中 華 大 學

中 華 大 學 碩 士 論 文

題目：應用重新取樣本質發展快速偽造圖片偵測 技術

Fast Forgery Detection with the Intrinsic Properties of Resampling Scheme

系 所 別：資訊工程學系碩士班 學號姓名：M09602021 石正崙 指導教授：周 智 勳 博 士 連 振 昌 博 士

中華民國 九十九 年 二 月

一

摘要

在本論文中，針對擁有來自不同照片物件的偽造圖片，為了讓圖片看起來比 較自然，勢必有一個物件必須做某種程度的放大或是縮小，於是我們提出一個以 重新取樣所遺留下來的特性為基礎的快速偽造偵測演算法，主要利用偵測重新取 樣的過程中所會產生隱藏在訊號裡面的週期特性來做為判斷的依據，進而判斷數 位影像的真偽。實驗結果顯示，我們提出來的方法能夠有效的偵測出部分偽造的 數位影像區域，並且執行效率上也能達到令人滿意的結果。

二

致謝

很幸運的能夠有機會在中華大學資訊工程學系碩士班中求學，度過值得回憶 的研究生活並順利取得到碩士學位。在這之中，首先我要感謝我的指導教授 連 振昌老師與周智勳老師在這段期間不僅在專業知識上對我的幫助與教導，在人生 的態度以及做人處世的道理上更是讓我獲益良多。同時，也感謝石昭玲老師以及 李建興老師在求學過程中給予課業上的教導以及平時的加油打氣。

其次，我要感謝智慧型多媒體實驗室中許許多多朝夕相處夥伴們，尤其感謝 揚凱、清乾、政達、昭偉、懷三、銘輝、雅麟、岳珉與佐民等學長姊在論文研究 上給予的莫大指導和幫助，偉欣和明修同學間相互的支持與督促，以及信吉、琮 瑋、雅婷、佩蓉和珮筠學弟妹的協助和陪伴，使得我的研究生生活得以過的多彩 多姿。

最後，感謝父母家人無時無刻對我的叮嚀與照顧，使得我能如期完成我的碩 士論文。

三

目錄

摘要... 一

致謝... 二

目錄... 三

第一章 簡介... 四

第二章 重新取樣與典型相關偵測技術 ... 五

第三章 預測誤差值分析 ... 六

第四章 實驗結果... 七

第五章 結論... 八

英文附錄... 九

四

第一章 簡介

近幾年來，高解析度和低價位的消費型數位相機越來越普遍，再加上方便取 得以及容易操作的數位影像修改軟體問世，一個發生在國內由新聞媒體刊登出來 的圖片被人證實經過人為的修改之後造成了不小的轟動，也不禁讓人開始懷疑所 接觸到的數位影像照片還保有多少真實性。事實上，在偽造影像偵測的研究領域 上已有針對不同的特性來提出探討，例如，同一張影像能找出兩個相似度極高的 區塊、偵測重新取樣所遺留下來的週期特性、數位相機感光元件所產生的雜訊是 否一致以及圖片中物體受光角度不同等等。在這裡我們所提出的方法屬於偵測重 新取樣這一大類，而在與同領域的方法比較下能有相近的正確率，並在執行速度 上有明顯的提升。第二章將會介紹重新取樣的基本步驟以及兩個典型的相關偵測 演算法，第三章則會介紹我們如何利用事前建置的權重表(weighting table)來 計算預測誤差值，第四章是實驗結果，第五章則是結論。

五

第二章 重新取樣與典型相關偵測技術

在 這 一 章 節 ， 我 們 首 先 介 紹 重 新 取 樣 主 要 分 成 三 大 步 驟 ， 放 大 取 樣 (up-sample)、內插(interpolation)和縮小取樣(down-sample)，並指出在內插 的過程中會使部分訊號與周圍的訊號有高度的相關性。隨後介紹兩個常見的重新 取樣偵測技術，Farid 演算法和 Mahdian 演算法。Farid 演算法利用經過內插後 的訊號與周遭的訊號有相關性，進而利用 EM 演算法訓練出相關係數，最後用相 關系數分析每個訊號是否屬於內插值的方式來檢驗分佈是否具有規則性。而 Madian 演算法則先証明重新取樣後的訊號的導數值俱有規律的變化，再分析其 訊號導數值並檢驗是否有週期性。

