### ppt slides

```A Comprehensive Study on Third Order
Statistical Features for Image Splicing
Detection
Xudong Zhao, Shilin Wang, Shenghong Li and Jianhua Li
Shanghai 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 forgeries
http://www.fourandsix.com/photo-tampering-history
2. Proposed method
2.1 Preprocessing
8*8 block DCT domain
 X 11

X 21

 

 X m1
X 12

X 22



X m2

X ij  U X ijU ,
T
s
X 1m 

X 2m

 

X mm 
1  i, j  m
1

U
(
n
,
k
)

,
k  0, 0  n  7

2 2

U ( n , k )  1 cos(  (2 n  1) k ),
1  k  7, 0  n  7

2
16
E h ( i , j )  X ( i , j )  X ( i  1, j )
E v ( i , j )  X ( i , j )  X ( i , j  1)
2.2 Third order statistical features
States :  ,  ,..., 
Conditional Co-occurrence Probability Matrix
(CCPM)
1
2
N
 P ( 1 ,  1  1 )

P ( 1 ,  1  2 )

CCPM 



 P ( 1 ,  1  N )
P ( 2 ,  1  1 )

P ( 2 ,  1  2 )



P ( 2 ,  1  N )

P ( N ,  N  1 ) 

P ( N ,  N  2 ) 



P ( N ,  N  N ) 
2nd Markov
2
nd
 P ( 1  1 ,  1 )

P ( 2  1 ,  1 )

Markov 



 P ( N  1 ,  1 )
P ( 1  1 ,  2 )

P ( 2  1 ,  2 )



P ( N  1 ,  2 )

P ( 1  N ,  N ) 

P ( 2  N ,  N ) 



P ( N  N ,  N ) 
2nd CPM
 P ( 1 ,  1 ,  1 )

P ( 2 ,  1 ,  1 )
nd

2 CPM 



 P ( N ,  1 ,  1 )
P ( 1 ,  1 ,  2 )

P ( 2 ,  1 ,  2 )



P ( N ,  1 ,  2 )

P ( 1 ,  N ,  N ) 

P ( 2 ,  N ,  N )




P ( N ,  N ,  N ) 
• 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)
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.
```