Journal of Information Security, 2010, 1, 11-22
doi:10.4236/jis.2010.11002 Published Online July 2010 (http://www.SciRP.org/journal/jis)
Fast Forgery Detection with the Intrinsic
Resampling Properties
Cheng-Chang Lien, Cheng-Lun Shih, Chih-Hsun Chou
Department of C om put er Science and Inform at i on E ngineering,
Chung Hua University, Hsinchu, Taiwan, China
Received June 21 , 2010; revised July 20, 2010; accepted July 25, 2010
Abstract
With the rapid progress of the image processing software, the image forgery can leave no visual clues on the
tampered regions and make us unable to authenticate the image. In general, the image forgery technologies
often utilizes the scaling, rotation or skewing operations to tamper some regions in the image, in which the
resampling and interpolation processes are often demanded. By observing the detectable periodic distribution
properties generated from the resampling and interpolation processes, we propose a novel method based on
the intrinsic properties of resampling scheme to detect the tampered regions. The proposed method applies
the pre-calculated resampling weighting table to detect the periodic properties of prediction error distribution.
The experimental results show that the proposed method outperforms the conventional methods in terms of
efficiency and accuracy.
Keywords: Image Forgery, Resampling, Forgery Detection, Intrinsic Properties of Resampling
1. Introduction
In recent years, with the rapid progress of image proc-
essing software, it becomes a great challenge to verify
whether the digital image is tampered or not because the
image processing software can create a sophisticated
digital forgery and leav e no visual clues on the tampered
regions. For example, the Liberty Times newspaper in
January 2008 (newspaper in Taiwan) published a photo-
graph shown in Figure 1(b) in which the picture “Miss
Wang” had been removed intentional l y .
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 hid in the image for the
purpose of authentication [1-4]. In addition, the embed-
ded watermarks need to be robust enough to resist the
various kinds of image attacks. On the contrary, the pas-
sive approaches [5-17] do not need any prior information
for the forgery detection and can be further categorized
into the methods of detecting copy-pasted regions, defo-
cus blur edges, resampling, sensor noise pattern, differ-
ent lighting conditions and block artifact inconsistency.
In [5], the author provided a method to identify the
digital forgery regions that are copied and pasted from
the same image by applying the method of block match-
ing. However, the matching process can fail if the tam-
pered region is cropped from different images. 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 and the erosion operation is applied for detecting
the manual blur edge. Another typical method developed
by Popescu [7] detected 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 the resampling coef-
ficients and then calculate the resampling probability
map. Based on the spectral analysis of the probability
map, the magnitude peak can be used to identify the for-
gery patterns. Moreover, Popescu [8] utilize d the specific
interpolation coefficients of color filter array for each
brand of digital camera to identify the digital forgery.
Kirchner [9] proposed a more efficient method by di-
rectly applying the converged resampling coefficients to
detect the tempered regions. As same as tracing the pe-
riodic characteristic of the resa mpled signals, Prasad [10 ]
and Mahdian [11,12] proposed their method to extract
the periodical property of the resampled signals based on
analyzing the periodic characteristic of the covariance of
the second order derivatives. In [13,14], Lukáš et al.

