A study of image authentication based on self-similarity.

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A study ofimage authentication based on

selfttsiIIlilarity.

Yoko MAEMURA

Summary The conception of copyright

protection for digital image is of great in‐

terest in recently.Several digital watermark― ing schemes have an effect on piracy prevent―

ing, but they have some degradation of the originalimages because of the embedded sig― natte.It is therefore necessatt to authenti‐

cate the digitalimage、 vith no degradation es― pecially for the、 vorks of art. In this paper,

the author introduces the conception of the

ilnage authentication system using the

parameters of fractal coding based on the

self―similarity of the image structures and ini

vestigates the fundamental properties of this system.The address of best rnatched domain block, one of the fractal coding parameters

shows the information of geometrical correla‐ tions beh〆een the partitioned images and has

marked characteristics depending on each

iFnage.The detection rate of the best match―

ed domain blocks can be increased by the op― tinlization of the size of the partitioned image after the rnanipulations because of the relaxa― tion effect of geometrical distortions。

Key WVords: Authentication,ヽ Vaterl■ark,

Fract』 Compression,Similarity.

1. Introduction

During the last decade, digital technoト ogies have grown drastically. Digital audio,

video and softwal‐e are widely used not onけ

in office computer but also、 vithin home conl―

puter and open net、 varks. Neverthless one

particular problem of digital content is their ability to be easily processed. Several apph… cations of、vatermarking has been considered by many researchers [1]. Each、 vaterlnark… ing application has its o、vn specittc require‐

ments.Therefore,there is no set of require― ments to be met by all watemarking tech― niques.Neverthless,some general directions can be given for rnost of the apphcations,the mark had to be robustto image compression,

quantization, D― AIA―]D conversion,ftttering,

contrast transfornl and geometic transform.

The problem is that the、

vatermarking

schemes can not avoid the degradation of the

original image becausc of the embedding

marks. It is necessary for the authors、 vho

make works of arts desire to distribute their own original images、 vith no marks.The im―

age authentication with no degradation is re―

quired in this case.The requirements of this system is also robust to any manipulations.

The fractal code is generated by cal― culating an lterated Function Systenl from the image in the fractal compression scheme. This fractal coding parameter(called c01lage

map)is he infomation of the geometrical

correlations betヽ veen the block images and haVe Fnarked characteristics、 7hiCh depend on

each image.It is therefore useful to apply the

collage map for the image authentication.

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Jouma1 0f the Faculty of Global CO■ lmunication Siebold Universiり _{Of Nagasaki No 3}

using a collage map is cOnsidered as one par―

ticular scheme to authenticate the image fOr

the authOrs、vhO desire tO distribute the Origi‐

nal images、 vith nO degradatiOn caused by

、vatermarking.A conage map detected from

the image after geOmetrical translatiOns and

classical processed is used for certificatiOn of

ilnage.The vernani cipher constructed of the binalized mean values of the detected b10cks

and the content II)are used tO certificate the

COpright infOrmatiOn data for this system. The evaluatiOn of this system is the same as that Of、vatermarking schemes.The results of

the、veakness Of this system against the clas―

sical image processing operations and the Stirmark attack[2]are investigated.

2. Fractal COde

The coding―decoding syste■l of the frac‐ tal compression is based On the construcion ofthe image.This Iイactal cOde,、vhich can be seen as a collage map, extracts the self‐ silnilarities of the image. The present ap‐ proach is based on the block based fractal

compression scheme developed by Jacquin [3].This scheme express the image by a

fractal code.It cOnsists in searching an lterat―

ed Function System in the image:

1. An image is partitioned into non‐ _Overlap‐

ping square b10cks caned range b10cks。 The dOmain blocks、 7hiCh have the same size as the range blocks are extracted

froni the image。

2. The f0110、 ving step consists in building a fractal code which can be seen as a col‐

lage map! 、ve associate、vith each b10ck 島 of the partitiOn R,he block Dy which is mOre similar to鳥 _{(except itself).}

This test of self―similarity cOnsists in minilnizing a quadratic error bet、_veen the blockぢ時and the affine transfOrlned

blockち.

