A robust detection algorithm for copy-move forgery in digital images

A robust detection algorithm for copy-move forgery in digital images

Presented by Issam Laradji

Authors: Yanjun Cao, Tiegang Gao, Li Fan, Qunting Yang

Course: COE589-Digital Forensics

Date: 18 September, 2012

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Outline

– Introduction– Challenges– Background Concepts– Related Work– Proposed Approach– Experimental Results– Summary

Most definitions were obtained from Wikipedia, others are from online tutorials

Introduction

Some statistics state that around 20% of accepted manuscripts are tempered– 1% are fraudulent manipulations– Innocent people can get framed of crimes they

didn’t commit– Negative social impact– Premature propaganda

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Challenges

Sophisticated tools– 3D Max, Photoshop– Automated lighting, and processing that

conceal forgery Increase of large size images

– High-definition images– Much more costly to process

4

Background Concepts

Normal Distribution– Used to describe real-valued random variables that cluster around

a single mean value

– The most prominent distribution

– All distributions areas add up to 1, bell-shaped

– Allows for tractable analysis

– Observational error in an experiment is usually assumed to follow a normal distribution

– Has a symmetric distribution about its mean

5Normal distribution formula

Background Concepts (2)

Energy of the image– Amount of information present:

• High energy: city, lots of details

• Low energy: plain, minimal details

Feature vector– N-dimensional vector of numerical features to represent

some object• Facilitates statistical analysis

• Explanatory “independent” variables used in procedures such as linear regression

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Feature vector cont.– Linear regression can be used to model the relationship

between independent variable X (Feature vector) and dependent variable Y

– least square is commonly used for fitting Time Complexity

– The time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the length of the variables representing the input

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Global and local features– Global features represent details about the

whole image• Color distribution, brightness, and sharpness

• Faster to process

– Local features represent more finer details such as the relationship between pixels

• Similarities and differences between pixels

• Much more costly in processing

8


Eigenvector & Eigenvalue– An eigenvector of a square matrix is a non-zero vector that,

when multiplied by the matrix, yields a vector that is parallel to the original

– The eigenvalue is the scalar value that corresponds to the eigenvector λ

In this case, [3;-3] is an eigenvector of A, with eigenvalue 1 (MATLAB syntax)

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Principal analysis component– Mathematical procedure that uses orthogonal

transformation

– Converts correlated variables to linearly uncorrelated variables called principal components

– Principal components are guaranteed to be independent only if the data set is normally distributed

– Identifies patterns in data• Highlighting their similarities and differences

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Principal analysis component cont.– Eigenvalue decomposition of data correlation

– Eigenvalues obtained can measure weights of different image features

– Main advantage• Data compression without much loss of information

– Applications• Data mining, image processing, marketing, and chemical

research

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Scale-invariant feature transform (or SIFT) – An algorithm in computer vision to detect and describe

local features in images

– Local image features helps in object recognition

– Invariant to image scale and rotation

– Robust to changes in illumination, noise, and minor changes in viewpoint

– Applications• Object/face recognition, navigation, gesture recognition, and

tracking

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Discrete Cosine transform– Transforms image from spatial to “frequency domain”

in which it can be efficiently encoded

– Discard high frequency “sharp variations” components which refines the details of the image

– Focuses on the low frequency “smooth variations”, holds the base of an image

13Zigzag scanningDCT basis (64)


Discrete Cosine transform cont.– Removes redundancy between neighboring pixels

– Prepares image for compression / quantization

– Quantization:

• Maps large set of values to smaller set

• Reduces the number of bits needed to store the coefficients by removing less important high frequency.

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Why DCT?– Approximates better with fewer coefficients as

compared to other contemporary transforms• However wavelet transforms is the new trend

– Less space required to represent the image features, hence easier to store in memory

– Applications:• Lossy compression for .mp3 and .jpg

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Related Work

Straightforward approach – Compare each group of pixels with the rest, and check

for similarities!