六

第三章 預測誤差值分析

這裡我們指出在縮小取樣(down-sample)的過程中，原始訊號與內插訊號的配 置存在著某種週期特性，而每個內插訊號又可視為由周遭的原始訊號線性組合而 成。因此，我們收集了許多不同的相 關係數組成不同的權重表(weighting tables)，並根據那些權重表去預測每一個參與內插計算的原始訊號，最後在固 定週期點位置的預測值與原始值會重疊，並在選擇到正確的權重表情況底下，兩 值的誤差會有較小值，而我們則利用這兩個值的誤差變化否有週期特性來判斷屬 於偽造圖片的可能性。

七

第四章 實驗結果

在實驗階段，我們準備了四種不同比例的放大取樣圖片代表偽造圖片，分別 是 5%、10%、20%和 25%，並與原始未經修改的影像各 40 張共 200 張影像來測試 我們提出的方法、Farid 演算法和 Mahdian 演算法的正確率。結果顯示 Farid 演 算法有最高的正確率(將近 100%)，但卻需要花費較多的時間在相關係數的訓練 上(每張圖約 30 秒)，而我們的方法則可以達到與 Farid 演算法相近的正確率(平 均 95%)，卻在執行效率上有較高的速度(每張圖約 3 秒)，最後，雖然 Mahdian 有最快的執行速度，但由於導數特徵較容易被灰階變化影響，因此正確率較不為 理想(平均 72%)。

八

第五章 結論

在論文中，我們利用不同的權重表去計算、分析預測誤差值來判斷是否含有 週期特性，進而判斷此數位影像的真實性，最後透過與兩個典型的偵測方式比較 正確率與執行速度，並證明了我們所提出來的方法能夠在維持高水準的正確率底 下並大幅提升執行效率。未來，我們更期望將實驗擴展到偵測其它型態的重新取 樣。

九

英文附錄

1

Fast Forgery Detection with the Intrinsic Properties of Resampling Scheme

Prepared by Cheng-Lun Shih Directed by Dr. Chih-Hsun Chou Directed by Dr. Cheng-Chang Lien

Computer Science and Information Engineering Chung-Hua University

Hsin-Chu, Taiwan, R.O.C.

February, 2010

2

Abstract

With the rapid progress of the image editing software, the unique stature of digital photographs as a definitive content recording no longer exists. In addition, a perfect image forgery can leave no visual clues on the tempered regions and makes us unable to judge the image authenticity. In general, the digital image forgery often utilizes the scaling, rotation or skewing operations that will involve the resampling and interpolation processes. With the detectable periodic properties introduced from the resampling and interpolation processes, we propose an novel method based on the intrinsic properties of resampling scheme to detect the forgery regions with the pre-calculated resampling weighting table and the periodic properties of vertical and horizontal prediction error even in the absence of digital watermark or signature. In the experimental results, the proposed method shows the robust property with the great change in gray level than the conventional methods in terms of efficiency and accuracy was near 95%.

Keywords—Image forgery, resampling, interpolation, forgery detection, intrinsic properties of resampling.