3. PropOsed rethOd

A conage map indices Obtained froni the fractal cOmpression scheme Fnentioned abOve are composed of the associated b10ck address of partitiOn D,the affine transforms τ_,the

scale factor s and the offset _ο_{parameters fOr}

each range blocks, Indeed it is statisticatty

rare tO ind a b10ck equalto another in an or‐

dinary image except、_{vhen the image is a frac‐}

tal imageo Contrary to Jacqin's scheme, present scheme dose not use the decoding

process,therefore the size Of dOmain blocks or range b10cks can be identical.The process

of the image authenticatiOn is as follo、_vs:

1. The original image

売

T∝

ッ)0=1,_.,Ⅳ

;ノ=1,…

.,刀

is partitiOned intO nonoverlapping square

range b10cks of size,P× BR pixels,

鳥

°

管

(ケ=1,2,中 o,ηl%=ハ

ち

/BR×n//8R).

2.

_元管(χ,ノ)is partitiOned into square

domain b10cks Of size BD× BD p els,

3°管0こ1,2,_.,物￨%=(N― BD)/S× (J〃生 BD)/S).

S is the searching step cell stte.

3.The best matched domain b10ck η

'6′

is satisfied the following equatiOns fOr

畔亀; '(鳥 9勺

_{島婢)=minヵ}

,与

。

,(鳥

°

粍9),

where,(島

?T,2")means the RMS

(Root Mean Sqtlare)between′ _{働9T and}

身 'が

.

4.Arι

∈

ADl,・

…

,4D.ShOW the address of

)'かof the Orlglnal image Obtained frOm the abOve procedure.

5. The image to be conirmed the authenti‐ cation is processed by the same proce― dure as fOr the ottginal image.The ad―

dresses of the best matched dOmain

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Yoko MAEMURA:A study of image authenticttion based on sel工 si画よlarlサ

are generated.4′ _rサ

∈ス′

Dど,.… ,4′D″ are

compared with Arケ

∈ス仇

,…

・

,4仇 and

the informaiton of the remained block can be detected.

Arサ is seemed to be robust to image

processing such as compresslon and/or filter― ing because the most silnilar domain block is selected for each range block. It is further―

more robust to the geometrical attack added

locally because the large size of domain

blocks reduces relaxation of the local distor―

tion. However it appears that the quahty of

fractal codes relies veげ heavily on block das― sification and analysis for large size of block.

This problem is dealt覇/ith an image、 vhich is

composed of the offset values of a collage

map in the preprocessing phase.The mean

value of the block is used as an offset value in this inethod.

The bit pattern of authentication(called authentication data)is generated as the ver―

nam cipher composed of the binalzed mean

values of the original image data and the bit

pattem of content ID(called ID data).ID

data and the authentication data are

registered and should be in safekeeping at the certiication center.The center correlates

the ID data deduced from the distributed iHl― age with the regestered ID data in the center. The lnean valuc of the block,、 vhere the best matched doコnain block are detected success―

fu■y are used for the threshold for he binah― zation.Therefore,the length of ID data is BR

×BR.

4. Sil■

ulation Results

The original gray scale image ``Lenna" (Fig■

)of SIDBA for the simulation.The

simulation to evaluate the proposed scheme

has been performed by testing robustness

against several kind of attack processing!the

Stilrnark attack as an geometrical transfor■ 1,

jpeg compression,median iltering and ran‐ dom nolse adding.

The Stiェrnark distortion is a attack lead― ing to a geometrical distoコしion that cannot be modeled by an attine transfornl on theヽ〃hole image.The Stirmark 3.O algorithm has been

widely used for the evaluation test for robust‐ ness.The system M/hich is robust to the Stir‐

mark attack means that it robust to other processes.Fig.l and Fig。 2 sho、v the original

ixnage and the Stirmark attacked image,

respect ely.