12 C.-C. LIEN ET AL.
(a)
(b)
Figure 1. (a) The original image; (b) The tampered image.
proposed a method that utilize the imaging sensor noise
as a unique stochastic characteristic to detect the forger-
ies. Johnson et al. [15] discovered that the light condition
of the tampered area will be inconsistent to the original
image. For the compressed image, Ye et al. [16] pro-
posed a method based on the different block artifacts
caused by different quantization tables.
Generally, each kind of digital forgery detection me-
thod can solve only one kind of forgery pattern. In this
study, we only address on the detection of resampling
forgery. Two related researches addressed on the detec-
tion of resampling forgery are the methods proposed by
Popescu [7] and Mahdian [11]. Howev er, there exist two
major dr awb ack s in th e abov e-me ntio n ed a lgor ithms . F or
the Popescu’s method [7], high computation cost in the
iterative computing procedure is required . It takes almost
5 minutes to generate the probability map for the image
with resolution 512 × 512 pixels. For the method pro-
posed by Mahdian [11], we found that the derivative
kernel used in [11] will destroy the periodicity of the
correlation function at the high texture regions. 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.
Based on the periodical property that the original val-
ues can be selected from the resampling process, some of
the reconstructed values would exactly overlap the
original values in resampled signal and then the error
between the predicted value and the resampled value
would be very small. By analyzing the prediction error
distribution generated by the weighting tables from dif-
ferent resampling rates, we can detect the digital forger-
ies. To enhance the periodical property, the projection
operation is used for creating one-dimensiona l prominent
periodical patterns. In addition, both of the vertical and
horizontal predicting error variations are considered si-
multaneously.
The rest of this paper is organized as follows. In Sec-
tion 2, two typical forgery detection methods are de-
scribed. In Section 3, a new forgery detection method
based on the intrinsic properties of resampling is pro-
posed, which can detect the tampered regions more effi-
ciently. In Section 4, we present the efficiency and accu-
racy analyses among the proposed method and other ap-
proaches. Finally, we summarize the contributions and
future works in Section 5.
2. Related Works
In this section, two typical forgery detection methods for
the resampling forgery techniques are introduced. These
methods detect the forgery by tracing the interpolation
clues of resampled signal
2.1. The Popescu’s Method
A well known forgery detection method proposed by
Popescu [7] assume that the interpolated samples are the
linear combination of their neighboring pixels and try to
train a set of resampling coefficients to estimate the
probability map. 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. In the E-step, the probability for
M1 model for every sample is calculated. In the M-step,
the specific correlation coefficients are estimated and
updated continuously. The detailed description of the
forgery detection algorithm is described in the sequel.
2.1.1. E-Step
The conditional probability for sample y [i] belonging to
M1 model is calculated by the following formula.

C.-C. LIEN ET AL.
13
 

 
1
2
2
Pr
1exp 2
2
N
k
kN
yi yiM
yiyi k 






 
















(1)
2.1.2. M- Step
Minimize the quadratic error function defined in Equa-
tion (2) by updating the correlation coefficients

it-
eratively.
   
2
N
k
ikN
Eiyiyi k  








(2)
where
  

1
PriyiMy  i.
After applying the Popescu’s method to the image, we
can obtain a probability map. The peak ratio of fre-
quency response of the probability map can be used to
identify the digital forgery. Figure 2 illustrates that the
peaks of frequency response exist in the tampered image.
On the contrary, no peaks exist in the original image
shown in Figure 2(a).
2.2. The Mahdian’s Method
Another method proposed by Mahdian and Saic [11] de-
monstrates that the interpolation operation can exhibit
periodicity in their derivative distributions. To emphasize
the periodical property, they employ the radon transfor-
mation to project the derivatives along a certain orienta-
tion. The radon transformation is defined as:
Figure 2. The frequency response of the probability maps
generated from Popescu’s method for the original image,
resampled images with up-sampling rate 10% and 20%
respectively.






22
,,
L
Dbxy Dbxydl   (3)
where, b (x, y) denotes the pixel in the block with size of
R × R and D2{*} denotes the derivative kernel of order 2.
The radon transform along angle

(0 ~ 179°) is de-
fined in Equation (4).
 

