UNIVERSAL COUNTER FORENSICS METHODS FOR FIRST ORDER STATIST

UNIVERSAL COUNTER FORENSICS METHODS FOR FIRST ORDER STATISTICS

M. Barni, M. Fontani, B. Tondi, G. Di DomenicoDept. of Information Engineering, University of Siena (IT)

Outline

MultiMedia

Forensics & Counter-Forensics

Universal counter-forensics

Proposed approach

Application to pixel domain

Application to DCT domain

Results and discussion

MM Forensics & Counter-Forensics

MM Forensics:Goal: investigate the history of a MM contentRapidly evolving field, but…Countermeasures are evolving too!Counter-Forensics:Goal: edit a content without leaving traces (fingerprints)

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roject

www.rewindproject.eu

Forensics & Counter-Forensics

MM Forensics is evolving rapidly…Countermeasures are evolving too!Counter-Forensics goal: allow to alter a content without leaving traces (fingerprints)

[K07] M

. Kirchner and R.

Böhme

, “Tamper hiding: Defeating image forensics,” in

Information Hiding,

ser. Lecture Notes in Computer Science, vol.4567. Springer,2007,pp. 326–341.

Universal Counter - Forensics

General idea: If you know what statistic is used by the analystjust adapt the statistic of your forgery to be very close to the statistic of “good” sequences Any detector based on that statistic will be fooled!Game Theory:This scenario can be seen as a game [B12]Forensic Analyst vs. AttackerDifferent games are possible:The adversary directly know the statistic of the “untouched sequences”The adversary only has a training set of “untouched sequences”

[B12]

M.

Barni

. A game theoretic approach to source identification with known statistics. In Proc. of ICASSP 2012, IEEE Int. Conference on Acoustics, Speech, and Signal Processing, 2012.

Fool a detector = force it to misclassify

Approach: make the processed image statistic close to that of (an) untouched image If it’s close enough… the detector must do a false-positive or a false-negative errorAssumptions:Analyst’s detector relies only on first order statisticsAdversary has a database (DB) of histograms of untouched imagesSo the adversary:Processes the imageSearches the DB for the nearest untouched histogramComputes a transformation map from one histogram to the anotherApplies the transformation, minimizing perceptual distortion

Outline of the scheme

Practical applications

We show how the proposed method can be used for two different CF tasks:

Hiding traces left by processing operations in the histogram of pixel values

Hiding traces left by double JPEG compression in the histogram of quantized DCT coefficients

You will notice that switching between different domains

do not change the scheme

, but just the implementation of each “block”

Application #1Conceal traces in the image histogram

We propose a method to conceal traces left by any processing operation in the image histogramMany detectors exist based on histogram analysis: Detection of Contrast Enhancement (pixel histogram) [S08]Detection of double JPEG compression (histograms of DCT coefficients) [B12]We make no assumptions on the previous processing

[S08]

M. C.

Stamm

and K. J. R. Liu. Blind forensics of contrast enhancement in digital images. In Proc. of

ICIP

2008

,

pages 3112–3115, 2008.

[B12]

T.Bianchi

,

A.Piva

, "Image Forgery Localization via Block-Grained Analysis of JPEG Artifacts",

IEEE Transactions on Information Forensics & Security

, Volume: 7, Issue: 3 , Page(s): 1003 - 1017

Basic notation

Y and

h

Y

denote the processed image and its histogram

X and

h

X

denote the untouched image and its histogram

Z and

h

Z

denote the attacked image and its histogram

Γ

denotes the set of histograms (in the database) respecting possible constraints imposed by the attacker

(

e.g

: retaining a

minimum contrast

)

With

ν

*

we always denote the normalized version of the h

*

histogram

Goal: search a database of untouched image histograms to find h* such that:It has the most similar shape w.r.t. hY It belongs to ΓWe propose to use the Chi-square distance, defined asTherefore, the retrieved histogram is

Phase 1: histogram retrieval

Phase 2: histogram mapping

Goal: find the best mapping matrix that turns to number of pixels to be moved from value toA maximum distortion constraint is given, that avoid changes bigger than of the value of a pixelWe choose the Kullback-Leibler divergence to measure the statistical dissimilarity between the histograms, and yield the following optimization problem:

Convex!



