Usingefficient linearlocalfeaturesinthecopy-moveforgerydetection task

ANDRE Y KU ZNE T SOV, V L ADISL AV MYASN IKOV

SAMARA STAT E A E ROSPACE UN IV E RS IT Y ( SSAU ) , WWW.SSAU .RU

KUZNE T SOFF.ANDRE Y@GMA IL .COM

A IST-2016

Contents1.Introduction toimageforgerydetectionproblem

2.Theproposed approach

3.Conductedexperiments

4.Conclusion

2

Imageforgery– whatisit?

Mainforgerytypes

1. Changing localcharacteristics

2. Copy-move(plain,transformed)

3. Splicing

4. Objectsmodelling

3

Copy-moveexample

Protectiontypes

1. Active(digitalwatermarks)

2. Passive(forgerydetectionalgorithms)

Digitaldataisusedeverywhere(research,commercialandmilitarypurposes)

Plaincopy-moveexample

4

Initialimage Imageforgery

Theproposedapproach

5

Problem: thereisno copy-movedetectionalgorithmwith~100%precision [1]

Thekeyfeaturesof theproposed algorithm:- 100%recall- highcalculationspeed(for real-timeimageanalysis)- lowcomputationalcomplexity- 99,9%precision

Themainstepsofthealgorithm1. Slidingwindowanalysismode2. Usespecialstructuralpattern3. Hashvaluescalculation( basedonlinearlocalfeatures)4. Storehashvaluesinahashtable

1. Christlein, V., Riess, C., Jordan, J., Riess, C., Angelopoulou, E.: An evaluation of popular copy-move forgery detectionapproaches. In: IEEE Transactions on Information Forensics and Security. Volume 7(6). (2012). 1841–1854

Structuralpattern

6

Astructuralpattern isdefinedasfollows:

,where

thesetofcoordinatesisdefinedasfollows:

( )ba,,Λℵ

( )( )

( )nmbabanm

,,,,,,

Π≡ΛℵΛ∈!

( )nmba ,,,Π

( )( ) ( ) ( )

( ) ( )⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

−+−+−+

−++

≡Π

1,1,,,1

,1,,,1,,,,,,

bnamnam

bnmnmnmnmba

!!

!

Letbeananalyzedimage( )nmf ,

– asimplified formofastructuralpattern( ){ }( )ba,,0,0ℵ

( ) 5,3,3, =ΛΛℵ

7

Duplicate

7

Thereareduplicatesbyapattern ( )ba,,Λℵ ,ifthereareatleast2pairsofcoordinates( )nm ʹʹ, ( )nm ʹ́ʹ́,and thatsatisfythefollowingequalities:

( ) ( )( ) ( ).,,,

,,,banm

nnmmfnnmmfΛℵ∈∀

+ʹ́+ʹ́=+ʹ+ʹ

Thetaskistodetermineforeachimagepixel,whichcorresponds totheupper leftpointofanimagefragment(withaformofastructuralpattern),aunique integernumber:0 – nocopy-move,>0– copy-movetype

(m’,n’) 1 2

3 4 5

6 7 8

(m’’,n’’) 1 2

3 4 5

6 7 8

Duplicates

Copy-movedetectionscheme

8

Hashvaluescalculation

Hashtable(containsabsolutefrequenciesofhashvalues)

Animagefragmentisidentified asaduplicate,ifitsabsolutefrequencyisgreaterthan1

01234

Hashvalues

Twohashingapproaches• Cryptographic• Perceptual

Linearlocalfeatures

9

Linearlocalfeature(LLF)overGaloisfieldGF(p): ,where( ){ }( )Amh Mm ,10−=

( ){ } 10−=Mmmh isakernel,AisaconvolutionalgorithmoverGF(p),p isaprimenumber

Ahashvalue isaresultof convolutionofanimagefragmentandakernel ( ){ } 10−=Mmmh

Linearlocalfeatures

10

( )