3

Contents

Abstract...2

Contents ...3

Chapter 1. Introduction ...4

Chapter 2. Basic Procedures of Resampling and Review of Typical Forgery Detection Methods...7

2.1 The Concept of Resampling Process ...7

2.2 Typical Forgery Detection Methods...8

2.2.1 Farid’s Method [7] ...8

2.2.2 Mahdian’s Method [11]...10

Chapter 3. Analyses of the Intrinsic Properties in Resampled Signal...13

3.1 Intrinsic Properties of Resampled Signal...14

3.2 Periodicity of the Prediction Error...15

Chapter 4. Experimental Results...22

Chapter 5. Conclusion...31

Reference ...32

4

Chapter 1. Introduction

In recent years, with the rapid progress of image editing software, it becomes a great challenge to verify whether the digital image is tampered or not because the image editing software can create a sophisticated digital forgery and leave no visual clues on the tampered areas. For example, The Liberty Times newspaper in January of 2008 (newspaper in Taiwan) published a photograph shown in Fig. 1-(b) in which the people “Miss Wang” has been removed intentionally and introduced a serious dispute.

(a) (b) Fig. 1. (a) The original image. (b) The tempered image.

In general, the digital forgery detection methods can be roughly categorized into the active [1-4] and passive methods [5-16]. In the active methods [1-4], the digital watermarking or signatures are hided in the image for the purpose of authentication [1-4]. Unfortunately, these approaches only work when the images are watermarked.

In addition, the embedded watermarks need to be robust enough to resist the various kinds of image attacks. On the contrary, the passive approaches [5-17] do not need any prior information for the forgery detection and can be further categorized into copy-pasted, manual blur edge, resampling, sensor noise pattern, light condition and compress format inconsistent methods. In [5], the author provided a method to

5

identify the digital forgery regions that are copied and pasted from the same image by applying the method of block matching. However, if the tempered region is cropped from different images, then the matching process will fail.

L. Zhou et al. [6] proposed a method to identify the digital forgeries by using the edge preserving smoothing filter in which the manual blur edge is discriminated from the defocus blur edge, then the erosion operation in mathematical morphology is proceed for manual blur edge. However, this method needs the smooth operation on the edge when forgeries are created.

Another typical method developed by H. Farid et al. [7] detects the digital forgeries by tracing the characteristic of the resampled signals. The major concept of this method is to apply the EM(expectation/maximization) algorithm to acquire of the resampling coefficients and then calculate the probability of the resampled signals.

Based on the frequency response of the probability map will exhibit a magnitude peak to identify the forgery patterns. Moreover, H. Farid [8] utilized the specific interpolation coefficients of color filter array in each brand of digital camera to identify the digital forgery. M. Kirchner [9] proposed a more efficient method by directly applying the converged resampling coefficients to detect the tempered regions.

As same as tracing the periodic characteristic of the resampled signals, S. Prasad et al. [10] and B. Mahdian et al. [11, 12] provided their method to extract the period property of the resampled signals base on analyze and describe the periodic characteristic of the covariance structure of the second order derivative which is different from Farid’s method.

In [13, 14], J. Lukáš et al. proposed a method that focus on the digital camera and take the imaging sensor noise as a unique stochastic characteristic to detect the

6

forgeries which lacks the pattern noise. Another approach, take light to be a considerable feature, M. K. Johnson et al. [15] addressed a key point that the light condition of the tempered area will be inconsistencies because of forgeries are usually splice together from tow or more different sources.

For the compress format, S. Ye et al. [16] proposed a method depends on the different blocking artifacts caused by quantization table inconsistent.

Each kind of forgery detection method can only solve one kind of forgery pattern.

In this study, we only address on the resampling forgery. Here, we propose a fast and blind method for detect the forgery portion from entire image base on the periodic properties of the correlation between samples, and analyze their prediction error by vary weighting tables from different resampling rate. For the reason to enhance the property of periodic, the project operation is used for creating a one dimension and more stable periodic result. Otherwise, in order to double check if the region has been tampered, both of the vertical and horizontal direction predicts error variation is considered simultaneously.

The rest of this paper is organized as follows. In section 2, the basic procedures about resample and two typical forgery detection methods are described. In section 3, a new forgery detection method based on the intrinsic properties of resampling is proposed, which can detect the tempered regions more efficiently. In section 4, we present the efficiency and accuracy analyses among the proposed method and other approaches. Finally, we summarize the contributions and future works in section 5.