M

ixed

I

nteger

Non Linear Problem



Phase 3: pixel remapping

We have the mapping matrix, but which specific pixels should be changed?Intuition: editing pixels in textured/high-variance regions causes smaller perceptual impactWe propose an iterative approach: for each couple (i,j)Evaluate the SSIM map between Z and YFind pixels having value i, and:scan these pixels by decreasing SSIM, change the first n(ij) to jmark edited pixels as “unchangeable”, repeat 2. for (i, j+1)If no more pixel of value i have to be remapped, repeat from 1., with (i+1,j)RemarksSSIM map evaluated iteratively, to take into account on-going modificationsObtained image will have, by construction, the desired histogram

Pixel Remapping

DB

Advantage of iterative remapping

If SSIM map is not iteratively computed, visible artifact are likely to appear…

Without iterative update

With iterative update

Experimental validation

We use the proposed technique to hide traces left by:Gamma-correctionHistogram StretchingBoth these operators leave strong traces in image histogram:

14\

Original

Gamma Corrected

Equalized

Original

Gamma Corrected

Original

Equalized

Experimental validation

We use the proposed technique to hide traces left by:Gamma-correctionHistogram Stretching (equalization)Both these operators leave strong traces in image histogram

Original

Gamma

Corrected

Equalized

Case study

Original Image

Processed image (gamma-correction)

Resulting histogram

Remapped histogram

Remapped image

Histogram from DB

Histogram Database

Search

Best match

DB histogram

Before Counter-Forensics

After Counter-Forensics

D

max

= 4

Histogram enhancement detection

Stamm’s detector [S08]It detects the peak-and-gap behavior of the histogramThis is done by considering the contribution of high-frequencies in the Fourier transform of the histogram

Original

Gamma Corrected

Equalized

[S08] M. C.

Stamm

and K. J. R. Liu. Blind forensics of contrast enhancement in digital images. In Proc. of

ICIP 2008

, pages 3112–3115, 2008.

Dataset & Experiment setup

Database of untouched histograms from 25.000 JPEG images (MIRFLICKR dataset). Total

weigth

: ~10MB

Apply gamma-correction and histogram equalization to 1300 images from the UCID dataset

Each processed image is “attacked” with the proposed technique, using {2,4,6} as values for the

D

max

constraint

We constrain the database search to histograms whose contrast is not smaller than that of the enhanced image (this is our

Γ

)

We evaluate performance of

Stamm

detector in distinguishing:

P

rocessed vs. untouched images

Processed&Attacked

vs. untouched images

We evaluate the similarity between attacked and processed images using:

PSNR (“mathematical” metric)

Structural Similarity Index (“perceptual” metric) [W04]

Experimental results

Results in countering detection of gamma-correction

Attacked – Processed distance

Experimental results

Results in countering detection of histogram equalization

Attacked – Processed distance

Application #2Conceal traces in the image histogram

Method to conceal traces left by double compression in the histograms of quantized DCT coefficientsHuge number of detectors exploit double quantization, e.g.: Estimation of previous compression [P08]Forgery detection [H06]

[P08]

 T.

Pevny

and J.

Fridrich

, “Estimation of primary quantization matrix for steganalysis of double-compressed JPEG images,” Proceedings of SPIE, vol. 6819, pp. 681911–681911–13,

2008

[H06]

 J. He, Z. Lin, L. Wang, and X. Tang, “Detecting doctored JPEG images via DCT coefficient analysis,” in Lecture Notes in Computer Science. Springer, 2006, pp. 423–435.

Double Quantization

DQ is a sequence of three steps: quantization with step b de-quantization with step bquantization with step a

Characteristic

gaps

More on DQ…

Why is it interesting?Allows forgery detectionTells something about thehistory of the content(e.g. fake quality problem)NOTICE:Effect is visible when first quantization is stronger than the secondThe behavior is observed in the histogram of quantized DCT coefficientsIf JPEG compression has been carried, holes are always present in the histogram of de-quantized coefficients

More on DCT histograms…

Double JPEG compression leaves the trace in the histogram of each DCT coefficientHow is this histogram calculated?Intuition:

8x8DCT

Single blocks

Image

Block-wise DCT

Coeff

.

