Authentication of Volume Data Using Wavelet-Based Foveation

Wavelet-Based Foveation

M.S.Kankanhalli 1

, E.-C.Chang 1

,X.Guan 2

,Z.Huang 1

,and

Y.Wu 1

1

DepartmentofComputerScience

fmohan, changec, huangzy, wuyinghug@comp.nus.edu .sg

http://www.comp.nus.ed u. sg /

2

DepartmentofComputationalScience

NationalUniversityofSingapore

guanxin@cz3.nus.edu.s g

http://www.cz3.nus.ed u. sg/

Abstract. 3D volume datahasbeen increasinglyused inmany appli-

cations. The digital nature of the data allows easy creation, copying

anddistribution.However,italsoallowseaseofmanipulationwhichcan

enablewilfulorinadvertentmisrepresentationofthecontent.Foranap-

plicationlikemedicalimaging,thiscanhaveseriousdiagnosticandlegal

implications.Thusthereisastrongneedtoestablish theintegrityofa

particularvolumedata-set.Wearguethatthetraditionaldataauthenti-

cationmechanismslikedigitalsignaturesorcryptographic methodsare

not very useful in this context due to their extreme fragility. What is

requiredisamethodthatcandetecttheintegrityforallowablecontent-

preservingmanipulations.Wehavedevelopedanovelauthenticationpro-

cedurewhichisrobustagainstbenigncontentmanipulation.Thevolume

datacanberobustlyauthenticatedundernormaloperationssuchasscal-

ing,resamplingandadditiveGaussiannoise.Ontheotherhand,itoers

protectionagainstanymalecorunintentionaldatamanipulationwhich

signicantlychangesthecontent ofthe volumedata-set.Suchmanipu-

lationsincludecropping,changingofvoxelvaluesetc.Ourmethoduses

segmentation, wavelet-based foveation, and encryption to achieve this.

Wehaveimplementedthemethodandtested itsrobustness forseveral

manipulations.

Keywords:VolumeData,Authentication,Foveation,Wavelets

1 Introduction

3D volume data has been increasingly used in many applications [11]. Medi-

cal imaging is one area which generates an enormous amount of volume data.

Recently, there has been increasing awareness about the problem of copyright

protectionofdigitalimages,videoandaudio[10].Researchershavestartedrais-

ing concerns aboutthe copyright protectionand piracy of 3D data as well. In

thecopyrightproblem,nottheintegrityproblem.Inthispaper,weaddressthe

problem of authenticating 3D volume data i.e. verication of the genuineness

of the data-set.For example, given a medical volume data set which shows a

medicalconditionlikeatumor,wedonotwantthepatienttofraudulentlyalter

the data-set so that the tumor is removed and thus mis-representthe medical

condition to an insurance company. Similarly, wewould notlikea medicalin-

stitution to alter the data-set in order to introduce artifactswhich represents

someabnormalityandmakeapatientgothroughunnecessaryexpensivemedical

procedures. In such situations, preserving and checkingthe veracityof a data-

setassumestremendousimportance.Evenforvolumedatasetswhichrepresent

art objectsor manufacturedobjects,theaccuracyand integrityof thedata-set

needstobe preserved. Basically,a secureauthenticationsystemcanprovethat

notamperinghasoccurredduringsituationswherethecredibilityofthevolume

data may be questioned.In the two hypothetical scenarios present, there is a

need to detect that some illegal manipulation has taken place. On the other

handifsomeallowablemodication(likere-samplingofthedata-set)isdone,it

should detectthis manipulation butit should indicatethat thedata-set is still

usable.

We propose that this problem can be addressed by use of a content-based

digital signature which is robust yet eective. The idea is that at the time of

datacreation (which isthrougheither some physicalscanning devicelikeaCT

Scannerorthroughsomesoftware),acontent-baseddigitalsignatureassociated

withthedata-set issimultaneously created.Forallfurther authenticity checks,

thisdata-setcanbeveriedagainstthisdigitalsignature.Ifthereisamis-match,

thenthedataisconsideredunreliableanditshouldnotbeused.

Twosolutionpossibilitiesnaturallyarisewhenconsideringthisproblem.One

couldarguethateithertraditionalgeneralmessageauthenticationtechniquescan

beusedorperhapssemi-fragilewatermarkingtechniquescouldbeused.Wewill

nowarguewhyneitherofthispossibilityisapplicablefor3Dvolumedata.