2{(, )}cos
sin ,sincos
xDbxyx
yxy d


 


 
y





(4)
After projecting all the deriv atives to one directio n and
forming 1-D projection vectors, the autocovariance func-
tion can be used to emphasize the periodicity and defined
as:
 




i
Rk iki





   
 (5)
Then, the Fourier transformation of R


are also
computed to identify the periodic peaks which can indi-
cate the existing of digital forg ery. Th e simulation resu lts
are shown in Figure 3. It shows that the resampled im-
age can have strong peaks in the frequency response of
the derivative covariance.
3. Forgery Detection Using the Resampling
Intrinsic Properties
There exist two major drawbacks in the above-mentioned
algorithms. For the Popescu’s method [7], high computa-
tion cost in the iterative co mputin g pro cedure is requ ired.
It takes almost 5 minutes to generate the probability map
for an image with resolution 512 × 512 pixels. For the
method proposed by Mahdian [11], we found that the
derivative kernel used in [11] can reduce the periodicity
of the correlation function at the high texture region.
Hence, in this study we try to investigate and an alyze the
intrinsic properties of resampling process and develop a
new more efficient algorithm. The system flowchart is
shown in Figure 4 and the detailed function for each
block will be described in the following subsections.
3.1. Intrinsic Properties of Resampled Signal
In this section, we firstly introduce the procedures of
general resampling process. The up-sampling process is
illustrated in Figure 5(a) and the original values are de-
noted as red bars. Figure 5(b) shows that interpolation
operation fills the empty points with the linear combina-
tion of the adjacent signals’ values which are denoted as
yellow bars. Finally, the samples selected for decimation
process which are denoted as blue bars are shown in
Figure 5(c). Through the observation of the resampling
process, it gives us an important clue to design a new

14 C.-C. LIEN ET AL.
(a) (b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 3. (a) The original image; (b) Resampled image with
up-sample rate 20%; (c) The magnitudes of row-based de-
rivative projection for

= 90o of (a); (d) The magnitudes
of row-based derivative projection for = 90o of (b); (e)
The auto-covariance of (c); (f) The auto-covariance of (d);
(g) The frequency response of (e); (h) The frequency re-
sponse of (f).

forgery detection algorithm, i.e., the original value will
appear periodically in the resampling process. According
to this property, the new detection scheme can be devel-
oped that will be illustrated in the Subsection 3.2.

C.-C. LIEN ET AL.
15
3.2. Periodicity of the Prediction Error
Every resampled value denoted as blue bar in Figure 5
can be approximated by the linear combinations of the
adjacent original values denoted as red bar with different
weights according to their positions, i.e., the weightin g in
the linear interpolation algorithm is propositional to the
distance to their neighbors. Here, we pre-calculate the
weighing table (shown in Table 1) for each resampling
rates. If the resampling rate is known, then the original
values can be approximated by the linear combination of
the interpolated values. Based on the periodical property
of the original values selected from resampling, some of
the approximated values would exactly overlap the ori-
ginal values in resampled signal (see the green bar in
Figure 6). Ideally, the error between the predicted value
and the resampled value would be very small at the posi-
tion where the original value is resampled (the green bar
in Figure 6). Moreover, the variation of the prediction
error will distribute periodically. The weighting table WT
[i], i = 1, 2,…, N, should be calculated in advance for
Input image
Vertical resampling
rate predictiont
Horizontal
resampling rate
prediction
Prediction error
variation analysisPrediction error variation analysis
DCT DCT
Peak searching< threshold
> threshold
Tampered Image
Original image
Figure 4. Flowchart of the proposed forgery detection sys-
tem.
(a)
(b)
(c)
Figure 5. An example for illustrating the intrinsic property
of resampled signal. The scaling factor used here is 6/5. (a)
The up-sampling for the original values (red bars); (b) Lin-
ear interpolation denoted as yellow bars; (c) Down sam-
pling of signal in (b). The resampled signal is denoted as
blue bars. The blue bars labeled the w hite node denote that
the original values are chosen.
Figure 6. 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.
Table 1. Weighting table for resampling rate 6/5.
WTL [i] WTR [i]
1 1/6 5/6
2 2/6 4/6
3 3/6 3/6
4 4/6 2/6
5 5/6 1/6
each resampling rate. The prediction process is described
in Figure 6.
In Figure 6, the interpolated values can be computed
as:




i1 1 1 iL iR
BRWT iRWTi



(6)