( ) ( ) [ ]

( ) [ ]

( ) ( ) ( ) [ ]

( ) ( ) [ ]

( ) ( ) .01~1

,2,,0~

,1,1,0~

,/1,,0

,/1,1,0

,10

1

1

1

1

=−++−

Θ−+∈=+−

Θ−∈=−−−

Θ−+∈=−

Θ−∈=−−

=

∑

∑

∑

∑

=

=

=

=

KMMha

KMMmmkmha

Mmmkmhamh

KMMmkmha

Mmkmhamh

h

K

K

kk

K

kk

K

kk

K

kk

ϕ

ϕ

ϕ

!

!

FIRvaluesarecalculatedusing thefollowingsystemoflinearequations(SLE):( ){ } 10−=Mmmh

( ){ } 1,0~: +=Θ≠∈=Θ + Knn ϕZSetofirregularities:

SLEaresolvedtoselecttheoptimalconvolutionkernel

12

−−+

KKMC

Recursive LLF calculation( ) ( ) ( ) ( )

1,0

~1

−=

−+−= ∑∑Θ∈=

Nn

mmnxknyanym

K

kk ϕ

(LLF weredevelopedby V.Myasnikov in2007)

Copy-movealgorithm

11

LetH(t) beahash-table,P(m,n) bea2Darrayofpotentialduplicates

nosubwindowsintersection

maximumsubwindowsintersection

false;

Experiments

12

Let us use a number of false detected duplicates (collisions) as a quality parameter colK

Test set: 10 satellite images SPOT-4, 5000x7000, without duplicates

,Precisionfptp

tp+

=

,Recallfntp

tp+

=

Metricsforqualityestimation

tp – truepositivefp – falsepositivefn – falsenegative

PCused:IntelCorei53470,8GBRAM

{ }Kkka 1= aredefinedasfollows:

(a)Fibonaccisequenceelements:K=2 –K=3 –K=4 –

(b) Polynomial coefficients:( ) k

Kk

k Ca 1−=

2,1 21 == aa3,2,1 321 === aaa

5,3,2,1 4321 ==== aaaa

Experiments.Accuracy

13

0

2000

4000

6000

8000

10x10 9x9 8x8 7x7 6x6

axb

Slidingwindowsize11×11, Slidingwindowsize18×18, 9=Λ4=Λ

024681012

16x16 14x14 12x12 10x10 8x8 7x7 6x6axb

Results:• a>8,b>8• 6>Λ

colKcolK

KcolProposedsolution 2DRabin-

Karprollinghash(a) (b)

2 240854 1338933 12353 242 230 12354 232 225 1235

Experiments.Accuracy

14

Method Precision,% Recall,%Circle 92.1 100FMT 90.57 100Lin 94.12 100Surf 91.49 89.58Zernike 92.31 100Ourapproach 99.9 100

Database[1]contains48 imageswithresolution3000x2300pixels

[1] Imagemanipulationdataset is created at the Friedrich-Alexander-Universität Erlangen-Nürnberg byV. Christlein et al.

Examples

15

Experiments.Computationalcomplexity

16

12000

12500

13000

13500

14000

9x9 9x10 11x11 13x13 15x15Avg.im

ageanalysistim

e,

ms

a×b

Average image analysis time is 12.5 s, because of recursive hash values calculation

Method Totaltime,s

Circle 5103.43

FMT 6948.03

Lin 4785.71

Surf 1052.12

Zernike 7065.18

Ourapproach 420.12

Resultsandconclusion

17

Plansforfuture1. Designing transformedcopy-movedetection(affine, JPEG,

contrastenhancement,etc.)2. ComparewithGPU-basedversionofthealgorithm

Results1. Thealgorithmhas0-falsenegativeerror2. Executionspeed isveryhighduetolowcomputational

complexity(including recursivehashcalculation)3. Falsepositiveerrorisinaverage%10 5−

18

Thanksforattention!Questions?