IDENTIFYING SOURCE CELL PHONE USING CHROMATIC ABERRATION

Lanh Tran VanDepartment of Computer Science

Uppsala UniversitySweden

Sabu EmmanuelSchool of Computer EngineeringNanyang Technological University

Singapore

Mohan S KankanhalliSchool of Computing

National University of SingaporeSingapore

ABSTRACT

Chromatic aberration is the phenomenon where light ofdifferent wavelengths fail to converge at the same positionon the focal plane. There are two kinds of chromaticaberration: longitudinal aberration causes differentwavelengths to focus at different distances from the lenswhile lateral aberration is attributed to different wavelengthsfocusing at different positions on the sensor. In this paper,we estimate the parameters of lateral chromatic aberrationby maximizing the mutual information between thecorrected R and B channels with the G channel. Theextracted parameters are then used as input features to aSVM classifier for identifying source cell phone of images.By considering only a certain part of the image whenestimating the parameters, we reduce the runtimecomplexity of the algorithm dramatically while preservingthe accuracy at a high level.

1. INTRODUCTION

With the increasing popularity of cell phones equipped withcamera in recent years, so does the need to accuratelyidentify the source cell phone of a given digital image.Multimedia forensics uses multimedia objects to trace backto the original digital device which created the objects. Thiskind of identification would be useful in legal disputes suchas claiming of multimedia assets ownership (copyright), andmore importantly, being used as digital evidence in thecourt.

There are currently a limited number of source cameraidentification methods. These methods explore differentparts or processing stages of the digital camera to find theclues that can help identifying correctly the source camera.They can be roughly classified into four approaches basedon the camera parts that they examine.

The first approach takes advantages of camera lensdistortions. Choi et al [1] measure the lens radial distortionand use it as a fingerprint to identify source camera. Radialdistortion parameters are estimated using the straight linemethod which extracts the distorted line segments andmeasures the distortion error between the distorted linesegments and the corresponding straight lines.

The second approach distinguishes the cameras throughthe imperfections of image sensors. Lukas et al [2] usesensor pattern noise as a clue for tracing back to the sourcecamera. This method can distinguish cameras of the samemodel and brand.

The third approach is based on Color Filter Array (CFA)interpolation. Bayram et al [3] explore the CFAinterpolation process to determine the correlation structurepresent in each color band which can be used for imageidentification. Long and Huang [4] obtain a coefficientmatrix from a quadratic pixel correlation model wherespatially periodic inter-pixel correlation follows a quadraticform. This coefficient matrix of each image is then fed intoa neural network for classification in order to identify thesource camera. In [5], Celiktutan et al use a set of Binarysimilarity measures, which are the metrics used formeasuring the similarity between the bit-planes of an image.The underlying assumption is that proprietary CFAinterpolation algorithm leaves correlations across adjacentbit-planes of an image that can be represented by thesemeasures. 108 binary similarity measures are obtained forimage classification purpose.

The fourth approach employs a set of image features forclassifying source cameras. Kharrazi et al [6] identify a setof 34 features to be used for image classification; thesefeatures include RGB features, image quality metrics, andwavelet domain statistics.

In this paper, for the purpose of source cell phoneidentification, we modify and use the lateral chromaticaberration based method proposed for image forgerydetection by Johnson and Farid [7]. Johnson and Farid uselateral chromatic aberration to detect image forgeries byestimating the chromatic aberration parameters of selectedblocks on an image and compare them with the chromaticaberration parameters obtained for the whole image. Imagetampering is then detected if inconsistency is found. In thiswork, we estimate the distortion parameters of thechromatic aberration of the image and use these extractedfeatures to identify source cell phone through the use ofSVM classifier. Our motivation arrives from twoobservations. Firstly, the aberration is more severe incamera phones whose lens system consists of low-endplastic materials instead of high-end, low dispersionaspherical lenses. Secondly, each camera model possesses a

1-4244-1017-7/07/$25.00 C2007 IEEE 883 ICME 2007

different lens structure thus it will experience somewhatdifferent chromatic aberration. This difference can beexpressed in terms of the distortion parameters.

The remainder of this paper is organized as follows. Inthe next section, we introduce chromatic aberration and theproposed method to estimate the distortion parameters. Insection 3, we perform several experiments on different cellphone models and provide the results. Section 4 gives someobservations and discussions on the strengths and weaknessof our method as well as the direction for future works.Section 5 concludes the paper.

2. CHROMATIC ABERRATION

2.1. Background of Chromatic AberrationIn optics, dispersion is the phenomenon of lens havingdifferent refractive indexes for different wavelengths oflight. Since the focal length of a lens is dependent on therefractive index, different wavelengths of light will befocused on different positions. This phenomenon is knownas chromatic aberration, where light of differentwavelengths fail to converge at the same position on thefocal plane (image sensor in a camera).

There are two kinds of chromatic aberrations [8]. Figure1(a) shows longitudinal aberration where differentwavelengths focus at different distances from the lens.Lateral aberration, on the other hand, is the phenomenonattributed to different wavelengths focusing at differentpositions on the focal plane, as shown in Figure 1(b).

b

whte 1ight sensor

(a) longitudinal aberration

rr

Although both chromatic aberrations affect the imagestaken be the cameras, for simplicity we will concentrateonly on lateral chromatic aberration in this paper.

b~

white liLht sensor

Figure 2. Modeling of lateral chromatic aberration.