16 C.-C. LIEN ET AL.
Then, the predicted resampling values can be comput-
ed as:







1
1
2
12
3
23
11
.
.
L
R
L
R
NmL
mN N
R
BRWTi
pre RWT i
BpreWTi
pre RWT i
BpreWTi
pre RB
WT i










 
(7)
Finally, the prediction error within the certain sliding
window can be computed as:
1
Prediction error
N
m
Bpre

 (8)
For the case of resampling rate 120%, the difference
between pre5 and B7 will be very small. When the sliding
window for calculating the sample prediction is moving
(shown in Figure 7), the prediction error will increase
and then decrease to the mini mum value until the sliding
window moves to the next periodical position (B14,
B21…). Such a periodical property makes the sequence of
prediction error distribute periodically shown in Figure 8.
In order to enhance this property, the projection opera-
tion 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.
Figure 7. The sliding window for calculating the sample
prediction using the pre-calculate d weighting table.
(a) (b)
(c)
(d)
(e)

C.-C. LIEN ET AL.
17
(f)
Figure 8. (a) The original image; (b) Resampled image with
up-sampled rate 10%; (c) The magnitudes of row-based
prediction error variation projection of (a); (d) The magni-
tudes of row-based prediction error variation projection 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. The
first one is the position where the peak occurs and the
second one is the peak ratio. According to the different
weighting tables (different resampling rate) for the for-
gery detection and the specific periodical property for
each resampling rate, the expected position where the
peak occurs could be forecasted. Then, we can match the
peak position to the forecasted position where the spe-
cific resampling rate generates for identifying the exis-
tence of digital forgery. If the ratio is larg er than a speci-
fied threshold, we can identify that existence of digital
forgery. Finally, the flowchart of the proposed system is
shown in Figure 9. To detect the tampered region, the
image is scanned from left-top to right-bottom with dif-
ferent block sizes. In each block, the proposed method is
applied to detect the tampered regions.
4. Experimental Results
In this section, the efficiency and accuracy for Popescu’d
method [7], Mahdian’s method [11], and the proposed
method are analyzed. The experimental database is con-
structed with 160 gray level images with resolution 512
× 512 and each image is partial tampered in BMP format.
The image tampering is based on the resampling process
with the different bi-linear sampling rates: 105%, 110%,
120% and 125%. The forgery detections are performed
by scanning the image with the block size of 128 × 128
pixels.
Before analyzing the accuracy of forgery detection, we
firstly describe the detection rules for the Popescu’s [7],
Mahdian’s [11], and our methods. Here, the forgery de-
tection of Popescu’s and Mahdian’s methods is deter-
Figure 9. The flowchart of the proposed method.
mined by evaluating whether the ratio of peak-to-average
frequency response is larger than a predefined threshold
value or not. The ratio of peak-to-average frequency re-
sponse is defined as:
maximum
sec average Pop uMahdian
magnitude
RR magnitude 
For our method, the forgery detection is determined by
evaluating whether the ratio of forecasted peak-to-average
frequency response is larger than a predefined threshold
value or not. The ratio of forecasted peak-to-average
frequency resp onse is defined as:
forecasted position
average
our
magnitude
Rmagnitude 
The resampled image with rate 120% shown in Figure
10(a) is used as the tampered image for analyzing the
detection accuracy for the three methods. Figure 10(b)
shows the probability map produced by the Popescu’s
method and Figure 10(c) shows the frequency response
of the probability map. Figure 11(a) shows the radon
transformation of the derivative along horizontal direc-