Traditionalmessageauthenticationtechniqueslikehashing-baseddigitalsig-

natures or cryptographic authentication [20] cannot be used because of their

extreme fragility. These techniques do not tolerate ipping of even one bit of

information of a message. For example, we could use the traditional message

digestbaseddigitalsignatureforavolumedata-set.Evenifoneleastsignicant

bitofa voxelischanged,theauthenticationprocedurewill agthisdata-setas

unreliable.However,forvolumedata,certainoperationssuch asscaling,resam-

plingetc.arevalidoperationsinwhichcasesthemanipulationsarebenign.They

arenotintendedtochange thesignicantcontentofthedata-set andthusthey

donotimpacttheintegrityofthedata. Oneexampleisthecontent-based dig-

italsignatureproposed in[16]whichused thehistogramof divideddata blocks

as the content to be hashed. If thevoxelvalues are uniformly deduced byone

unit, or more generally, a Gaussian noise with a non-zero mean is added, this

signaturemayfailtoauthenticatethedata.Therefore,weneedanoveldigitalsig-

somebodyreallytamperswiththecontent,e.g.cropsoutthetumorregion,then

thedigital signatureshouldindicate thatdata-set hasbeentampered withand

thus isunreliable. Thus traditionaldigital signaturesare notuseful but robust

authentication (robustnesstoallowablemanipulations)isrequired.

Thesecondpossibilityis theuseofsemi-fragile watermarks forthepurpose

ofauthentication[13].Manytechniqueshavebeendevelopedfor2Ddigitalim-

age data which could perhaps be adapted for 3D volume data. Unfortunately,

this is not possible for two reasons. Firstly, theimage watermarks usually ex-

ploitthecharacteristicsofthehuman visualsystem(HVS) inorderto hidethe

secondary watermark information.In caseofvolumedata, the HVScannot be

exploitedbecausewecanonlyvisualizethe3Dvolumedatathroughsurfaceand

volumerendering. Secondly, there is anevenmore serious problem. All water-

markingtechniques involvethemodicationofthevoxelvaluesforthepurpose

of embedding thewatermark. However, forthecaseof volume data (andespe-

cially relatedtomedicalimaging), distortionof thevoxelvalues isnotallowed.

Evenifsmallperturbationsinthevoxelvalueswereallowed,there isnowater-

marking method which can provably bound thedistortion ofthe voxelvalues.

WhiletheParseval'stheorem[6]canguaranteethebounding oftheoverallwa-

termarksignal energy, simultaneouslylimitingthemaximumdistortionlevelin

thespatialdomainandfrequencydomainappearstobeverydiÆcult.Therefore,

watermarkingtechniquesarealsonotusefulforauthenticating3Dvolumedata.

In this paper, we present a new technique for authenticating 3D volume

data using a robust content-based digital signature. This signature is derived

from the signicant features of volume data so that if any of these features

are altered signicantly, the signature will not match the data-set. The term

content-based refers to the fact the important features of the data (whose in-

tegrityweareinterestedincertifying)shouldbesomehowincorporatedintothe

digital signature.Therationale beingthat ifsomeimportantcontentfeature is

deleted/modied/added, then the digital signature should not match the doc-

tored data-set.Theterm robustrefers tothefactthat anymanipulation which

does not change the signicant features should not aect the veracity of the

signature. For such benign operations, the digital signature should indeed au-

thenticate the data-set.Common typesof operations on volume data-sets are

scaling, thresholding, cropping, cut-and-replace a sub-volume, ltering, addi-

tion/removal of noise and aÆne transformations. As long as these operations

donotchangethecontentfeatures,theyareconsideredbenign.Weuseanovel

wavelet-basedfoveationtechniquetoaccuratelyand succinctlycapturethesig-

nicantcontentfeatures. Moreover,theschemeallowsaexiblethresholdtobe

setwhichcandeterminetheextentofthemanipulationswhichcanbeconsidered

Wewillnowprovideanoveralldescription ofthemethodforgeneratingthero-

bustcontent-baseddigitalsignatureandthemethodforauthenticatingavolume

data-setusingthisdigital signature.Forthegenerationofthedigital signature,

thefollowingstepsarerequired:

1. Feature extraction:Thebasicideahere isto capturethe essentialfeatures which

needto be preserved forauthentication. Since the size of a3D volumedata-set

ishuge,this also allows us to createa compactkey derived fromthe important

features.Theprocessisdoneinthreesteps:

(a) Volumesegmentation:Thevoxelsoftheinput 3Dvolumedataareseparated

intotwoclasses{thesignicant\foreground"andtherelativelylessimportant

\background".Whilewepresentamethodfordoingthesegmentationinthis

paper,werecognizethatdierenttypesofdata-setsneedtheirownspecialized

segmentation technique. Our authentication method is exible inthe sense

that it doesnot really depend onthe particular details ofthe segmentation

algorithmused.Ifrequired,thispartcanbecustomizedeitherforaparticular

applicationdomainorforanindividualvolumedata-set.