The rate of the remained parameter of conage map after the distortion by Stirmark

attack for the vanous block size are sho、 7n in Fig。

3.MV,SD and ABMDB are the

parameters of co■ age map,、vhich mean the mean value,the standard deviation and the address of the best matched domain block, respect ely in the figures.The rate of the remained parameter is increased in the block size because the distortion locany added by Stirmark is relaxed.The address of the best matched domain block shows the relationship

betttreen range and domain. On the other

hand,the mean value and the standard devia― tion are statically obtained. It is therefore that the address of the best matched domain

block is more robust than other t、 vo

parameters.The problem to setthe block size large is the large amotmt of calculation.The mean mask are introduced in preprocessing phase against this problem.The rate of the

remained parameter for the various mean

mask size are shoH〃n in Fig。4.「Phere is no influence of the size of mean masks. The

results for the mask size of 2x2 are sho、 vn in

Fig.5. The similar tendency are seen in this igure.

The simulations have been done for

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Journal of hc F“ ulけof Global Conlmunicaとon Sicbold Un ersiけ of Nagasaki No 3

the remained parameter are calculated for

the different qtlality of factors with the ipeg

compression scheme in Fig.6覇嵐th the lnean mask size of 2x2. It can be seen that the results for the large size of block is more robustto thejpeg compression than the small one,

The results against the median iltering

are sho、vn in Fig.7、vith the mean mask size of 2x2. It can be noticed that the results of the address of the best rnatched domain block

is rnore robust than other parameters frhis is due to the lo、v pass component of the image can be remained after iltering process.

The results are calculated for the differ―

ent random noise level in Fig.8 、vith the

mean mask size of 2x2. The large size of

block is more robust than the small one ex―

cept for the standard deviation.

The ID data deduced from the manipu‐ lated image are successfully detected for an kind of attack using a maioriサ ■Ogic as seen in Tab.1.

5, COnclusion

The conception of image authentication system using the fractal code based on selニ similarity of the image structures has been

proposed in this M「 ork.The present study in―

dicates that the address of the best rnatched

domain block is more robust than other

parameters of fractal code to be used for the

authentication. The general frame、パ/ork per―

■ts to foresee many perspectives to in―

troduce this characteristics to the覇 /atermark‐

ing schemes.

References

[1]G.C.Langelaar,IoSetyawan,R.L.Lagen―

dttk,“ヽヽratermarking Digital lmage and

Video Data", IEEE Signal Processing

h/1agazine,Sep,2000.

[2]M.G.Kuhn,Stirmark,http7/Ⅵ螂岬_「.d.cam

ac.uk/fapp2/、

vatermarking/image_

watermarking/stirmark/,1997.

[3]A.E.Jacquin, “IInage coding based on a

fractal theory of iterated contractive im―

age transformations", IEEE Trans.IIn― age Processing, ヽrol.1, No.1, pp.18-30, 1992.

Fig l:Original image

Fig 2:Attacked image by the Stirmark

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MV

―■‐ …… SD ｀ミぶ洋……型

ABMDB

―

e―

白】ど,那

p中

心｀

5 10 15 20 25 30

block size[piXel]

Fig.3:The remaining rate of conage map data for the block size ttrith no mean mask

MV

一 ― ―

SD

_・ざ｀_冬_{‐ ヽ}一ヽ

ABMDB e―

012345

size of mean mask[piXell

Fig.4:lΓ he remaining rate of couage map data for the different mean mask size.

MV 4-―

SD ｀｀｀Ⅲ………

ABMDB

―

C―

0 2 4 6 8 10 12 14 16

block size[PiICl]

Fig 5:「Fhe remaing rate of conage map data for the block size with the mean mask size of

2×2

Fig. 6: The remaining rate of a couage map after ipeg COmpression for the different qua五け

factors.

MV

―モ‐ … … SD ｀ヾミ｀N・・…ヽ ABMD】尊轄卜韓電

0 2 4 6 8 10 12 14 16

block s'7e[piXCI]

Fig, 7: The remaining rate of a conage map after median filtering(3x3)

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Joumal of he Facdty Of O10bal Commu cat10n Siebold University of Nagasaki No.3

Tab.ユ:The detection rate Of ID data,

１００削側４０２００［ゞ︼＝鼠 ∞ 目召︻_目３脂

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頑

100

ご

80 震 60

・

_:t40 昌 20 営 0

Fig.8:The remaining rate of a cdlage map after

randokn noise adding fOr different level,

Attack Stirmark Jpeg Median

Random

NOise

閉

恥

醜

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