18 C.-C. LIEN ET AL.
tion generated by Mahdian’s method and Figure 11(b)
shows its auto-covariance. Figure 11(c) shows the fre-
quency response of the au to-covariance values. Based on
the proposed method, the prediction error generated by
the novel algorithm is shown in Figure 12(a). Figure
12(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 Figure 11(c). The accuracy analyses of
forgery detections for different resampling rates are ana-
lyzed in Table 2.
(a)
(b)
(c)
Figure 10. (a) The tampered image; (b) The probability
map generated by the P opescu’s method; (c) The fre quency
response of (b).
(a)
(b)
(c)
Figure 11. (a) The radon transformation output of Figure
13 by the Mahdian’s method; (b) The autocovariance of (a);
(c) The frequency response of (b).
The ROC curves with different up-sampling rates for
Popescu’s, Mahdian’s and our methods are shown in
Figure 13. In this Figure, the detection accuracy of
Popescu’s method is the highest one and the detection
accuracy of our method is close to the Popescu’s curve.
However, our method is the fastest one that will be men-
tioned later. The detection accuracy of Mahdian’s me-
thod is the lowest because the detection accuracy is af-
fected by the high texture regions.

C.-C. LIEN ET AL.
19
(a) (b)
Figure 12. (a) The prediction error of the tampered image shown in Figure 10, which is generated by the proposed method; (b)
The frequency response of (a).
Table 2. The accuracy analysis for the methods of our, Popescu’s and Mahdian’s with 40 resampled images for different
rates.
Popescu’s method Our method Mahdian’s method
Up-sampling 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%
(a) (b)
(c) (d)
Figure 13. The ROC curves of (a) Up-sampling 5%; (b) Up-sampling 10%; (c) Up-sampling 20%; (d) Up-sampling 25%.

C.-C. LIEN ET AL.
20
In addition, we compare the efficiency among Pope-
scu’s [7], Mahdian’s [11] and our methods with the PC
of 1.8 GHz. The efficiency analysis is shown in Figure
14. Here, we perform the efficiency analysis from block
size 64 × 64 to 512 × 512 and assume there are 21
weighting tables for 21 resampling rates used in [7]. Be-
cause the iterative EM algorithm is very time-consuming,
the efficiency of Popescu’s method is the lowest. On the
contrary, the highest efficiency is presented in Mahdian’s
method because the operations in his method are very
simple. It’s worthy to conclude that detection accuracy
and efficiency of our method can approach both of the
benefits of Popescu’s and Mahdian’s methods.
Figures 15-16 show the detection results of the pro-
Figure 14. Efficiency analysis.
(a) (b)
(c) (d)
(e)
Figure 15. (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.

C.-C. LIEN ET AL.
21
(a) (b)
(c) (d)
Figure 16. (a) Original image; (b) Forgery image composed from up-sample (a) 10% and put the bottle near beside; (c) De-
tection result with 64 × 64 block size; (d) Detection result with 128 × 128 block size.
-posed method for different resampling rates with two
block sizes. In Figure 15, the man’s head in Figure 15(b)
is cropped and replaced the head region in Figure 15(a)
to synthesize the forgery image shown in Figure 15(c).
Figure 15(d) and Figure 15(e) show the detection result
with 64 × 64 and 128 × 128 block sizes. Figure 16(a)
shows an original bottle image and Figure 16(b) shows
that a resized bottle is put on the left side of the tampered
image. Figures 16(c) and 16(d) show the detection re-
sults with different block sizes. Here, we observe that the
detection accuracy for the smaller block size is lower
than the accuracy with larger block size because more
periodical patterns can be collected in larger blocks.
5. Conclusions
In this paper, we propose a novel method based on the
intrinsic properties of resampling scheme to detect the
forgery regions with the pre-calculated resampling wei-
ghting tables and the detecting of periodic patterns for
the vertical and horizontal prediction error. In Popescu’s
method, high accuracy can be obtained with high com-
putation cost. On the contrary, in Mahdian’s method, the
detecting accuracy can be affected on the high texture
regions. The detection accuracy and efficiency of our
method can approach both of the benefits of Popescu’s
and Mahdian’s methods. The detection accuracy of our
method is about 95% and the time for detecting a 512 ×
512 image needs only 50 seconds.
6. References
[1] R. B. Wolfgang and E. J. Delp, “A Watermark for Digital
Image,” Proceedings of the International Conference on
Image Processing, Vol. 3, 1996, pp. 219-222.
[2] R. B. Wolfgang, C. I. Podilchuk and E. J. Delp, “Percep-
tual Watermarks for Digital Images and Video,” Pro-
ceedings of the IEEE, Special Issue on Identification and
Protection of Multimedia Information, Vol. 87, No. 7,
1999, pp. 1108-1126.
[3] M. Wu and B. Liu, “Watermarking for Image Authenti-
cation,” IEEE International Conference on Image Proc-
essing, Vol. 2, 1998, pp. 437-441.
[4] M. Yeung and F. Mintzer, “An Invisible Watermarking
Technique for Image Verification,” Proceedings of the
International Conference on Image Processing, Vol. 1,