– Very impractical, exponential time complexity

– False positives could be high Related work

1. Exhaustive search

2. Fridrich used DCT-based features for duplication detection

• Sensitive to variations (additive noise)16

Related Work (2)

3. Haung et al. increased performance by reducing feature vector dimensions

However, none considered multiple copy-move forgery

4. Popescu: PCA-based feature, – Can endure additive noise – Low in accuracy

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Related Work (3)

5. Luo proposed color features as well as block intensity ratio

6. Bayram et al. applied Fourier-Mellin transform to each block, then projected to one dimension to form the feature vector

7. B. Mahdian, and S. Saic used a method based on blur moments invariants to locate the forgery regions

8. X. Pan, and S. Lyu took the advantages of SIFT features to detect the duplication regions

However, all these are of higher time complexity than the proposed approach!

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Proposed Approach

Basically, the algorithm divides the original image into overlapping blocks, then similarities between these blocks are calculated, based on some threshold the duplicated regions are highlighted in the output image

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Proposed approach advantages (contributions)

Improved version of copy-move forgery detection algorithm– Lower feature vector dimension

– Robust to various attacks: multiple copy-move forgery, Gaussian blurring, and noise contamination

– Lower time complexity

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Step 1- dividing the image into blocks Say we have an input image of size m x n If its not gray scale

The image is converted to Grayscale using the formulae: I=0.228R+0.587G+0.114B

Human eye is most sensitive to green and red That’s why most weights are on green and red

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Green channel gives the clearest image

Step 1- dividing the image into blocks (2)

The input image is split into overlapping blocks The standard block size is 8 x 8

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n

B

B

m

B

BGenerates

(m-b+1)(n-b+1) = N Blocks

Let ‘N’, and ‘b’ be the number of blocks obtained, and the height of the block respectively

Each block differ by one row or one column by its preceding block

Step 1- dividing the image into blocks (3)

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155 155 155 158 158 156 158 159

155 155 155 158 158 156 158 159

155 155 155 158 158 156 158 159

155 155 155 158 158 156 158 159

155 155 155 158 158 156 158 159

151 151 151 154 157 156 156 156

155 155 155 156 157 158 156 153

149 149 149 153 155 154 153 154

Original image …

Block size : 8 x 8

155 155 155 158 158 156 158 159

155 155 155 158 158 156 158 159

155 155 155 158 158 156 158 159

155 155 155 158 158 156 158 159

155 155 155 158 158 156 158 159

151 151 151 154 157 156 156 156

155 155 155 156 157 158 156 153

149 149 149 153 155 154 153 154

Dividing into blocks

Complexity: O(N) where N is the number of blocks

…

Step 2 – Applying DCT transform

For each block, DCT is applied We get DCT coefficients matrix

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155 155 155 158

155 155 155 158

155 155 155 158

155 155 155 158

420.75 37.70297 -3.25 4.136577

-2.98619 0.926777 2.1744 -0.32322

-0.25 -5.44081 0.75 -0.72292

2.589912 0.676777 -0.63007 0.573223

DCT Transfor

m

Original Sample block DCT coefficient block

Step 2 – Applying DCT transform (1) The block is compared with its 64 DCT

basis to get the correlation coefficients

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DCT basis (64)

155 155 155 158 158 156 158 159

155 155 155 158 158 156 158 159

155 155 155 158 158 156 158 159

155 155 155 158 158 156 158 159

155 155 155 158 158 156 158 159

151 151 151 154 157 156 156 156

155 155 155 156 157 158 156 153

149 149 149 153 155 154 153 154

… … … … … … … …

.. … … … … … … …

Discrete Coefficients

Step 2 – Applying DCT transform (2) The transformation allows us to focus on the low

frequency coefficients which hold the basis of the image Zigzag extraction is done so that coefficients are in order

of increasing frequency– Allows for zeroing the high frequency blocks

Time complexity: O(N x b x b)

26(a) the Lena image (b) Zigzag order scanning (c) the reconstruction image of Lena by using 1/4 DCT coefficients.

