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AFFINE TRANSFOR M RESILIENT IMAGE FINGERPRINTINGJin S.Seo', Juup Huitsmu2,TonKulke? an d Chang D. Yoo'

'Dept. of EECS , KAIST, 373-1 Guseong Dong, Yuseong Gu, Daejeon 30 57 01 , Koreajsseo@mail.kaist.ac.kr, cdyoo@ee.kaist.ac.kr'Philips Research Eindhoven, Prof. Holstlaan 4,5 65 6A A, Eindhoven, The Netherlands{jaap.haitsma,ton.kalker} @philips.comABSTRACT

Affine transformations are a well-known robustness issue in manymultimedia fingerprinting system s. Since it is quite easy withmodem computers to apply aff ine transformations to audio, imageand video content, there is an obvious necessity for affine trans-forma tion resilient fingerprinting. In this paper we present a newmethod for affine transformation resilient fingerprints that is basedupon the auto-correlation of the Radon transform, the log map-ping and the Fourier transform. Besides robustness, we also ad -dress other issues such as security, database search efficiency andindependence with perceptually different inputs. Experimental re-sults show that the proposed fingerprints are highly robust to affinetransformations.

1. INTRODUCTIONMultimedia fingerprinting (also known as robust hashing) is anemerging research area that i s receiving increased attention. Fin-gerprints are perceptual featu res or short summa ries of a multime-dia object. This concept is an analogy with cryptographic hashfunction that maps arbitrary length data to a small and fixed num-ber of bits [6]. Although cryptographic hashing is a proven methodin message encryption and authentication, it is no t possihle to di-rectly apply it to multimedia fingerprinting. Cryptographic hashfunctions are bit sensitive: an alteration of a single bit in the con-tent will result in a completely different hash value. Th is renderscryptographic hash functions not applicable to multimedia objectsthat often undergo various manipulations including compression,enhancement, geometrical distortions and analog-to-digital con-version during distribution. By noting these deficiencies of cryp-tographic hash functions we arrive at the notion of m ultimedia fin-gerprinting, sometimes referred to as robust hash functions [ ] 131.Promising applications of multimedia fingerprinting are in authen-tication [SI, iltering for file-sharing services [I], supporting digitalwatermarking [91, automated monitoring for broadcasting stations[2] and automated indexing of large multimedia archives.Resilience to affine transformations has been one of the mainissues in many image processing research areas, such as patternrecognition and watermarking. T his paper deals with this impar-tan1 topic in the context of image fingerprinting. To improve ro-bustness to affine transformations. we propose an image finger-print extraction method that is based on the Radon transform. Animage is first projected onto radial directions using Radon trans-form, and for each radial direct ion the affine invariant features areextracted based on the auto-correlation. the log mapping and theFourier transform. The fingerprint bits are determined from the

obtained features. The affine invariant features used in this pa-per have been successfully utilized in extracting speed-change re-silient audio fingerprints [2]. This work is an extension of ouraudio fingerprinting methods in [I] [2]. A different fingerprintingmethod based on Radon transform was proposed in [SI, where themedium point of each projection is used as a fingerprint. However,it needs search and energy m odification for rotation and scaling re-spectively and does not provide keyed hash function [ 5 ] . The pro-posed m ethod does not need any search or modification of finger-print bits, provides keyed hashing sch eme by random perm utationand achieves collision-free property with relatively small amountof fingerprint bits (400bits per image).This paper is organized as follows. Section 2 describe s the re-quirements of image fingerprints. Section 3 describes the extrac-tion of the affine invariant features used in the proposed method.Section 4 evaluates the performance of the proposed fingerprint.

2. REQUIREMENTS ON IMAGE FINGERPRINTSA cryptographic hash function H ( X )maps an (usually large) ob-ject X to a (usually small) hash value. It allows com paring twolarge objects A and Y, by only comparing their respective hashvalues H ( X ) and H ( Y ) . Marhemarical equaliry of H ( X ) ndH ( Y ) implies the equality of X and Y with only a very low proba-bility oferror. Fo ra properly designed cryptographic hash functionthis should be 2 - L , where L equals the number of bits in the hashvalue. However, in case of multimedia fingerprinting the percep-tual similarib is more important rather than mathematical similar-ity. We should construct a fingerprint function in such a way thatperceptually sim ilar image objects result in simila r fingerprints [I].The m odified version of the image should have the same or similarfingerprints with the original image. Requirements on image fin-gerprints are summarized in [4]. The main requirements for imagefingerprints are as follows.