(b) Selection ofkey voxels: Ingeneral,the numberofvoxelsintheforeground is

quitelarge.Toreducethe amountof data,afew \keyvoxels"are chosenfor

thepurposeofdatareduction.

(c) Wavelet-basedfoveation:Tomakesurethatimportantcontentthroughoutthe

foregroundiscaptured,weapplythefoveationtechniquewhichisbasicallya

space-variant lteringtechnique. We believe itis very important to use this

sinceitsummarizesalltheimportantcontentthroughouttheforegroundwith

thekeyvoxelsasthefoci.Thusallsignicantfeaturesarecompactlycaptured.

Additionally sinceit is amany-to-onemapping, it oerssecurity.Thus, this

informationcanbeusedasakey.

2. Encryption:Foradditionalsecurity,public-keycryptography[20]isutilizedtoen-

cryptthekeyderivedintheprevious step.Basically,thesecretkey oftheowner

ofthevolumedataisusedtoencryptthefeaturekeyobtained.Forthepurposeof

authentication,thepublic-keyoftheownercanbeusedtodecryptthisinformation

andthefeaturekeycanbethusrecovered. Sincethis stepis well-understood,we

willnotdiscussitfurtherinthispaper.

For authenticating a particular volume data-set, the following steps are per-

formed:

1. AÆnetransformationparametersrecovery:Since,oneofthebenignmanipulations

could be the aÆne transformation of the volume, the transform parametersare

computedrst.

2. Matching:Thecontentfeaturesofthetransformedvolumearecomparedwiththe

content features of the original data-set(obtainedfrom the digitalsignature af-

terdecryptionusingtheowner'spublickey).Amatchvaluebetweentheoriginal

featuresandthetransformedvolumefeaturesiscomputed.Ifthismatchvalueex-

ceedsacertainthreshold,thenthevolumeiscertiedasgenuineelseitisconsidered

Given a volume data-set, we rst extract the feature points (key voxels) af-

ter performing segmentation. Thenumber of the feature points must be small

in order to guarantee the acceptable small size of the signature. Basedon the

extracted featurepoints, a weightednorm isselected. Thevolume isthenloss-

ilycompressedusingthisweightednormasthemeasure. Thedescriptionofthe

weightednormandthecompresseddataareencryptedusingpublic-keycryptog-

raphyandtheyconstitutetherobustcontent-based digitalsignatureassociated

withthisvolumedata-set.

3.1 FeatureExtractionof Volume Data

Inthissubsection,wedescribetheprocessofextractingfromtheoriginalvolume

data a smallnumber of voxel groupsthat representthe importantinformation

(features).Itconsistsoftwosteps:volumesegmentationandkeyvoxelsampling.

Volumesegmentationis toidentifyanddemarcateinto foreground/background

thevoxelintheoriginalvolumedata.Notethattheforegroundvoxelscanbelong

todierentsub-categories(likebone,skin, softtissues,etc.).Thisresultsinthe

segments (a connected sub-volume) with each one representing an important

featureofthedata.Itissimilartoimagesegmentation,acommontechniqueused

in computer vision. Usuallythe number of voxelsin each segmentis too large

tobedirectlyusedforthesignature.Thus,keyvoxelsamplingisusedtoderive

a few keyvoxels from each segment forthe foveation process which eectively

summarizes thesignicant content of thedata-set, and will be detailed in the

nextsubsection.

Wepropose a segmentation method based on thevoxel valueanalysis and

bounding boxinformation of the isosurfaces.It can be summarizedas follows.

Weassumethatthevoxelvaluesarescalar fortheeaseofdescription.

1. Partitionofthevoxelvaluesbydataanalysis.First,allthevoxelvaluesaresorted

inthenon-descendingorder. Second,partitionthesortedlistusingthethreshold

value.Thethresholdvalueisspeciedbytheuserinourcurrentimplementation.