Step 3 – feature extraction

The coefficients matrix are divided and represented by four parts: C1,C2, C3, and C4

p_ratio=c_area/m_area is approximately 0.79 The circle block represents the low frequency, hence

decreasing the computation cost without affecting efficiency

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Generate matching feature ：

,

, ( , _ , 1,2,3,4)_i i

i

f x yv f x y c area i

c area

1 2 3 4 : , , ,feature vector V v v v v

420.75 37.70297 -3.25 4.136577

-2.98619 0.926777 2.1744 -0.32322

-0.25 -5.44081 0.75 -0.72292

2.589912 0.676777 -0.63007 0.573223

DCT coefficient block

C2C2C1C1

C3C3C4C4

Step 3 – feature extraction (2) Each v is quantized by its corresponding c_area Four features that represent the matrix are obtained vi is the mean of the coefficients value, corresponding to each ci

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DCT coefficient block

Matching features generated:

2

2

_ 4

_ 4 / 4 1, 2,3,4i

r

c area r

c area for i

1

420.75 37.70297 2.98619 0.926777v

≒ 145.2746

2

( 3.25) 4.136577 2.1744 ( 0.32322)v

≒ 0.8715

3

0.75 ( 0.72292) ( 0.63007) 0.573223v

≒ -0.0095

420.75 37.70297 -3.25 4.136577

-2.98619 0.926777 2.1744 -0.32322

-0.25 -5.44081 0.75 -0.72292

2.589912 0.676777 -0.63007 0.573223

C2C2C1C1

C3C3C4C4

Step 3 – feature extraction (3)

The extracted features are invariant to a lot of processing operations according to the results below

Time complexity of feature extraction: O(N x 4 x b x b)

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Step 4 – Matching

The extracted feature vectors are arranged in a matrix A

A is then lexicographically sorted , with time complexity of O(N log N)

Each element (vector) of A is compared to each subsequent vector to check if the thresholds Dsimilar, Nd, are satisfied i.e. the equations:

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1

2

( 1)( 1)

N B N B

V

VA

V

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1

_ ( , ) ( )k ki i j i i j similar

k

m match A A v v D

2 2( , )i i j i i j i i j dd V V x x y y N

Step 4 – Matching (2)

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145.2746,0.8715, 0.0095, 0.7716

196.6815,0.7681,0.2534,1.6032

145.1673,0.9771,0.0032, 1.0438

179.2334,4.8015, 0.4968,4.1904

A

Pr :

0.4, 25similar d

edict value

D N

2 2 2 21 116_ ( , ) (145.2746 196.6815) (0.8715 0.7681) ( 0.0095 0.2534) ( 0.7716 1.6032) 51.4625m match A A similarD

Not Similar

Not Similar


Step 4 – Matching (3)

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145.2746,0.8715, 0.0095, 0.7716

196.6815,0.7681,0.2534,1.6032

145.1673,0.9771,0.0032, 1.0438

179.2334,4.8015, 0.4968,4.1904

A

Pr : 0.4, 25similar dedict value D N


2 2

1 117( , ) 1 100 1 81d V V ≒ 127.28 5dN

SimilarSimilar

1 (1,1)V

117 (100,81)V

Detected image

Step 5 – Displaying duplicated regions Finally, regions showing the duplicated

regions are expected to be displayed

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The green rectanglesindicate a duplicated region

The computational complexities of extraction methods are compared

Time complexity analysis

As claimed, the total computation complexity:– O(N)+O(Nxbxb)+O(Nx4xbxb)+O(4NxlogN)