According to Johnson and Farid [7], the relationshipbetween the red ray and blue ray (in other words, the lateralchromatic aberration between red and blue wavelengths) asshown in Figure 2 can be modeled as xr ;OCXbwhere a = nb /nr , nb and n, are the refractive index of thelens for blue and red wavelength respectively. In the case of2D, we have a similar formula

(Xrrr a (XbIYb) 1

For a better model, we also need to take into account thecentre of distortion (x0 , y0), which is normally not the same

as the centre of image. The model now becomes:

(2){ Xr = a(Xb x0) +xoYr °a (Yb )Yo) + Yo

2.2. Chromatic Aberration EstimationChromatic aberration causes misalignment between theRGB channels. Our task is to estimate the distortedparameters to compensate for the distortion. In this part, wewill estimate the parameters (al , xI y, ) between the red andgreen channels and the parameters (a2, x2, Y2) between theblue and green channels. These six parameters then can beused as features for distinguishing source cell phones.

Let R(x, y) and G(x, y) be the red and green channelrespectively. Then, the corrected red channel R(xr 'Yr) is

expressed as: Xr = a, (x - xI) +xI (3)lYr =1a(y y1)+y1

The parameters (a1,xx,yI) can be estimated bymaximizing the mutual information between R(xr n Yr)and G(x, y), which is computed as follows [7]:

white h1p:ht sensor

(b) lateral aberration

Figure 1. Chromatic aberration.

To reduce chromatic aberration, camera designerscombine convex and concave lenses of different refractiveindices. Another technique is to use low dispersionmaterials such as fluorite to make low dispersion lenses.

(4)I(R, G) = E E P(r, g) logr P(r, g)rRgEG yP(r)P(g))

Where R and G are the random variables representingthe values of the channels R(xr , Yr ) and G(x, y) respectively,P(r, g) is the joint probability, andP(r), P(g) are themarginal probability distributions. We maximize the mutualinformation using an iterative brute-force search asexplained in section 2.3. The estimation for parameters

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(a2,x2,Yy2) between the blue and green channels follows asimilar way.

2.3. Proposed MethodWe maximize the mutual information using iterative brute-force search. To ensure that the global maximum is found,the centers of distortion (xl, y]) and (x2, Y2) are consideredon the entire image. The value of a varies within the range[0.5, 1.5], which is determined empirically.

Searching over an entire image is very computationalintensive; hence, sampling of the search space is used ineach iteration to reduce computation. In each iteration, adistance 3 of roughly 115 the size of the current searchspace is used as a sampling distance for jumping to the nextcentre of distortion. Searching the target a follows a similarfashion where in each round the sampling distance 6sa istaken to be 1/10 the length of current a-range. Once thepoint that gives maximum mutual information is found, thenext iteration is started with a new search space around themaximum point with radius of 3 and a finer samplingdistance of 6110. Similarly, the new a-range is also limitedto the area with a radius of 6sa around the new a, with thenew sampling distance of 3a 10. The process is repeateduntil 3=1 and 6sa is less than a predefined epsilon &=0.0001.At the end of the execution, the parameters where themutual information attains maximum value are returned.

The major execution time in each iteration is due to theinterpolation to derive the values for R(xr Yr) and thecomputation of the mutual information betweenR(xr ,Yr) and G(x, y) . This time depends very much on thesize of the channel under interpolation and mutualinformation computation. To reduce run time, only a smallregion on each image is used for calculation. In ourimplementation, we use a region of lOOxlOO pixels at theimage centre for computing interpolation and mutualinformation. The accuracy rate remains the same butexecution time drops dramatically, from 3 hours to 10minutes per image on average. We also tried differentpositions (right top and bottom, left top and bottom) of1OOx100 pixel region instead of at the image centre and theresults are still comparable.

3. EXPERIMENTS AND RESULTS

3.1. Data CollectionWe take 90 photos with each of the four cell phones (twoMotorola V3i phones, one 02 XPhone II, and one SamsungZ140). The photos are taken with no zoom, using maximumresolution (Motorola's max resolution is 960x1280, othersare 640x480). All pictures are in JPEG format.

The six parameters (a, xl, y1) and (a2, x2, Y2) areextracted for each of the taken images and used as featuresfor image classification. One-third of the photos are fed intoa Support Vector Machine (SVM) for training, another one-

third is used for testing. To verify the effectiveness of ourmethod in the case modification and cropping attack is used,we modify and crop one third of the taken images and usethem to test the already trained model (initial trainingsequence remains the same). There are many SVM softwaretools available on the Internet, but we choose LIBSVM [12]for its simplicity. We use the provided script "easy.py" forrunning classification since its parameters are optimized.

3.2. Normal ClassificationIn the first experiment, we use the model to classify photostaken by three cell phones. The accuracy rate is high, withlowest rate of 86.67%, highest rate of 96.67% and theaverage rate of 92.22%. The confusion matrices areprovided in Table 1.