However,heuristicscanbeappliedifthedomainknowledgeisknownforthepar-

ticular class of volume data. For many volume data sets, the density values of

signicant content components aredistinguishable eventhoughthe voxelsrepre-

senting themare closelyconnectedto eachother. Sometimes,they may perhaps

evenhavesimilarvoxelvalues inwhichcasedomainknowledgecould beutilized

fordistinguishingthem.Forexample,humanCT/MRIvolumescanbepartitioned

byusingthedensityvaluesaswellasanatomicalknowledge.

2. Isosurfacing.From the partition, we derive a set of voxel values that partition

dierent parts.Thesevoxelvaluesareused toderivethe samenumberofsetsof

theisosurfaces.

3. Segmentation. One segment of voxels can be formed if they are bounded as a

closedsub-volumeby(1)oneisosurface,(2)severalisosurfaces,or(3)oneorseveral

isosurfaceswiththeoneorseveralborderplanesofthevolume.ItcanbeeÆciently

accumulatetheintervalsboundedbytheisosurfacesandborderplanesiteratively.

4. Featureextraction.Itisaprocessofselectionofkeyvoxels.A3DGaussianmask

isappliedonthevolumeseveraltimesaslowpassltering.Duetothelargesizeof

volumedata,wesimulatethe3DGaussianlteringasawindowedlowpassltering

dimensionbydimension.Inthehighlyblurredresultingvolume,thekeyvoxelsare

chosento belocalmaximum voxelswhichare aboveapredened threshold.The

key voxelsarethenusedastheinputtothefoveationprocedure.

Ifthe size ofvolumedata is N 3

, sorting in therst steptakesO(N 3

logN)

time. It is O(N 3

+logh) for isosurfacing in step 2 where h is the number of

dierentextremevalues(minormax)[5].ItisO(N 3

)forthescanconversionin

step3. Sotheoveralltime complexity isO(N 3

logN). Oneexampleas a result

ofthisprocedure isshownin Fig1.

50 100 150 200 250 300 350 400 450 500

50

100

150

200

250

300

350

(a) (b) (c)

Fig.1. Examples of volume segmentation results: (a) the skull bone, (b) the skull

muscleandsofttissue,and(c)theinternalpartofatomato.

3.2 Content-basedWeighted Norm

Wenowbrieypresenttheideabehindsummarizingthevolumeusing aspace-

variant wavelet basedlter. The basic idea is to summarize and compress the

importantcontentinformation.Most2D/3Dimagingsystemsusea norm(usu-

allytheEuclidean2-norm) tomeasuretheirperformance.However,the2-norm

treatseach pixel/voxelequally.However,inmostreal-lifedata,itispossible to

determine some regions that are more interesting for the application at hand.

Forexample,throughfeaturedetection,wecanndsignicantvoxelsinagiven

data-set.Insuchcases,aweightednormismoreappropriate.Theweightednorm

kk

w

forthevolumeV(x;y;z)withaweightingfunctionwisgivenby:

kVk 2

w

= X

x;y;z

w(x;y;z)V(x;y;z) 2

;

wherew(;;)istheweightingfunction.Inourauthenticationsystem,acontent-

basedweightednormisusedformeasurementofthedistortioncausedbyallow-

naturecreationprocess,theoriginalvolumedataislossilycompressedunderthe

weightednorm.ThehighlycompresseddataS,togetherwiththedescriptionof

weightingfunctionW, forms thesignature (S;W).This signature can then be

further encrypted.Because the description of theweighting functionis part of

thesignature, to satisfycompactness,w cannotcontainthe fullinformation of

theoriginaldataset.Wenowdescribein detailthewholeprocedure.

3.3 Wavelet-based Foveation Technique

Our visual system has a space-variant nature where the resolution is high in

a point (fovea) but falling o towards the peripheral[17]. This distribution of

resolution providesa fastandsimple way ofreducinginformationin thevisual

eld, without sacricing the size of the visual eld and the resolution around

the fovea. Asthe biological visualsystemis highly eective,this space-variant

naturehasinspiredthedesignofmanycomputervisionsystemswhichresembles

thebiologicalfoveatedvision[3,1,18],videoconferencing[2,7],andvisualization

systems [12].

Thefoveatedvolume isobtained froma uniformresolution volumethrough

aspace-variantsmoothingprocesswherethewidthofthesmoothingfunctionis

smallnearthefoveabutgraduallyincreasestowardstheperipheral.Theprocess

of going from a uniform volume to a foveated volume is known as foveation.

