Exposing Digital Forgeries in
Color Array Interpolated
Images
Presented by:
Ariel Hutterer
Final Fantasy ,2001
My eye
1
References

Alin C.Popescu and Hany Farid:


Yizhen Huang:


Exposing Digital Forgeries in Color Filter Array
Interpolated Images.
Can Digital Forgery Detection Unevadable?
A Case Study : Color Filter Array Interpolation
Statistical Feature Recovery.
Hagit El Or

Demosaicing.
2
Outline
Introduction
 Digital Cameras
 Interpolations
 Detecting CFA Interpolation
 Results
 Crack Methods
 Computer Graphics

3
Introduction- forgeries
Low cost: cameras ,photo editing software.
 Images can be manipulated easily.
 Splicing.

4
Introduction- forgeries
Images have a huge impact in public
opinion.
 Legal world.
 Scientific evidence.

5
Introduction - preventing forgeries
approaches

Two principal approaches to prevent forgeries:

Digital watermarking:


Means that image can be authenticated.
Drawbacks:
 Specially equipped digital cameras ,that insert the watermark.
 Assume that watermark cannot be easily removed and
reinserted. (but ….it is???)

Statistic analysis:

Most color digital cameras , introduces specific correlation:
 A third of the image are captured by a sensor.
 Two thirds of the image are interpolated.

Images manipulated must alter this specific statistic.
6
Outline
Introduction
 Digital Cameras
 Interpolations
 Detecting CFA Interpolation
 Results
 Crack Methods
 Computer Graphics

7
Digital Cameras

Most Color digital Cameras have a single
monochrome Array of sensors
8
Digital Cameras

How does color form with monochrome
sensor for each pixel?
9
Digital Cameras-Bayer Color Array

Half pixels are Green ,quarter are Red and
quarter are Blue
10
Digital Cameras-Bayer Color Array

Several possible
arranges
Bayer
Diagonal
Bayer
Diagonal
Striped
Psudo-random
Bayer
11
Digital cameras - forming color
12
Digital cameras - forming color
13
Digital cameras - forming color
I
n
t
e
r
p
o
l
a
ti
o
n
14
Digital cameras - forming color

Bayer Array For almost
all Digital Cameras

Color Interpolation
different for each make
of Digital Camera
Interpolation
15
Outline
Introduction
 Digital Cameras
 Interpolations
 Detecting CFA Interpolation
 Results
 Crack Methods
 Computer Graphics

16
Interpolations

Naive – per channel interpolation


Inter-channel dependencies and
correlations –


Nearest neighbor ,Bilinear interpolation
Reconstruct G channel, then reconstruct R & B
based on G. Reconstruct all 3 channels
constrained with inter-channel dependence.
Adaptive reconstruction –

Measure local image variations (e.g. edges,
gradients, business) and reconstruct
accordingly.
17
Interpolations - Aliasing
R
R
R
G
R
G
R
R
R
G
G
R
G
R
R
R
G
G
G
G
G
G
R
G
B
B
B
G
B
B
B
G
B
B
B
G
G
G
G
G
G
G
Interpolate
R R R R R
R R R R R
R R
R R
G G G G G
G G G G G
G G
G G
B B
B B
B B B
B B B
B B
B B
R R R R R
R R R R R
R R
R R
G G G G G
G G G G G
G G
G G
B B
B B
B B B
B B B
B B
B B
R R R R R
R R R R R
R R
R R
G G G G G
G G G G G
G G
G G
B B
B B
B B B
B B B
B B
B B
18
Interpolations - Aliasing
Result
R
R
R
G
R
G
R
R
R
G
G
R
G
R
R
R
G
G
G
G
G
G
R
G
B
B
B
G
B
B
B
G
B
B
B
G
G
G
G
G
G
G
Interpolate
R R R R R
R R R R R
R R
R R
G G G G G
G G G G G
G G
G G
B B
B B
B B B
B B B
B B
B B
R R R R R
R R R R R
R R
R R
G G G G G
G G G G G
G G
G G
B B
B B
B B B
B B B
B B
B B
R R R R R
R R R R R
R R
R R
G G G G G
G G G G G
G G
G G
B B
B B
B B B
B B B
B B
B B
19
Interpolations - Samples
20
Interpolation-Bilinear Bicubic

Red and Blue Kernels:

Separable 1-D filters
Rw
Rw = ½(Rnw+Rsw)
21
Interpolation-Bilinear Bicubic

Green kernels

2-D filters:
22
Interpolation- Gradient Based

First, calculate Green channel:

Calculate derivates estimators

Determination of Green’s values
23
Interpolation – Evaluation Tools
24
Interpolation -Results
Original
Linear
Kimmel
25
Outline
Introduction
 Digital Cameras
 Interpolations
 Detecting CFA Interpolation
 Results
 Cracks Methods
 Computers Graphics

26
Detecting CFA Interpolation
In Each pixel only one color derives from
the sensor ,two others derive from
interpolation from their neighbors .
 The correlation are periodic.
 Tampering will destroy these correlations.
 Splicing together two images from
different cameras will create inconsistent
correlations across the composite image.