22 C.-C. LIEN ET AL.
1997, pp. 680-683.
[5] J. Fridrich, D. Soukal and J. Lukáš, “Detection of Copy-
Move Forgery in Digital Images,” Proceedings of the
Digital Forensic Research Workshop, Cleveland, 2003.
[6] L. Zhou, D. Wang, Y. Guo and J. Zhang, “Blue Detection
of Digital Forgery Using Mathematical Morphology,”
Technical Report, KES AMSTA, Springer-Verlag, Berlin,
Heidelberg, 2007, pp. 990-998.
[7] A. C. Popescu and H. Farid, “Exposing Digital Forgeries
by Detecting Traces of Resampling,” IEEE Transactions
on Signal Processing, Vol. 53, No. 2, 2005, pp. 758-767.
[8] A. C. Popescu and H. Farid, “Exposing Digital Forgeries
in Color Filter Array Interpolated Images,” IEEE Trans-
actions on Signal Processing, Vol. 53, No. 10, 2005, pp.
3948-3959.
[9] M. Kirchner, “Fast and Reliable Resampling Detection
by Spectral Analysis of Fixed Linear Predictor Residue,”
MM & Sec’08, Proceedings of the Multimedia and Secu-
rity Workshop, 2008, pp. 11-20.
[10] S. Prasad and K. Ramakrishnan, “On Resampling Detec-
tion and its Application to Detect Image Tampering,”
Proceedings of the 2006 IEEE International Conference
on Multimedia and EXPO, 2006, pp. 1325-1328.
[11] B. Mahdian and S. Saic, “Blind Authentication Using
Periodic Properties of Interpolation,” IEEE Transactions
on Information Forensics and Security, Vol. 3, No. 3,
2008, pp. 529-538.
[12] B. Mahdian and S. Saic, “Detection of Resampling Supple-
mented with Noise Inconsistencies Analysis for Image Fo-
rensics,” International Conference on Computational Sci-
ences and its Applications, Vol. 81, No. 4, 2008, pp . 546-556.
[13] J. Lukáš, J. Fridrich and M. Goljan, “Detecting Digital
Image Forgeries Using Sensor Pattern Noise,” Proceed-
ings of the SPIE Conference on Security, Steganography
and Watermarking of Multimedia Contents, Vol. 6072,
2006, pp. 362-372.
[14] J. Lukáš, J. Fridrich and M. Goljan, “Digital Camera
Identification from Sensor Pattern Noise,” IEEE Trans-
actions on Information Security and Forensics, Vol. 1,
No. 2, 2006, pp. 205-214.
[15] M. K. Johnson and H. Farid, “Exposing Digital Forgeries
in Complex Lighting Environments,” IEEE Transactions
on Information Forensics and Security, Vol. 2, No. 4,
2007, pp. 450-461.
[16] S. Ye, Q. Sun and E. Chang, “Detecting Digital Image
Forgeries by Measuring Inconsistencies of Blocking Ar-
tifact,” IEEE International Conference on Multimedia
and EXPO, 2007, pp. 12-15.
[17] M. C. Stamm and K. J. R. Liu, “Forensic Detection of
Image Tampering Using Intrinsic Statistical Fingerprints
in Histograms,” Proceedings of the APSIPA Annual
Summit and Conference, Sapporo, 2009.