Thefoveationofa functionV :R d

!Risdeterminedbya smoothingfunction

g:R d

!R,anda weightfunction w:R d

!R

0 .

(TV)(x):=

Z

R d

V(t)w(x)g(w(x)kt xk

2

)dt: (1)

Theweightingfunctionwdepends uponthreeparameters andtakestheform

w(x)= kx k d

+

1

: (2)

We call the rate as it determines how fast resolution falling o, call

thefovea as itdeterminesthepointofhighestresolution, and call thefoveal

resolution as itdetermines theresolution at the fovea. Both and are non-

negativeandthesmoothingfunctiongisnormalizedsothat R

1

1

g(x)dx=1.In

general,wecouldreplacetheweightingfunctionbyany non-negativefunction.

This generalizationis useful when we are interested in volumes with multiple

foveae.Giventwo weightingfunctionsw

1 ,w

2

,theblendedw

3 is

w

3

(x)=maxfw

1 (x);w

2

(x)g: (3)

Foveated volumes can also be treated as the approximation of an volume

using axed numberof bit,using aweightednormas theunderlyingmeasure.

Thisweightednormcanbederivedfrom(1)andhastheform,

kVk

w

= Z

d V(x)

w(x)

dx; (4)

Wavelet bases have importantapplications in mathematics and signal pro-

cessing due to their ability to build sparse representation for large classes of

functionsand signal[14].Itisa naturalchoice forfoveatedvolumeduetotheir

localityinspaceandfrequency.Interesting,thechoiceoftheweightingfunction

(2) gives a self-similarity across scales [4], which is illustrated in Fig 2. This

propertyleads toasimple butfastextractionalgorithm[4].

HHH3 LLL

HHH 1 HHH 2

HHH3 LLL

HHH 1 HHH 2

HHH3 LLL

HHH 1 HHH 2

(a) (b) (c)

Fig.2.AllowableLowpassFiltering:(a)OriginalwaveletcoeÆcients(Cw); (b)After

allowablelowpassltering(C 0

w

);(c)RemainingcoeÆcients(C

w

).C

w C

0

w

=C

w

.

3.4 Extracting the CoeÆcients

Recallthattherstpartofthesignature(S;W)isthehighlycompressedvolume.

ToobtainS,onecouldrstcomputethefoveation(1)withrespecttothemulti-

foveaeweightingfunction,andthencompressthefoveatedvolumeusingaknown

lossyorlosslesscompressiontechniqueforuniformvolumes.Becausecomputing

(1)directlyiscomputationalintensive,weusetheapproximation(5).

(T fov

I)IDWT(M DWT(I)): (5)

In our implementation, S is extracted from the volume by quantizing the

wavelet coeÆcientsM DWT(I),followed byalossless compressionusinggzip.

Foran intuitiveillustration,weuse a 2Dimage to showits compressionresult

(Fig3).The(S;W)canthenbeencryptedandbestoredasthedigitalsignature

forthatimage.

Notethatgzipisagenerallosslesscompressiontool,whichdoesnotexploit

propertiesofvolumes,especiallythecoherenceofwaveletcoeÆcientsacrossspace

and scale. Thus it is not the best technique for our application. A possible

improvementcan be donebyincorporatingthe well-known zero-treealgorithm

Fig.3.(a)ThemaskMfortheweightingfunction.(b)Theoriginalimage(262Kbytes).

(c)Thecompressedimage(4Kbytes)usingthemaskM.

4 Implementation and Experiment Results

TherstphaseoftheauthenticationprocessisdetectionoftheallowableaÆne

translation applied to the volume data-set. For consistency, the norm used in

thedetectionis theweightednormwhose weightingfunctionispart ofthesig-

nature. That is, the detection nds the aÆne transformation T

min

such that

h

0

= kT

min

(S) Vk

w

is minimum. Through our preliminary experiment, we

nd that such T

min

can be accuratelydetermined fortranslation androtation.

In the rest of this section, we assume that no aÆne transformation has been

appliedto thedata-set.

Inthesecondphaseofauthentication,thesimilarityvalueh

0

=kS Vk

w is

comparedwithapredeterminedthresholdA

0

H,whereA

0

isanormalizingfactor

dependingonlyonthesizeandmeanofthevolumedata-set.Ifhissmaller,then

thevolumeisdeclared tobe authenticated. Otherwise,itis rejectedandhence

considered unreliable. The choice of the H depends on the level of allowable

attacks.Itcanbedeterminedanalyticallybyassumingacertaindistributionon

the voxel, or through experiment conducted a-prior to the signature creation.

