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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP2012 Steganalysis by Ensemble Classifiers with Boosting by Regression, and Post-Selection of Features Marc Chaumont, Sarra Kouider LIRMM, Montpellier, France October 2, 2012 IEEE

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012

Steganalysis by Ensemble Classifiers with Boosting by Regression, and Post-Selection of Features

Marc Chaumont, Sarra Kouider LIRMM, Montpellier, France October 2, 2012

IEEE International Conference on Image Processing 2012,

  • Sept. 30 - Oct. 3 2012, Orlando, USA.
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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Preamble

Outline

1

Preamble

2

The Kodovsky’s Ensemble Classifiers

3

Boosting by regression

4

Post-selection of features

5

Experiments

6

Conclusion

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Preamble

Steganography vs Steganalysis

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Preamble

The proposition

An Improvement of a state-of-the-art steganalyzer PE ց of the steganalyzer THANKS TO boosting by regression of low complexity, post-selection of features of low complexity.

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 The Kodovsky’s Ensemble Classifiers

Outline

1

Preamble

2

The Kodovsky’s Ensemble Classifiers

3

Boosting by regression

4

Post-selection of features

5

Experiments

6

Conclusion

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 The Kodovsky’s Ensemble Classifiers

Notable properties

Appeared during BOSS challenge (sept. 2010 - jan. 2011), Performances ≡ to SVM, Scalable regarding the dimension of the features vector, Low computational complexity, Low memory complexity, Easily parallelizable.

  • J. Kodovsk´

y, J. Fridrich, and V. Holub, “Ensemble classifiers for steganalysis of digital media,” IEEE Transactions on Information Forensics and Security, vol. 7, no. 2, pp. 432– 444, 2012.

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 The Kodovsky’s Ensemble Classifiers

Definition of a weak classifier

Ensemble Classifiers is made of L weak classifiers Let x ∈ Rd a feature vector, A weak classifier, hl, returns 0 for cover, 1 for stego : hl : Rd → {0, 1} x → hl(x)

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 The Kodovsky’s Ensemble Classifiers

How does classification work?

1 Take an image to analys (i.e. classify in cover or stego), 2 Extract the features vector x ∈ Rd, 3 Decide to classify cover or stego (majority vote):

C(x) =

  • 0 if l=L

l=1 hl(x) ≤ L/2,

1 otherwise.

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Boosting by regression

Outline

1

Preamble

2

The Kodovsky’s Ensemble Classifiers

3

Boosting by regression

4

Post-selection of features

5

Experiments

6

Conclusion

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Boosting by regression

Weighting the weak classifiers

1 Take an image to analys (i.e. classify in cover or stego), 2 Extract the features vector x ∈ Rd, 3 Decide to classify cover or stego (majority vote):

C(x) =

  • 0 if l=L

l=1 hl(x) ≤ L/2,

1 otherwise. The classification (steganalysis) process was:

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Boosting by regression

Weighting the weak classifiers

BUT : some weak classifiers are less efficient than others. THEN : introduce weights !

1 Take an image to analys (i.e. classify in cover or stego), 2 Extract the features vector x ∈ Rd, 3 Decide to classify cover or stego (majority vote):

C(x) =

  • 0 if l=L

l=1 hl(x) ≤ L/2,

1 otherwise. The classification (steganalysis) process was:

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Boosting by regression

Weighting the weak classifiers

1 Take an image to analys (i.e. classify in cover or stego), 2 Extract the features vector x ∈ Rd, 3 Decide to classify cover or stego (weighted vote):

C(x) =

  • 0 if l=L

l=1 αlhl(x) ≤ l=L

l=1 αl

2

, 1 otherwise. The classification (steganalysis) process is now:

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Boosting by regression

Weighting the weak classifiers

How to calculate those weights with a small computational complexity ?

1 Take an image to analys (i.e. classify in cover or stego), 2 Extract the features vector x ∈ Rd, 3 Decide to classify cover or stego (weighted vote):

C(x) =

  • 0 if l=L

l=1 αlhl(x) ≤ l=L

l=1 αl

2

, 1 otherwise. The classification (steganalysis) process is now:

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Boosting by regression

Analytic expression of the weights

During learning step: {αl} = arg

{αl}

min PE. simplify PE expression, least squares problem ⇒ linear system A.X = B with X the weights : Ai,j =

n=N

  • n=1

hi(xn)hj(xn), Bi =

n=N

  • n=1

hi(xn)yn. ... solved thanks to a library of linear algebra.