7

Chapter 2. Basic Procedures of Resampling and Review of Typical Forgery Detection Methods

In this section, we will review the concept of resampling process in which the signal resampling process can be decomposed into three steps [7]. Furthermore, we will introduce two main detection algorithms used in the forgery detection.

2.1 The Concept of Resampling Process

Given a 1-D discrete signal x[i] with m samples shown in Fig. 2-(a), the algorithm of resampling the signal with a factor p/q can be describe in the following steps.

1. Up-sampling: Form the new signal xu[pi] = x[i], i = 1, 2,…, m. Otherwise, xu[i]

= 0 shown in Fig. 2-(b).

2. Interpolation: Convolve xu[i] with a low-pass filter h[i] ,i.e., xi[i] = xu[i]*h[i]

shown in Fig. 2-(c).

3. Down-sample: Take every q^th sample to generate the resampled signal, y[i] ≡ xd[i]

= xi[qi], i = 1, 2,…, n, shown in Fig. 2-(d).

1 32 63

number of samples

sample value

94

(a)

8

1 9

number of samples

sample value

6

(b)

1 96

number of samples

sample value

(c)

1 48

number of samples

sample value

95

(d)

Fig. 2. (a) Original signal with m samples (m=32) (b) Up-sampled signal, p =3. (c) Bi-linear interpolated signal. (d) Down-sample to samples ( =48), =2. n n q

2.2 Typical Forgery Detection Methods

Here, the two typical forgery detection methods for the resampling forgery techniques are introduced. These methods detect the forgery by tracing the clue of resampled signal and we will compare them with our proposed method in chapter 4.

2.2.1 Farid’s Method [7]

A well known forgery detection method was proposed by Popescu and Farid [7]

9

in which they assume that the interpolated samples are the linear combination of their surrounding neighbor pixels and try to train a set of resampling coefficients to examine the probability if the signal is a interpolated value. In this method, a digital sample can be categorized into two models: M1 and M2. M1 denotes the model that the sample is correlated to their neighbors; while M2 denotes that the sample isn’t correlated to its neighbors. The resampling coefficients can be acquired by the EM algorithm. The algorithm can be divided into two parts: E-step and M-step. In the E-step, they will calculate the probability for M1 model for every sample. In the M-step, the specific correlation coefficients are estimated and update continuously.

The detailed description of the EM algorithm is described in the sequel.

(I) E-step

The conditional probability of sample y[i] to M1 model is obtained by the following formula.

⎥⎥

⎥⎥

⎥

⎦

⎤

⎢⎢

⎢⎢

⎢

⎣

⎡ ⎟

⎠

⎜ ⎞

⎝

⎛ − +

−

=

∈

∑

−

= 2

2

1 2

] [ ]

[ 2 exp

} 1 ] [

| ] [

Pr{ σ

α π

σ

N

N k

ky i k i

y M

i y i

y (2.1)

(II) M-step

Minimize the quadratic error function defined in Eq. (2.2) by updating the correlation coefficients α^r iteratively.

(2.2)

2

] [ ]

[ ) ( )

( ⁼

∑

∑

−

= i

N

N k

ky i k i

y i

E α^r ω α

where ω(i)≡Pr{y[i]∈M₁|y[i]}

After applying the Farid’s method to the image, we can obtain a probability map in which the peaks of frequency response can identify the digital forgery. Fig. 3

10

illustrates that the high peaks of frequency response can indicate the image is resampled.

Fig. 3. The results of Farid’s method for original image for up-sample rate 10% and up-sample rate 20%.

