i)r b t=n-i,i=1,2, ... r-1 , 2 r

fi' , 0" .

fi' fi 0"2 = -fi)2 -n -r -fi)2 [en (n -+ + + + l)(a l)(b r

r

i?j

0' 0' 0'

1 O'X= (,) DI2 g(2JZ"O')

e

(10)

959

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It is easy to prove that L(X, (J) is exactly the solution of thermal diffusion equation given by:

D 2

8aL =_ VL = L 8xiXjL

2 2 i,j=i

-

{II

L(O,X) =L (X)

(11)

As can be seen from figure 2, the first derivative of the

gray profile has a step at the image mutation. Therefore, the amplitude of the first derivative can be used to detect if the edge exist or not, and according to the change of the second derivative's amplitude, the location of the edge can be obtained. For digital images, difference operation is often used to approximate differential operation.

Thermal diffusion equation belongs to the category of

physics, it describes the change process of heat distribution B. The Selection of Edge

The classical edge detection is based on the original image, over time. Thermal diffusion equation is linear, so the above

analysis of multi-scale is also referred to as linear scale space for each pixel, we inspect the step change of gray in its certain method. When the scale factor of Gaussian equation increases, nearby region. For edge detection, we use the variation of the the small-scale information, which is got from the convolution first or second directional derivative nearby the edge. There of Gaussian equation and input image, will be removed. With are several commonly used edge detection ways, such as the increase of the scale factor, the original image is bound to differential edge detection, Roberts edge detection operator, be smoother and smoother, therefore, sometimes the scale Sobel edge detection operator, Log edge detection operator, factor of Gaussian equation is also vividly called the Canny edge detection operator and so on.

As the differential detection of the edge demands the smoothing factor.

As the linear scale space reflects the thought of visual direction of the difference must perpendicular to the direction multi-scale analysis well, it is widely used in many fields, of the edge, which means that we need to deal the image with such as image filtering, deep structural analysis and so on. difference operation in different directions, but this will cause Moreover, the linear scale space also has other significant additional operation. The gradient made up of the first features: on one hand, the diffusion process that described by derivative is a vector that has both size and direction, thermal diffusion equation is isotropic, so when the image is therefore, compared with scalar, this vector has huger data smoothed, the spread of the gray value are the same in every storage. The LOG operator firstly use Gaussian function to direction, this would inevitably lead to the blur of the edge. smooth image, therefore, it is better at noise suppression, but On the other hand, contrast invariance and linearity are at the same time, it may smooth the original edge, and this conflicting, the linearity of thermal diffusion equation will cause that some edges can not be detected. In addition, determines that it can not satisfy the contrast invariance, for the choice of Gaussian distribution factor (J has great impact example, with the scale increasing, the image gradually on the result of edge detection. The larger (J is, the more become smooth, and the detail of the image gradually become abundant details can be obtained from the image, but the blurred, therefore the contrast has a significant change. For ability of noise immunity decreases, which may causes false this reason, the smoothing scale is the key to this paper. edge, otherwise, the ability of noise immunity increases, but

the accuracy of edge detection decreases, and many true edges

IV. THEORETICAL ANALYSIS OF EDGE DETECTION OPERATOR

may be lost. Therefore, this paper adopts Laplace-Gaussian

AND THE SELECTION OF EDGE

operator, which is a second derivative operator. The results of experiments show that LOG operator is the second derivative A. Theoretical Analysis of Edge Detection Operator

operator used to the operation of the two-dimensional

The edge is one of the basic characteristics of image,

function, it has nothing to do with the direction, and it is not

people mainly rely on the edge to identify the target. The edge sensitive to the orientation, so the calculated amount is smaller. refers to the set of pixels whose gray have spatial mutations.

The edge that is easy to get lost is defined as:

The mutation of gray is usually described and detected by

V2=V2[(X,y)]* f(x,y) (12) gdifferential coefficient. There are three common kinds

mutation of gray: the step-like, sloping and roof-like[5]-[7]. Where G is Gaussian function, the convolution kernel is

given by

profile First

derivative

2+ 2 2+ 2

2 2 X Y X Y

--V =V [g(x,y)]=K[ 2(]exp2) 2 (J 2(J

(13)

The 5 X 5 template used in this process is:

-2 -4 -4 -4 -2 -4

0 8 0

8

0 8 0

Second

derivative

Step-like edge

Roof-like edge

Sloping edge

-4 -4 -4

(14)

-4 -4

24

8

Fig. 2. edge of image and derivative rule of edge

-2 -4 -4 -4 -2

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