A Comprehensive Study on Third OrderStatistical Features for Image Splicing Detection

Xudong Zhao, Shilin Wang, Shenghong Li and Jianhua LiShanghai Jiao Tong University, Shanghai P. R. China

1. Introduction

• Digital Image Forensics:Active detection methods Watermarking, fingerprint, signature, etc.Passive detection methods Pixel based, camera based, physics based,

statistical features based, etc.

Latest image forgerieshttp://www.fourandsix.com/photo-tampering-history

2. Proposed method

2.1 Preprocessing 8*8 block DCT domain

mmmm

m

m

XXX

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21

22221

11211

mjiUXUX sij

Tij ,1,

1( , ) , 0, 0 7

2 21 (2 1)

( , ) cos( ), 1 7, 0 72 16

U n k k n

n kU n k k n

),1(),(),( jiXjiXjiEh

)1,(),(),( jiXjiXjiEv

2.2 Third order statistical featuresStates :Conditional Co-occurrence Probability Matrix

(CCPM)

N ,...,, 21

),(),(),(

),(),(),(

),(),(),(

1211

2212211

1112111

NNNNN

NN

NN

PPP

PPP

PPP

CCPM

2nd Markov

),(),(),(

),(),(),(

),(),(),(

2

2111

2212112

1211111

NNNNN

NN

NN

nd

PPP

PPP

PPP

Markov

2nd CPM

),,(),,(),,(

),,(),,(),,(

),,(),,(),,(

2

2111

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1211111

NNNNN

NN

NN

nd

PPP

PPP

PPP

CPM

• Class separability, an overview

• (a) (b) (c) Lda projections of (a) CCPM, (b) 2nd Markov and (c) 2nd CPM. All the

samples are extracted from Columbia Image Splicing Detection Evaluation Dataset.

2.3 Feature Dimensionality Reduction

Dimensionality of Proposed features N3 dimensional feature for each direction. (e.g. 7 states CCPM, there are totally 2*73 dimensional

features.)

PCA for Dimensionality Reduction PCA is a linear transform that maps the original

features onto an orthogonal vectors spanned subspace.

Coefficients and variances distributions of third order statistical features

3. Experimental Results and Performance Analysis

3.1 Image Dataset Columbia Image Splicing Detection Evaluation Dataset

3.2 Classifier Support vector machine (SVM) Radial basis function (RBF) ½ for training and the left ½ for testing Detecting accuracy is the average of 30 runs.

3.3 Detection Results Comparisons

(a) (b)

(a) (b)

• 3.4 Robustness Test Jpeg compression Gaussian low pass filtering Image scaling

Detecting results over Jpeg compressed image dataset

Detecting results over Gaussian low pass filtered image dataset

Detecting results over scaled image dataset

4. Conclusions

Third order statistical features, more discriminative information compared with lower order features

Detection performance of CCPM in Block DCT domain outperforms that of 2nd Markov and 2nd CPM

PCA maps the most discriminative features onto the first several principal components, which reduce the dimensionality greatly.

Robustness of both third order features and second order features will be further improved.