27
Detecting CFA Interpolation

Two different tools:

EM algorithm :



Produce Map of Probabilities and interpolation
coefficients
Used to detect kind of interpolation
Farid’s Indicator:


Produce Map of Similarities
Used to quantify the similarity to CFA Interpolated
Image
28
EM Algorithm
(Expectation/Maximization):

Two possible models:


M1:the sample is linearly correlated to its
neighbors
M2:the sample is not correlated to its
neighbors
29
EM Algorithm
(Expectation/Maximization):



f(x,y) – color channel
alpha - parameters ,where(0,0) = 0. denotes
the specific correlation.
n
- independent and identically samples
drawn from a Gaussian distribution, with 0
mean and unknown variance
30
EM Algorithm
(Expectation/Maximization):

Two-step iterative algorithm:



E-step : calculate the probability of each sample
M-step: the specific form of the correlation is
estimated.
Based in Bayes rule:
31
Farid’s indicator

The similarity between the probability and a
synthetic map is obtained by:

Where:

Similarity measure is phase insensitive
32
Farid’s indicator

How to use it:


CFA-Interpolated : if at least one channel is
greater than threshold1
Non CFA Interpolated: if all 3 channels are
smaller than threshold2
result
threshold2
Non CFA Interpolated
threshold1
Unknown
CFA Interpolated
Ind(cfa-sf)
33
Huang indicator


Motivation: Farid’s Indicator is proportional
to image size.
Table of Green Channel Indicator
Indicator
function

32x32
Farid
140
Huang
2.70
Huang Indicator:
128x128
256x256
512x512
2303
2.70
9419
2.84
52361
4.31
34
Outline
Introduction
 Digital Cameras
 Interpolations
 Detecting CFA Interpolation
 Results
 Cracks Methods
 Computers Graphics

35
Results
Detecting different interpolation methods
 Detecting tampering
 Measuring Sensitivity and robustness

36
Detecting different interpolation
methods
Hundreds of images from 2 digital
cameras
 Blur 3x3
 Down sampled
 Cropped
 Resample in CFA Interpolations

37
Detecting different interpolation
methods
38
Detecting different interpolation
methods
39
Detecting different interpolation
methods
40
Detecting different interpolation
methods
41
Detecting different interpolation
methods

Coefficients are 8 to each color so we are
a 24-D vector ,LDA classifier ,results:


97% Interpolations kinds was detected
2D projection of LDA
42
Detecting tampering

Hiding the damage of the car

Air-brushing ,smudging ,blurring and
duplication
43
Detecting tampering

Result:


Left F(p) : for tampered portion
Right F(p) : for unadulterated portion
44
Measuring Sensitivity and robustness

Testing different interpolations with Farid’s
indicator
False
0%
Median
5x5
97
Bilinear
100%
Gradient
based
100%
Bicubic
100%
Adaptive
97%
color plane
Median
3x3
99
Variable
number of
gradients
remember
100%
45
Measuring Sensitivity and robustness

Testing influence of jpeg
46
Measuring Sensitivity and robustness

Testing influence of Gaussian Noise
47
Outline
Introduction
 Digital Cameras
 Interpolations
 Detecting CFA Interpolation
 Results
 Crack Methods
 Computer Graphics

48
Cracking
What’s a “true digital image”
 General Model

49
True digital image

It was taken by a CCD/CMOS digital
camera, or other device with similar
function and remains intact after shooting
except for embedding ownership and
other routinely added information.
50
General Model

where:




W all images
S all possible images tacked by an ideal
camera c.
N are S enlarged because of noise.
Detection method:



Pm(I), a projection of Image I
I is true when:
I is Artificially CFA-interpolated
51
General Model
The result image should be as close as
possible to the original
 The mean of the difference to an ideally
CFA interpolated image should be
controlled in a specific range.
 Such difference should be distributed
averagely.

52
General Model



Im: Tampered Image
Im’: cracked Image
Int(I) : Ideal Interpolated
Dif(Im,Im’
,Int(Im’))
K2
K1
Dif(Im,Im’)
Dif(Im’,Int(Im’))
53
General Model
We are looking for
 We want to minimize the 3d distance:

54
Outline
Introduction
 Digital Cameras
 Interpolations
 Detecting CFA Interpolation
 Results
 Crack Methods
 Computer Graphics

55
Computer Graphic

A naïve approach:

Computer Graphic will be detected like non
CFA-Interpolated.
56
Computer Graphics
Huge improvement of dedicated hardware
in the last 7 years
 SGI:Onyx2 ,Infinity reality 3(2000) :





12 bits * 4 channels
No shaders
End User license ,250,000$
Pc d/core, geforce 8(2006):



32 bits * 4 channels
Shaders w/24 parallels pipes
1,500-5,000$
57
Computer Graphics

2001,Final fantasy ,first Film made with
PC.
58
Computer Graphics

See cg not like an Image, see it like
REALITY.
Render Reality high resolution ,by 32bits for each color
Optical distortions, ghost and blurring
Sensor CFA sampling and noise
Interpolation
Image
59
Computer Graphics
From Image Forgeries to Science Fiction

Image forgeries are a “positive issue“ for
development of:



Simulators.
Trainers.
Robots………
60
Computer Graphics
From Image Forgeries to Science Fiction
61
Conclusion
Detection CFA-Interpolated methods are
not enough robust.
 Compression like jpeg destroy the
interpolation correlation.
 Interpolation can be artificially made.

The End
62