2.2.2 Mahdian’s Method [11]

Another method proposed by Mahdian and Saic [11] demonstrates that the interpolation operation can exhibit periodicity in their derivatives. To emphasize the periodic property, they also employ a radon transformation to project the derivative magnitudes along a certain orientation and the radon operation is defined as:

(2.3)

( )

∫

D²{ } , | ²{ ( , )}| ρ

where, b(x,y) denotes the pixel in the block with size of R×R and D²{*} is the derivative kernel of order 2. The radon transform along angle θ (0 ~ 179^o) is defined in Eq. (2.5) and the rotation operation is defined in Eq. (2.4).

(2.4)

⎥⎦

⎢ ⎤

⎣

⎥ ⎡

⎦

⎢ ⎤

⎣

⎡

= −

⎥⎦

⎢ ⎤

⎣

⎡

′

′

y x y

x

cos sin

sin cos

θ θ

θ θ

11

(2.5) y

d y

x y

x y x b D

x′ =

∫

∞

−

) cos sin

, sin cos

(

| )}

, ( {

| )

( ² θ θ θ θ

ρ_θ

Fig. 4. Radon transformation along the angle θ.

After projecting all the derivatives to one direction and form 1-D projection vectors, the auto-covariance function can be used to emphasize the periodicity and defined as follows.

∑

=

i

i k

i k

R_ρθ( ) (ρ_θ( ) ρ_θ)(ρ_θ() ρ_θ) (2.6)

That is, this method focus on acquiring the strongest period presented in the autocovariance. The fast Fourier transformation of are also computed to identify the periodic peak which can indicate the existing of digital forgery, which is shown in Fig. 5.

ρθ

R

(a) (b)

12

(c) (d)

(e) (f)

(g) (h)

Fig. 5. (a) The original image. (b) Resampled image with up-sample rate 20%. (c) The magnitudes of row-based derivative projection for θ=90^o of (a). (d) The magnitudes of row-based derivative projection for θ=90^o of (b). (e) The auto-covariance of (c). (f) The auto-covariance of (d). (g) The frequency response of (e). (h) The frequency response of (f).

13

Chapter 3. Analyses of the Intrinsic Properties in Resampled Signal

As the description in last section, there exist two major drawbacks in the mentioned algorithms in section 2. For the Farid’s method [7], high computation cost for complex iterative computing procedure is required. It takes almost 5 minutes to generate the probability map for a image with resolution 512×512 pixels. For the method proposed by Mahdian [11], we found that the derivative kernel used in [11]

will destroy the periodicity of the correlation function at the high texture region.

Hence, in this study we try to investigate and analyze the intrinsic properties of resampling scheme and develop a new more efficient algorithm based on the intrinsic properties of resampling. The system flowchart is shown in Fig. 6.

14

Fig. 6. Flowchart of the proposed forgery detection system.

3.1 Intrinsic Properties of Resampled Signal

In this section, we firstly introduce the procedures of general resampling method.

In Fig. 7, the up-sampling process is performed in Fig. 7-(a) and the original values are denoted as red bars, then Fig. 7-(b) shows the interpolation operation that will filled the empty points with the linear combination of the adjacent signals’ values which are denoted as yellow bars. Finally, the samples selected for decimation process are shown in Fig. 7-(c) which is denoted as blue bars. Through the observation of the resampling process, it gives us an important clue to design a new forgery detection algorithm. The concept of new proposed method is based on the observation that the original value will appear periodically in the resampling process. According to this

15

property, the new detection scheme can be developed that will be illustrated in the section 3.2.

(a)

original value

interpolation value

(b)

Pick the

original Pick the

original Pick the

original

(c)

Fig. 7. An example for illustrating the intrinsic property of resampled signal. The scaling factor used is 6/5. (a) The up-sampling with original values (red bars). (b) Linear interpolation denoted as yellow bars. (c) Down sampling of signal in (b). The resampled signal is denoted as blue bars. The blue bars labeled the white node denote that the original values are chosen.