Order of complexity unchanged.

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Post-selection of features

Outline

1

Preamble

2

The Kodovsky’s Ensemble Classifiers

3

Boosting by regression

4

Post-selection of features

5

Experiments

6

Conclusion

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Post-selection of features

Reducing the dimension with few computations

Selection of features: Pre-selection may cost a lot. What about post-selection?

1 Take an image to analys (i.e. classify in cover or stego), 2 Extract the features vector x ∈ Rd, 3 Decide to classify cover or stego (weighted vote):

C(x) =

  • 0 if l=L

l=1 αlhl(x) ≤ l=L

l=1 αl

2

, 1 otherwise. Remember: The classification (steganalysis) process is now:

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Post-selection of features

Order of complexity unchanged.

Algorithm :

1 Compute a score for each feature; first database reading, 2 Define an order of selection of the features, 3 Find the best subset (lowest PE); second database reading.

Once a weak classifier learned : suppress the features reducing PE :

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Experiments

Outline

1

Preamble

2

The Kodovsky’s Ensemble Classifiers

3

Boosting by regression

4

Post-selection of features

5

Experiments

6

Conclusion

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Experiments

Experimental conditions

10 000 greyscale images (512×512, BOSS database), The same 10 000 embedded at 0.4 bpp with HUGO, Feature vector dimension d = 5330 features (HOLMES subset), 5 different splits, 5 different seeds,

HUGO: “Using High-Dimensional Image Models to Perform Highly Undetectable Steganography”

  • T. Pevn´

y, T. Filler, and P. Bas, in Information Hiding, IH’2010. HOLMES: “Steganalysis of Content-Adaptive Steganography in Spatial Domain”

  • J. Fridrich, J. Kodovsk´

y, V. Holub, and M. Goljan, in Information Hiding, IH’2011.

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Experiments

Steganalysis results

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Experiments

Steganalysis results

Recall increase = 1.7% Same computational complexity order

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Conclusion

Outline

1

Preamble

2

The Kodovsky’s Ensemble Classifiers

3

Boosting by regression

4

Post-selection of features

5

Experiments

6

Conclusion

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Conclusion

Summary

Two propositions for the Kodovsk´ y steganalyzer:

boosting by regression, post-selection of features.

Significant recall increase (1.7%) No change in computational complexity order

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Conclusion

Annex: Metrics (1)

Distance between the two classes: c(l)

1 [j] = |µ1[j] − µ0[j]|

  • σ2

1[j] + σ2 0[j]

. Influence of a feature on the final correlation/decision ( = dot product) used to classify: c(l)

2 [j] = i=N

  • i=1

count(x(l)

i [j], w(l)[j], yi),

with: count(x, w, y) =    1 if [(x.w > 0 and y = 1)

  • r (x.w < 0 and y = 0)],

0 otherwise. c(l)

3 [j] = i=N

  • i=1

count(x(l)

i [j], w(l)[j], yi)

k=dred

k=1

count(x(l)

i [k], w(l)[k], yi)

.

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Conclusion

Annex: Metrics (2)

Feature correlation with the class: c(l)

4 [j]

= corr(x(l)[j], y) = i=N

i=1

  • x(l)

i [j] − x(l)[j]

  • (yi − y)

i=N

i=1

  • x(l)

i [j] − x(l)[j]

2i=N

i=1 (yi − y)2

. Feature correlation with the weak classifier: c(l)

5 [j] = corr(x(l)[j].w(l)[j], y).

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Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP’2012 Conclusion

Annex: PE in the Boosting by Regression

During learning step: {αl} = arg

{αl}

min PE. PE = 1 N

i=N

  • i=1
  • f

l=L

  • l=1

αlhl(xi)

  • − yi
  • .

with f a thresholding function defined by: f : R → {0, 1} x → f (x) =

  • 0 if x ≤

l=L

l=1 αl

2

, 1 otherwise. Let’s simplify, PE: PE ≈ 1 N

i=N

  • i=1

l=L

  • l=1

αlhl(xi) − yi 2 . ⇒ least squares problem ... solved thanks to a library of linear algebra.