Analysis

Perception in the DCT domain

Understand relationship between changes in the DCT domain and effects in the spatial domainJust Noticeable Difference (JND) => minimum amount of change in a coefficient leading to a visible artifactWatson defined JND for the DCT case, taking into account Human Visual System (HVS) properties:More sensitive to low frequenciesLuminance masking: brighter blocks can be changed moreContrast masking: more contrast allows more editing

1.4

1.0

1.0

1.45

14.5

17.2

17.2

21

What we want to do

In this case, traces are left in DCT histograms of quantized coefficients…

We must change these histograms, to make them similar to those of an singly-compressed image!

We need to revisit the previous application to adapt to the DCT domain

More histograms (64 instead of 1)

More variables (coefficients vary from -1024 to 1016)

Less intuitive remapping rules…

Histogram retrieval… revisited!

Need all DCT histograms of singly compressed images

Just take some JPEG images and extract them?

NO!

DCT histograms depends on the undergone quantization

Search would be practically dominated by this fact

We need to

simulate

JPEG compressed images:

Take DCT histograms of never-compressed images

During search, quantize each of them with the same factor of the query histogram

Distances may be weighted, to give more importance to low frequency

coeffs

Histogram mapping… revisited!

The problem is the very same, repeated 64 timesProblem: how to set the perceptual constraint (Dmax)?Idea: make it depend on JNDs => allow at most the amount of change leading to a JNDHere we cannot exploit local information (luminance/contrast)

1.4

1.01.01.4514.517.217.221

Notice: we’re working on quantized coefficients!Changes will be expanded after de-quantization!=> Watson’s matrix must be divided by the quantization step

1 2 22 2 2 2 2

Pixel mapping… revisited!

We have to move some DCT coefficients from a value to another… how do we choose them?

We exploit Watson model again

This time, we can exploit local information too

Algorithm:

Evaluate the JND for all

blocks;

For each element n(

i



j

)

Find

coefficients

having value

i

, and:

scan these

coeffs

by

decreasing

JND,

change the first n(

i



j

) to j

mark edited

coeffs

as “unchangeable”, repeat 2. for (

i

, j+1)

If no more pixel of value

i

have to be remapped, repeat from

2.

, with (i+1,j)

Does it work so smoothly?

No, it doesn’t

Artifacts show up, probably due to the high number of changed coefficients in high frequencies

Possible solutions

Consider the joint impact of changes in more than one frequency

Anything else? [open question!]

However, most detectors usually rely on low-frequency coefficients

We made some experiments remapping only the first 16 (in

zig-zag

ordering) coefficients

Experimental setup: detector

We implement a detector for double compression based on calibrationCalibration allows toestimate the originaldistribution of a quantizedsignalBasic idea with JPEG:Cut small number of rows/columnsCompute 8x8 DCT andhistograms

Read from file

Estimated

Experimental setup: method

200 TIFF (never compressed) imagesExperiment consists in evaluating detector performance before and after counter – attack

Detector evaluated in these tasks:

Discriminate single- vs. double- compressed images

Discriminate single- vs. attacked images

We do not want to cheat

i.e., we do not use threshold values from the first experiment to do classification in the second

Experimental results

Mean SSIM:

0.968

Mean PSNR:

42.9 dB

Conclusions

Our universal CF methods allow to conceal traces left by any processing in the first-order statistic

Evaluation of the effectiveness should probably rely on statistic measures rather than on detectors

Future works

:

Explore

connections

with Optimal Transportation

theory

Explore the use on un-quantized DCT coefficients (conceal traces of single compression)

Develop an

integrated

method to re-compress an image without leaving traces

Explore the use of different objective function for the histogram mapping problem

Thank youQuestions?AcknowledgmentsThis work has been supported by the REWIND project