Image Forgery Detection

1
Image Forgery Detection

• by Gamma Correction Differences

2
Topics

• Introduction
• Definition of authenticity
• Image generation process
• Acquisition Difference
• Gamma Correction (reminder)
• Gradient on surface
• Conclusion

3
Introduction ( definitions )

• PIM photographic images
• PRCG photorealistic computer graphics
• We want to decide for image
• PIM
• PRCG

4
Introduction ( cont. )

• CG Images From the Google

5
Introduction ( cont. )

• Previous natural image statistic techniques can
  distinguish PIM or PRCG (wavelet method 67
  detection and 1 false alarm), but cant answer
  the question how PIM are actually different from
  PRCG.
• Here proposed new geometry-based image model
  which is inspired by the physical generation
  process of PIM and PRCG.

6
Definition of authenticity

• What about photographs of CG or forgery?
• So here defined two types of authenticity
• 1) image-process authenticity (here)
• 2) scene authenticity (statistic methods too)

7
Image generation process

• The main differences between PIM and PRCG
• 1) Object Model Difference The surface of
  real-world objects, except for man-made objects,
  are rarely smooth of simple geometry.

8
Object Model Difference
9
Image generation process (cont.)

• 2) Light Transport Difference The physical light
  field captured by a camera is a result of the
  physical light transport from the illumination
  source, reflected to the image acquisition device
  by an object.

10
Image generation process (cont.)

• 3) Acquisition Difference PIM carry the
  characteristics of the imaging process, while
  PRCG may undergo different types of
  post-processing. There is no standard set of
  post-processing techniques, but a few possible
  ones are the simulation of the camera effect,
  such as the depth of field, gamma correction,
  addition of noise, and retouching.

11
Image Acquisition Pipeline
12
Optics (mechanics)

• Different field of view, different size,
  different quality (cheap lenses causes more
  filtering and reflecting).
• Very important issue lens protectors (causes
  reflecting).

13
Detector (CCD)

• Each pixel converts number of photons to variable
  number of electrons.
• So we have the detector noise

14
Read Out

• We must to bring all pixels into dynamic range
  (similar to white balance).
• Electronic noise.
• After read out block we can see analog image.

15
Acquisition Difference Gamma Correction

• Gamma Correction - controls the overall
  brightness of an image. Images which are not
  properly corrected can look either bleached out,
  or too dark. In other words to enhance the
  contrast of the displayed images.

16
Gamma Correction (cont.)
   Sample Input         
Graph of Input   Gamma Corrected Input
         Graph of Correction L' L (1/2.5)
17
Gamma Correction (cont.)

• Most monitors have build-in Gamma correction. It
  will be compensated by image processing
  algorithm. For example
• For most CRT monitors, gamma correction
  must output gamma ½ to get correct image.

18
Gamma Correction (cont.)

• The left image too dark! Right image gamma
  corrected ( looks correct ).

19
Acquisition Difference Gradient on surface

• In this section, we will show that the surface
  gradient of the image intensity function I(x,y)
  can be used to distinguish PIM and PRCG.

20
Gradient on surface ( cont. )

• One main characteristic of the camera transfer
  function is that the irradiance of low values are
  stretched and those of high values are
  compressed. Let the image intensity function be
• I (x, y) f (M(x, y))
• where
• f R ? R
• is the camera transfer function and
• M R2 ? R
• is the image irradiance function.

21
Gradient on surface ( cont. )
22
Gradient on surface ( cont. )

• By the chain rule, we have

• The modulation factor , is the
  derivative of the camera function, which is
  larger (smaller) than 1 when M is small (large)

23
Gradient on surface ( cont. )

• Therefore, the Euclidean gradient

• of a transformed image is higher (lower) at
  the low (high) intensity than before the
  transformation.

24
Gradient on surface ( cont. )

• , the modulation term reveals a key
  difference between PIM and PRCG, when PRCG images
  are not subjected to such modulation on their
  gradient values. If the PRCG intensity functions
  have not undergone such transformation, it can be
  distinguished from PIM by the gradient
  distribution.

25
Gradient on surface ( cont. )

• The analysis above assumes that the image
  irradiance function M is continuous. There is a
  non-trivial issue involved in its implementation,
  when it comes to discrete sampled images.
  Consider approximating the gradient at two
  neighboring pixels at locations x and x ?x,
  intensity derivative Equation becomes

• Where
• ?Ix I (x ?x, y )-I (x, y)
• similarly for ?(f ?M )x and ?Mx.

26
Gradient on surface ( cont. )

• Note that, the modulation factor in this case
  becomes the slope of the chord on the camera
  transfer function connecting M (x?x) to M (x).
  One consequence is that the modulation will only
  be similar to the continuous case, when M (x ?x
  )-M (x) is small, because when M (x ?x
  )-M (x) is large, the slope of the chord is
  approaching 1 and modulation effect is weak. In
  other words, due to the discrete representation,
  the modulation effect shown in Equation will
  arise only at points having low gradient values.

27
Gradient on surface ( cont. )
28
Gradient on surface ( cont. )

• To emphasize the low-gradient region, we employ a
  tail-compressing transform, S

• In right Figure shows that the S transform is
  almost linear for the small values and it
  compresses the high values. The width of the
  linear range can be controlled by the constant,
  a.

29
Gradient on surface ( results )

• Next Figure shows the distribution of the mean of
  surface gradient
• grad (aI) a
  0.25
• (selected such that the linear range of the S
  transform covers the low and the intermediate of
  the Euclidean gradient), for three intensity
  ranges, i.e.
• 0, 0.33 , 0.33, 0.66, 0.66,
  1
• of the blue color channel (the same holds for
  the red and green channels).

30
Gradient on surface ( results )
31
Gradient on surface ( Results )

• These distributions are computed empirically
  from our actual dataset of PIM and PRCG. Notice
  that for the low intensity region, the mean of
  surface gradient for the PIM is higher than that
  of the PRCG and the opposite is observed for the
  high intensity region, while the distributions of
  the two are completely overlapped at the medium
  intensity range. This perfectly matches our
  prediction about the effect of the transfer
  function!

32
Conclusion

• We have proposed a new approach for PIM and PRCG
  classification in the context of image forgery
  detection. This approach dont need any natural
  image statistics information. Even can
  distinguish between PIM with different gamma
  correction function.

33
Discussion

• What about PRCG gamma correction?
• What about combining this method with others?

34
References

• 1 S. Lyu and H. Farid. How realistic is
  photorealistic? IEEE Trans. Signal Processing,
  53(2)845850, February 2005.
• 2 Tian-Tsong Ng, Shih-Fu Chang, Jessie Hsu,
  Lexing Xie. Physics-Motivated Features for
  Distinguishing Photographic Images and Computer
  Graphics.