• Where N, b are the number of blocks and the height of the block respectively

– Questionable?• The computation complexity of matching was not

calculated which could be O(NxN)• However, they stated that their computational

complexity is dominated by the matching blocks

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Experimental results - environment Photoshop 8.0 2.59 GHz, AMD processor Matlab2009a software First dataset

– Gray images of size of 128 x 128– DVMM lab at Columbia University

Second dataset– uncompressed colour PNG images of size 768 x 521– the Kodak Corporation

Third dataset – Internet collection of images of size 1600 x 1000

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Experimental results - Setting Thresholds

Detection accuracy rate (DAR) and False positive rate (FPR)

– psis & “psis tilde” are set as the copy region, and the detected copy respectively

– psit and “psit tilde” are set as the tampered region and detected tampered respectively

– Questionable?• Vague formulas

• Nothing in the paper have shown what the symbols really mean

• Accuracy check is normally calculated in ratios

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Experimental results - Setting Thresholds (2) Selecting the circle representation for matching features

extraction can be challenging– Therefore, 200 images are randomly chosen from the three

datasets

– Series of forgeries are applied to them

– Different circle radius ranging from 2 to 6 are used, with 1 increment

– Optimum at r = 4, as shown in the diagram below

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Experimental results - Setting Thresholds (3) Choosing the threshold parameters, b, Dsimilar, Nd, and Nnumber, is also

challenging Colour images:

– The optimal values: 8, 0.0015, 120 and 5 for b, Dsimilar, Nd, and Nnumber,, respectively

Gray images:– The optimal values: 8, 0.0025, 25 and 5 for b, Dsimilar, Nd, and Nnumber,

respectively

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Experimental results – Effective testing To test the proposed method, gray images of different sizes are chosen:

– Tempered regions of sizes: 32x32, 64x64, 96x96, 128x128, are tested

39The detection results (from left to right is the original image, tampered image, detection results)

Experimental results – Robustness and accuracy test

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Signal-to-noise ratio (SNR): level of a desired signal to the level of background noise

(a)–(b) DAR/FPR performance with SNR, and (c)–(d) DAR/FPR performance with Gaussian blurring

Experimental results – Robustness and accuracy test (2)

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DAR/FPR curves for DCT, DCT-improved, PCA, FMT, and Proposed methods when the duplicated region is 64 pixels 64 pixels. (a)–(b) with different SNR levels, and (c)–(d) with Gaussian blurring

Experimental results – Demonstration

42The detection results for non-regular copy-move forgery

Experimental results – Demonstration (2)

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The test results for multiple copy-move forgery under a mixed operation


44The top row are tampered images with duplicated region size of 32 pixels × 32 pixels. Shown below are the detection results using our algorithm


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c) The analyzed image (Python script)•Duplicated regions were detected

b) the manipulated image

a) the original image


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c) The analyzed image (Python script)• Used --blcoldev=0.05• False positive• Duplicate regions were not detected

b) Manipulated image

a) Original image


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c) The analyzed image (Python script)• Partial part of the duplicated region was detected

b) the manipulated image

a) the original image

Summary The chart illustrates a summary of how the proposed

algorithm works

48Flowchart of the proposed scheme

Summary(2)

Automatic and efficient detection algorithm for copy-move forgery have been presented

Contributions– Outperforms contemporary algorithms in speed and storage

– Robust to various attacks: multiple copy-move forgery, Gaussian blurring, and noise contamination

– Different way of representing blocks (circles), reducing memory requirements

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References

A robust detection algorithm for copy-move forgery in digital images; By: Yanjun Cao a,*, Tiegang Gao b, Li Fan a, Qunting Yang

Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc. 22 July 2004. Web. 10 Aug. 2004

cao2012-image-forgery-slides.ppt; By: Li-Ting Liao The Discrete Cosine Transform (DCT): Theory and

Application1; By: Syed Ali Khayam A tutorial on Principal Components Analysis; By:

Lindsay I Smith

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A robust detection algorithm for copy-move forgery in digital images

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