1) Robustness (Invariance under perceptual similarity): the fin-gerprinting system should give sam e or similar fingerprintsto the severely degraded images originated from the sameimage.

2) Painvise independence: if two images are different percep-tually, the fingerprints from two im ages should be differentconsiderably.3) Randomization (Security): the fingerprint bits should haveuniform distribution.

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3. P R O P O S E D F I N G E R P R I N T E X T R A C T IO N M E T H O DAn overview of the proposed algorith m is shown in Figure 1. First,an image is projected onto N (typically, N = 512) radial direc-tions using the Radon transform, and the auto-correlation of eachprojection is calculated . Through the log mapping and the Fouriertransform of the auto-correlation. the affine invariant features areextracted. From the affine-invariant features , a sub-fingerpr int typ-ically 20 bits) is obtained. A sub-fingerprint does not containenough information to identify an image, but a sequence of sub-fingerprints. which we refer to as a fingerprint block, does. An im-age fingerprint (fingerprint block) typically contain s M (typically,M = 20) sub-fingerpnnts and consequently 400 bits. Details ofthe proposed metho d are in the next subsections.

"age Rad on Auto- Log 2DTmnsform correlation Mapping FFT

Fig. 1. Overview of Affine transformation re silient fingerprint ex-traction

3.1. Radon t rans fo rm and i t s p roper t ie sThe Radon transform of an image f ( x , g ) , denoted as g(s,O), isdefined as its line integral along a line inclined at an angle 8 fromthe y-axis and at a distance s from the origin [7]. Mathematically,it is written asg ( s , ~ )=Sm f ( z : y ) s ( z c o s B + y s i n o - s ) d x d y (1 )where -co < s < 00, 0 5 0 < T . The Radon transform g(s, 8)is the one-dimensional projection of f ( x , y ) at an angle 8. Th eRadon transform has the follo wing useful properlies fo r the affinetransformations of an image.

-m -_

PI) The translation of an image by (xo,go) causes the Radontransform to be translated in the direction of s, i. e . ,f ( x - xo , y yo)H (s - o co sO - o s i n 8 , 8 ) .

P2) The scaling (retaining aspect ratio) of an image by a factorp ( p > 0) causes the Radon transform to be scaled throughthe sam e factor, i. e.,

P3) The rotation of an image by an angle 0, causes the Radontransform to be shifted through the same amount, i. e. ,

3.2. Affine invariant featu re extractionAffine transformations, we consider here, are translation, scaling(retaining aspect-ratio) and rotation. By using the abov e propertiesof Radon transfo rm, affine invariant features are obtain ed.For translation invariance, the normalized auto-correlation ofeach radial projection is calculated that is given as follows:

From P I the translation of an image causes translation in the Radondomain, but the amount of translation in each projection is differ-ent. By taking auto-correlation. we get translation-invariant sig-na l c(1,O) . Am ong the affine transfor matio ns, scaling and rotationare remained in c ( l , 8 ) .Consider the auto-correlation c ( l , 8 )of anoriginal image. From P2 and P3 , the auto-correlation of a scaledand rotated image is given as c'(1,8) = c(pZ, 8 - 8,) where p( p > 0) and 8, are the amount of scaling and rot ation respectively.To achieve invariance on the scaling and rota tion, the log mappingand the 2D Fourier transform are used. The log mapping translatesthe scaling of the signal to a shift. The subsequent Fourier trans-form transla tes this shift into a phase change. By the log mapping1 = e", the signal c ' ( l , 8 ) can be written as

c'(Z, 0) = c ( p l ,8 - ,)= c ( e x p [ p + l o g p ] , B - O , ) . ( 3 )

E'(p,8) = C ( ~ + l o g p , 8 - 8 B r ) . (4)Then the log-mapped signal E' (p: 8 ) is given by

The 2 0 Fourie r transform of the log-mapped si gnal is written as" - "-

= e x p [ ~ ~ i ~ o g p - i C o 8 ~ . l C ( S 1 , < n ) . ( 5 )Then the magnitude IC'(Ci,C O ) ~ nd phase $ ' ( C l , Co ) of the com-plex signal C ' ( ~ I ,O) are given by:

IC'(Ci,Co)I = IC(Ci,

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in either

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Table 2. Hits in the database for different kinds of signal degrada-tionsProcessingGaussina filtering 1 20 1 20 I 19 I 20