3.2 Periodicity of the Prediction Error

Obviously, every resampled value denoted as blue bar in Fig. 7 can be approximated by the linear combinations with the adjacent original values denoted as red bar with different weights according to their positions, i.e., the weighting in the

16

linear interpolation algorithm is propositional to the distance to their neighbors. In this study, we will pre-calculate the weighing tables for each resampling rates. If the resampling rate is known, then the original values can be reconstructed by the combination of the interpolation values.

Based on the periodical property of the original values selected from resampling, some of the reconstructed values would exactly overlap the original values in resampled signal (see the green bar in Fig. 8) and the error between the predicted value and the resampled value would be very small. Furthermore, the variation of the prediction error will exhibit the periodicity. However, the weighting table WT[i], i = 1, 2,…, up-rate-1, should be constructed in advance and then the prediction process is presented as follows shown in Fig. 8.

Fig. 8. The values (red bar) could be predicted by the resampled values (blue bar).

After a certain periodical time interval, the predicted value will overlap the original value denoted as green bar.

The predicted resampled values can be computed as Eq. (3.1), (3.2).

] [

* 6 ] [

* 5 6

. . .

] [

* 3 ] [

* 2 3

] [

* 2 ] [

* 1 2

i WT R i WT R B

i WT R i WT R B

i WT R i WT R B

R L

R L

R L

+

=

+

=

+

=

(3.1)

17

] 7 [

] [

* 6 6

. . .

] [

] [

* 3 3

] [

] [

* 1 2 2

5 4

1 2

1

i B WT

i WT pre R B

pre

i WT

i WT pre R B

pre

i WT

i WT R R B

pre

R L R

L R

L

− =

=

=

= −

=

= −

=

(3.2)

The prediction error values can be computed as Eq. (3.3).

Prediction error = |B7 – pre5| (3.3)

For the case of resampling rate 120%, the difference between pre5 and B7 will be very small. Furthermore, every time the window for calculating the sample prediction slides (shown in Fig. 9), the prediction error will increase and then decrease to the minimum distance until the window slides to the next periodical position (here is B14, B21…). Such a periodical property makes the sequence of prediction error distribute

periodically shown in Fig. 10. In order to enhance this property, the projection operation is also performed for every row and column (two directions are considered separately) before we utilize the frequency analysis to detect the forgery patterns (peaks in frequency response). If the test samples are not resampled or the wrong weighting table is selected, the distribution of prediction error would be irregular.

18

. . .

Fig. 9. The sliding window for calculating the sample prediction using the weighting table.

(a) (b)

(c) (d)

19

(e) (f)

Fig. 10. (a) The original image. (b) Resampled image with up-sample rate 20%. (c) The magnitudes of row-based prediction error variation projection (with 20% weight table) of (a). (d) The magnitudes of row-based prediction error variation projection (with 20% weight table) of (b). (e) The frequency response of (c). (f) The frequency response (d).

To develop an automatic forgery detection method, there are two main criteria should be considered in our algorithm. The first one is the position of the peak and the second one is the peak ratio. According to the different weighting tables (different resampling rate) for the forgery detection and the specific periodical property for each resampling rate, the expected position where the peak occurs for each weighting table could be forecasted. Then, we can match the peak position to the forecasted position where the specific resampling rate generates and verify the existence of digital forgery.

In this study, the tempered image can be discriminated from the original image according to the ratio that calculated by the spectrum magnitude in the forecasting position and the average magnitude. If the ratio is larger than a specified threshold t, we can identify that existence of digital forgery. Fig. 11-(a) shows the ratio distribution of the forecasted position with original images(blue curve) and the correct table for forgeries(red curve) observed from 2560 images (128×128), Fig. 11-(b) shows the threshold selected to separate the red curve and the blue curve away.

20

0 5 10 15 20 25 30 35

Number of samples

The ratio

original signal resampled signal

(a)

0 500 1000 1500 2000 2500

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 5.2 5.6 6 6.4 6.8 7.2

Threshold t

The quantity separated by t

(b)

Fig. 11. (a) The ratio distribution of the forecasted position in frequency domain with resampled signal (red curve) and the original signal (blue curve). (b) The distribution of threshold selected to discriminate the red curve and blue curve(increase 0.1 for each time, and the maximum appear in 4.6).

