universal counter forensics methods for first order statistics

UNIVERSAL COUNTER FORENSICS METHODS FOR FIRST ORDER STATISTICS

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

MM&SEC 2012 – Coventry, UKUniversal Counter-Forensics

Outline1. MultiMedia Forensics & Counter-Forensics

2. Universal counter-forensics

3. Proposed approach1. Application to pixel domain2. Application to DCT domain

4. Results and discussion


MM Forensics & Counter-Forensics• MM Forensics:• Goal: investigate the history of a

MM content• Rapidly evolving field, but…• Countermeasures are evolving

too!

• Counter-Forensics:• Goal: edit a content without

leaving traces (fingerprints)

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project 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)

Counter Forensics Taxonomy [K07]

Scope

Universal Targeted

Approach

Integrated Post-processing

[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:

A. If you know what statistic is used by the analystB. just adapt the statistic of your forgery to be very close to the

statistic of “good” sequencesC. Any detector based on that statistic will be fooled!

• Game Theory:• This scenario can be seen as a game [B12]• Forensic Analyst vs. Attacker• Different games are possible:

① The adversary directly know the statistic of the “untouched sequences”② 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 error• Assumptions:

• Analyst’s detector relies only on first order statistics• Adversary has a database (DB) of histograms of untouched

images• So the adversary:

• Processes the image• Searches the DB for the nearest untouched histogram• Computes a transformation map from one histogram to the

another• Applies 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 histogram• Many 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 hY denote the processed image and its histogram• X and hX denote the untouched image and its histogram• Z and hZ 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 Γ

• We propose to use the Chi-square distance, defined as

• Therefore, 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 to• A maximum distortion constraint is given, that avoid changes bigger

than of the value of a pixel• We choose the Kullback-Leibler divergence to measure the statistical

dissimilarity between the histograms, and yield the following optimization problem:

Convex! Mixed Integer 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 impact

• We propose an iterative approach: for each couple (i,j)1. Evaluate the SSIM map between Z and Y2. Find pixels having value i, and:

a. scan these pixels by decreasing SSIM, change the first n(ij) to jb. mark edited pixels as “unchangeable”, repeat 2. for (i, j+1)

3. If no more pixel of value i have to be remapped, repeat from 1., with (i+1,j)

• Remarks• SSIM map evaluated iteratively, to take into account on-going modifications• Obtained 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 updateWith iterative update


Experimental validation• We use the proposed technique to hide traces left by:

• Gamma-correction• Histogram Stretching (equalization)

• Both these operators leave strong traces in image histogram

Original Gamma Corrected Equalized


Case study

Original ImageProcessed image (gamma-correction)

Resulting histogramRemapped histogram

Remapped image

Histogram from DB

Histogram Database

Search

Best match


DB histogram

Before Counter-Forensics

After Counter-Forensics

Dmax = 4


Histogram enhancement detection• Stamm’s detector [S08]• It detects the peak-and-gap behavior of the histogram• This 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 Dmax 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:

• Processed 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 coefficients• Huge 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:

1. quantization with step b 2. de-quantization with step b3. quantization with step a

Characteristic gaps


More on DQ…• Why is it interesting?

• Allows forgery detection• Tells something about the

history of the content(e.g. fake quality problem)

• NOTICE:• Effect is visible when first quantization is stronger than the

second• The behavior is observed in the histogram of quantized DCT

coefficients• If 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 coefficient• How is this histogram calculated?• Intuition:

8x8DCT

Single blocksImage Block-wise DCT

Coeff.Analysis


Perception in the DCT domain• Understand relationship between changes in the DCT domain and

effects in the spatial domain• Just Noticeable Difference (JND) => minimum amount of change in

a coefficient leading to a visible artifact• Watson defined JND for the DCT case,

taking into account Human Visual System (HVS) properties:• More sensitive to low frequencies• Luminance masking: brighter

blocks can be changed more• Contrast 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 times• Problem: how to set the perceptual constraint (Dmax)?• Idea: make it depend on JNDs

=> allow at most the amount of change leading to a JND• Here we cannot exploit local information (luminance/contrast)

1.4 1.0

1.0 1.45

14.5 17.2

17.2 21

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

2 2

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:

1. Evaluate the JND for all blocks;

2. For each element n(ij)a. Find coefficients having value i, and:b. scan these coeffs by decreasing JND, change the first n(ij) to jc. mark edited coeffs as “unchangeable”, repeat 2. for (i, j+1)

3. 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 calibration• Calibration allows to

estimate the originaldistribution of a quantizedsignal

• Basic idea with JPEG:• Cut small number of rows/

columns• Compute 8x8 DCT and

histograms

Read from file

Estimated


Experimental setup: method• 200 TIFF (never compressed) images• Experiment consists in evaluating detector performance

before and after counter – attack

Compress

Run detector

Re-Compres

s

Run detector

Remove traces

Run detector

• 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:0.968Mean 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

universal counter forensics methods for first order statistics

Documents

counterforensics goal

il counterforensics

defeating image forensics

untouched imagesso

statistic of good sequences

analysts detector

information hiding

game theory