I A IR 1 BOAT 1 LENA I PE PJPEG (Q=lO%) 1 . 1 7 1 17 I 20 I 18Sharpening filtering I 17 1 18 I 16 I 19Median filtering(4 x 4) I 19 1 15 I 17 I 18Rotation I I I I(worst case 45.176)Rotation (90)Scaling ( p = 0.5)Scaling ( p = 0.15)Cropping (2%)Cropping (5%) 417 cnlllmn5 TOW removedShearing (1%)Shearing (5%)Random bending attack

[ I ] , the threshold for the BER was determined to be 0.3 with verylow false positive rate. It means that out of 400 bits there mustbe less than 120 bits in error in order to decide that the fingerprintblocks originat e from the sam e image. De tails of the false positiveanalysis are in [I].To test security of the proposed m ethod, w e generated 100 fin-gerprin ts from the Lena image using different interleaving. Sim ilarwith the above analysis, the BER between all possible pairs of thefingerprints were calculated. The histogram of the measured B ERis shown in Figure 3b. The mean and the standard deviation ofthe measured BER were 0.5002 an d 0.0264 respectively. This re-sult clearly shows the fingerprint is significantly dependent on thekey information (interleaving). In terms of security, such a strong

dependency on the key is significant. Once a key is broken, theuser can simply change it, like a password [3]without modifyingoverall system.

5. C O N C L U S I O NFor the multimedia fingerprinting, extracting features that allowdirect acce ss to the relevant distinguishing in form ation is crucial.The features used in fingerprint extraction are directly related tothe performance of the fingerprinting system. In this paper, wepresented a new fingerprint extraction method that is resilient toaffine transformations. The robustness again st affine transforma-tions are essent ial because it is quite easy to im pose affine transfor-mations to im ages with modem computers. The experimental re-sults show that the proposed method i s highly robust against affinetransformations and most of the other image processing steps. Itwas experimentally verified that the proposed image fingerprintssatisfy the main requirements of fingerp rints; robustness underquality preserving signal processing step s, pairwise independencewith differe nt inputs and sufficient randomization (uniform distri-bution) of fingerprint bits. Fu ture work include s more robust imagefingerprinting and extension of the proposed method to video.

Fig. 3. (a ) Histogram of measured BER between the fingerprintsfrom different images. (b) Histogram of measured BER betweenfingerp rints of Lena generated with different keys

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6. R E F E R E N C E SJ.A. Haitsma and T. Kalker, A Highly Robust Aud io Finger-printing System: Proc. lnrernnrional Co nj on Music Infor-marion Retrieval ( I SM IR )2002, Paris. Oct. 2002.J.S. Seo, J.A. Haitsma and T. Kalker, Linear Speed-ChangeResilient Audio Fingerprinting, Proc. IEEE Benelur Work-shop on Model Based Processing and Coding of Audio( M P C A )2002, Leuven, Belgium, Nov. 2002.R. Venkatesan, S:M. Kaon, M. H. Jakubowski, and P.Moulin, Robust Image Hashing, Proc. IEEE K I P 2000,Vancouver, CA, Sept. 2000.M. K. Mihcak and R. Venkatesan, New Iterative GeometricMethods for Robust Perceptual Image Hashing, Proc.ACMWorkshop on Security and Privacy in Digiral Rights Man-agemenr, Philadelphia, PA, Nov. 2001.E Lefebvre, B. Macq and J.-D. Legat, RASHRadon SoftHash Algorithm, Pmc. European Signal Processing Conf2002, Toulouse, France, Sept. 2002.A. Menezes, P. Oorshot, and S. Vanstone, Handbook of A p -plied Cryprography, CRC press, 1997.A.K. l a in , Fundamenrals of Digital Image Processing,Prentice-Hall, 1989.M. Schneider and S.-F. Chang, A Robust Content BasedDigital Signature for Image Authentication, Proc. IEEEK I P 96, Laussane, Sw itzerland, Oct. 1996.J. Fridrich, Robust Bit Extraction from Images, Proc. IEEEInremarional Con$ on Mulrimedia Computing and Sysrems(ICMCS)99, Florence, Italy, June 1999.F.A.P. Fetitcolas, Watermarking Schemes Evaluation,IEEE Signal procssing Mag.,vol. 17, no. 5 , Sept. 2000.

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