In our experiments,we choose H =0:08, which is analytically determined by

assuming that the allowablelow-pass will lter outonly therst level wavelet

coeÆcientsasillustratedinFigure2.

Wedid experiments ontwo volume datasets with 256 graylevels, SKULL

(646464)andTOMATO(12812864).Intheselectionofkeyvoxels,we

usedawindowedlowpass lteringforvetimeswiththewindowsize9andthe

threshold 1:5. Theresulting numbers ofkeyvoxelsare 25for SKULL and124

forTOMATO.Thesizes ofthesignaturesare8Kand19Kbytesrespectively.

Fiveexperimentsweredonewiththesetwovolumedatasets.Therstthree

experiments examine the signature robustness under global manipulation like

low-pass ltering, sharpening, and lossy compression, whereasthelast two ex-

perimentsconsider localmanipulationlikecroppingand localizedmodication.

Intherstexperiment,thevolumedata-setsaresubjectedtolowpassltering.

Thelowlteringis achievedbya rectanglewindow.FromFigure4(a),thesig-

of our signature under lossy compression, weapplied zero-thresholding to the

volumedata-set.Thatis,givenathresholdT,allwaveletcoeÆcientCsatisfying

jCj<T arereplacedbyzeros.TheresultsfordierentT isshowninFigure 5.

Figure 6 (a) shows the robustness after thevoxelsin the center region are

replaced by zeros, and Figure 6(b) shows the robustness after the volume is

cropped.

3 4 5 6 7 8 9

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Lowpass Filtering. Inplemented as Moving Average with Window Size X.

Window Size

Similiarity Value

SKULL TOMATO Threshold (Below: Accept)

0 5 10 15 20 25 30 35 40 45

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Adding White Noise with σ ² = X.

σ ²

Similiarity Value

SKULL TOMATO Threshold (Below: Accept)

(a) (b)

Fig.4.ResultsforLowpassFiltering(a)andAdditionofWhiteNoise(b)

200 220 240 260 280 300 320 340 360 380 400

0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12

Lossy Compression. With wavelet compression threshold = X.

Wavelet compression threshold

Similiarity Value

SKULL TOMATO Threshold (Below: Accept)

Fig.5.ResultsforLossyCompression

Modication of information ofa volume data can take three forms. One is

tomodifyaparticularpartofthevoxelvaluestoothervalues,e.g.,setallvoxel

remains. Since ourmethod of important feature extraction does not aim at a

particularregionofthevolume,itisenough togivefalse-signaturealarm when

toomuchinformationhasbeenremoved.ThiscanbeseeninFig 6.Inreal-world

applications, users can dene the regions-of-interest for feature extraction, for

example, tumorsor abnormal bones. The third modication is theaddition of

previouslynon-existentcontentfeature.Thisis handledin a mannersimilar to

the onefor theremoval case.Thus, withtheproposed robustdigital signature

scheme,thesignaturewillmatchonlywhenall(andnomore)regions-of-interest

canbe detected.

0 5 10 15 20 25 30 35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Remove of Central Part of Size X ³ .

Removed part size: X ³ .

Similiarity Value

SKULL TOMATO Threshold (Below: Accept)

35 40 45 50 55 60 65

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cropped to be the central part of original volume with size X ³ .

Cropped size: X ³

Similiarity Value

SKULL TOMATO Threshold (Below: Accept)

(a) (b)

Fig.6.ResultsforRemoval(a)andCropping(b)

5 Conclusion

We have described a novel robust content-based authentication technique for

volume data. Thetechniqueuses segmentation followed by keyvoxelselection

which are used as fovea for a wavelet-based foveation procedure to derive the

content-based key for the volume data-set. This key is then encrypted using

public-key cryptography and used as a robust digital signature. For authenti-

catingaquestionablevolumedata-set,theaÆnetransformationparametersare

rstdeterminedandfeatureextractionisdoneforthetransformedvolume.The

featureforthetransformedvolumeisthenmatchedagainstthefeaturevaluesin

the original digital signatureto determine whether the volume data is reliable

or not.Themethod hasbeenimplementedand testedagainstvarious manipu-

lations. Theexperimental resultsshowthatthis isaverypromisingapproach.

Ourfuturework is to come upwith a reliable volume authentication tech-

nique which can be incorporated into all types of scanners (like CTScanners

theEGMM2001reviewersforthehelpfulcomments.

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