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Pseudo Cod

--- Initial

choose a resample rate r for test

set a specific weighting table WT[i] by r

define R is the ratio of frequency magnitude between expected position and average FOR the number of image width- period

Initial the first predicted value FOR the number of rate period

Progressing the predicted values ENDFOR

Record the prediction error for each rate period Projected the prediction error to one dimension signal ENDFOR

Analyze the frequency response of the one dimension signal IF R > threshold AND peak exist in the right position THEN

Forgery identified ELSE

Original image ENDIF

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Chapter 4. Experimental Results

In this section, the efficiency and accuracy for Farid’d method [7], Mahdian’s method [11], and the proposed method are analyzed. The experimental database is constructed with 160 gray level images with resolution 512×512 and each image is partial tempered in BMP format. The image tempering is based on the resampling process with the different bi-linear sampling rates: 105%, 110%, 120% and 125%.

The flowchart of the proposed system is shown in Fig. 12. The forgery detections are performed by scanning the image with the block size of 128×128 pixels.

Fig. 12. The flowchart of the proposed method.

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In order to analyze the accuracy of forgery detection, we firstly illustrate the rules of the judgment for each method, then, introduce some important results generated from EM-based algorithm, derivative-based, and the proposed methods.

The forgery detecting criteria for each method is judging the ratio greater than threshold or not, in Farid’s method we choose the first maximum and second maximum magnitude of the frequency response in two dimension(usually produce by the period of vertical and horizontal direction) and ratio the average of the two maximum to the global average. In Mahdian’s solution, the peak must greater than it’s neighbors in gradually, here we considered two units for each side. Finally, we ratio the peak magnitude to the local average and keep the maximum ratio for examine. In our method, we ratio the magnitude of frequency response in expected position to the average for vertical and horizontal directions and average both two ratios as criterion.

Fig. 13 is the resampled image with rate 120%, which is used as the tempered image for analyzing the detection accuracy for the three methods.

Fig. 14-(a) shows the probability map produced by the Farid’s method and Fig.

14-(b) shows the frequency response of the probability map. Fig. 15-(a) shows the radon transformation of the derivative along horizontal direction, Fig. 15-(b) shows the auto-covariance of Fig. 15-(a) and Fig. 15-(c) shows the frequency response of the auto-covariance values. The prediction error produced by our method is shown in Fig.

16-(a). Fig. 16-(b) presents the frequency response of the prediction error. An obvious drawback of the Mahdian’s method is that the weak periodical patterns occur at the high texture regions shown in Fig. 15-(c). The accuracy of forgery detections for several methods are analyzed in Table 1. The detection rate shows that the proposed method outperforms the Mahdian’s method [11].

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Fig. 13. The resampled image.

(a) (b)

Fig. 14. (a) The probability map of Fig. 13 produced by the Farid’s method. (b) The frequency response of (a).

(a) (b)

(c)

Fig. 15. (a) The radon transformation output of Fig. 13 by the Mahdian’s method. (b) The autocovariance of (a). (c) The frequency response of (b).

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(a) (b)

Fig. 16. (a) The prediction error of the tempered image shown in Fig. 13, which is generated by the proposed method. (b) The frequency response of (a).

Table 1. The accuracy analysis for the methods of our, Farid’s and Mahdian’s with 40 resampled images for different rates.

Farid’s method Our method Mahdian’s method

Up-sampli ng rate

5% 10% 20% 25% 5% 10

%

20% 25% 5% 10% 20% 25%

Positive 40 40 40 40 40 40 40 40 40 40 40 40

Negative 40 40 40 40 40 40 40 40 40 40 40 40

True positive

40 39 40 40 38 39 40 40 21 22 37 37

True

negative 40 40 40 40 35 37 38 38 25 33 28 30

Accuracy 100

% 98.7

% 100

% 100

% 91.2

% 95

% 97.5

% 97.5

% 57.5

% 68.7

% 81.2

% 83.7

%

The ROC curves with different up-sampling rate for Farid’s method, Mahdian’s method, and our method are shown in Fig. 17.

5%

0 0.2 0.4 0.6 0.8 1

0 0.5 1

FPR

TPR

Farid Mahdian our

10%

0 0.2 0.4 0.6 0.8 1

0 0.5 1

FPR

TPR

Farid Mahdian our

(a) (b)

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20%

0 0.2 0.4 0.6 0.8 1

0 0.5 1

FPR

TPR

Farid Mahdian our

25%

0 0.2 0.4 0.6 0.8 1

0 0.5 1

FPR

TPR

Farid Mahdian our

(c) (d)

Fig. 17. The ROC curves of (a) Up-sampling 5%. (b) Up-sampling 10%. (c) Up-sampling 20%. (d) Up-sampling 25%.

Figures 18-20 show the detection results of the proposed method for different resampling rates with two block sizes. In Fig. 18, the man’s head in Fig. 18-(b) is cropped and replace the head region in Fig. 18-(a) to compose the forgery image shown in Fig. 18-(c), Fig. 18-(d), Fig. 18-(e) shows the 64×64 and 128×128 block size detection result individual. Fig 19-(a) shows an original bottle image and Fig. 19-(b) shows that a resized bottle is put on the left side of the tempered image. Figures 19-(c) and 19-(d) show the detection results with different block sizes. In Fig. 19-(d), the smooth region in the bottle can’t be detected because of lacking smooth texture information. In Fig. 20-(c), the tempered image is created from cropping region of man sitting in front of his own desk in Fig. 20-(b) and replacing the seat region in Fig.

20-(a). Figures 20-(d) and 20-(e) show detection results with the 64×64 and 128×128 block sizes.

In this series experiment, we discovered that the smaller block size in Fig. 18-(d) is much easier to interfere with the low frequency noise, otherwise, the small block size has a higher probability to obtain the over smooth area and failed the detection, shown in Fig. 19-(d).

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(a) (b)

(c)

(d) (e)

Fig. 18. (a) Original image. (b) Image with up-sample rate 5%. (c) Forgery image composed from (a), (b). (d) Detection result with 64×64 block size. (e) Detection result with 128×128 block size.

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(a)

(b)

(c) (d)

Fig. 19. (a) Original image. (b) Forgery image composed from up-sample (a) 10% and put the bottle near beside. (c) Detection result with 64×64 block size. (d) Detection result with 128×128 block size.

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(a) (b)

(c)

(d) (e)

Fig. 20. (a) Original image. (b) Image with up-sample rate 20%. (c) Forgery image composed from (a), (b). (d) Detection result with block size 64×64. (e) Detection result with block size 128×128.

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In addition, we compare the efficiency among Farid’s method [7], Mahdian’s method [11] and our method with the PC with 1.8 GHz. The efficiency analysis is shown in Fig. 21. Here, we perform the efficiency analysis from block size 64×64 to 512×512 and assume there are 21 weighting tables according resampling rates used in [7].

Fig. 21. Time cost comparison chart.

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Chapter 5. Conclusion

In this thesis, we propose a block-based forgery detection method by the periodic property of the original value chose from resample scheme, and using the different weighting tables to examine whether the image has a matching period or not. The results of experiment shows the high accuracy of our method that is much robust than Mahdian’s method [11] to serious change in gray level. The accuracy of proposed method was near 95% and cost 50 seconds to the 512×512 image which has approach detection rate but much faster than Farid’s method [7]. At the last, we show the great ability of automatically detecting partial tempered image with proposed algorithm.

The future works will focus on the detection of rotated images and the temper with different interpolation method.

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