Predicted (%)02XII Z140 V3i

02XphoneII 86.67 13.33 0Actual±(%) SamsungZ140 3.33 96.67 0

MotorolaV3i 6.67 0 93.33

Table 1. Classification of three cell phones.

3.3. Same Model ClassificationIn this experiment, we try to classify two cell phones ofexactly the same model (Motorola V3i). The result isprovided in Table 2. The accuracy of differentiating thesetwo cameras is as low as 5000, which is not a practicalnumber. This result shows that lateral chromatic aberrationalone is not enough for identifying source cameras of thesame model. Other forms of lens distortions may beadditionally needed for a higher accuracy rate.

Predicted (%)

02XII Z140 V3i#1 2

02XII 86.67 13.33 0 0Actual Z 140 3.33 96.67 0 0(%) V3i#1 3.33 0 50 46.67

V3i#2 6.67 0 36.67 56.67

Table 2. Classification of cell phones of the same model.

Table 3. Classification of modified images.

3.4. Modified Images ClassificationGoing a step further, we make some modifications to one-third of the taken images and use them for testing. Themodifications include heavy JPEG compression, adding 500Gaussian noise, and image sharpening. The confusion

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matrix is shown in Table 3. The accuracy for 02XphoneII islow (46.67%) while prediction rates for others remain high.

3.5. Cropped Images ClassificationTo see how well this method identifying source cell phoneof cropped images, we perform the following experiment.For each of the 30 images from each camera phone, werandomly crop a region and extract the chromatic aberrationparameters for the region then use them as features forimage classification. The classification result is shown inTable 4. Although the accuracy is quite low forSamsungZ140, the result for other two camera phones isencouraging. It seems that the prediction accuracy dependsvery much on the target cell phones.

Predicted (%)02XII Z 140 V3i

02XphoneII 83.33 10 6.67

Actu(al SamsungZ140 76.67 20 3.33MotorolaV3i 20 10 70

Table 4. Classification of cropped images.

4. DISCUSSIONS

When compared to the camera identification methodsreviewed in section 1, this method has comparableperformance to most of them, if not better than some of themethods. For instance, the method based on CFAinterpolation [3] has prediction rate as low as 75%0 for onecamera when classifying three cameras, whether our lowestrate is 86.67%. Similarly, the result in [5] is lower than ourswhen classifying some of the groups of three cameras, inparticular, the lowest accuracy is only 710% compared to ourlowest 87.67%. The paper [5] use different set of models ofcell phones for experiments, however the results arecomparable. Most of the methods suffer heavily from imagemodification attack. Our method also suffers from this, butthe degree of suffering is not that severe (some cameramodel, like MotorolaV3i, can even have 100% predictionaccuracy). Another point worth mentioning is that ourmethod does not impose any restriction, while some of thelisted methods have restrictions that sometimes are not easyto achieve in practice (e.g. all cameras must take the sameimage contents with same resolution, etc).

As part of the future work, we plan to use longitudinalchromatic aberration as well for obtaining a betterperformance and higher reliability. Alternatively, we canalso consider other ways of measuring chromatic aberration,such as the method using reference edges proposed byWillson and Shafer [10]. If optical zooming becomes acommon feature in mobile phones, the impact of opticalzooming on source cell phone identification could beanother area to be investigated. There have been several

digital camera identification methods [11 - 13] proposed,which can also be investigated for cell phone environment.

5. CONCLUSION

In this paper, we introduce a method for identifying sourcecell phone based on the footprints of lateral chromaticaberration left on images. By estimating the parameters oflateral chromatic aberration and using them as features forclassification, we are able to identify the source cell phoneof the given images with reasonably high accuracy. We alsoimprove the runtime complexity of the lateral chromaticaberration based algorithm dramatically, by consideringonly a certain part of an image when estimating theparameters while preserving the accuracy at the same level.

6. REFERENCES

[1] Choi, Kai San; Lam, Edmund Y.; Wong, Kenneth K. Y.,"Source camera identification using footprints from lensaberration", Proceedings of the SPIE 2006.[2] Lukas J., Fridrich J. and Goljan M., "Digital CameraIdentification from Sensor Pattern Noise", IEEE Transactions onInformation Forensics and Security, June 2006.[3] S. Bayram, H. T. Sencar, N. Memon, I. Avcibas, "SourceCamera Identification Based on CFA Interpolation", ICIP 2005.[4] Yangjing Long, and Yizhen Huang, "Image Based SourceCamera Identification using Demosaicking", IEEE InternationalWorkshop on Multimedia Signal Processing, MMSP 2006.[5] 0. Celiktutan, I. Avcibas, B. Sankur, and N. Memon, "Sourcecell -phone identification", Proc. ADCOM, 2005.[6] M. Kharrazi, H. T. Sencar, and N. D. Memon, "Blind sourcecamera identification", ICIP, 2004.[7] M.K. Johnson and H. Farid, "Exposing Digital Forgeriesthrough Chromatic Aberration", ACM Multimedia and SecurityWorkshop, Geneva, Switzerland, 2006.[8] M.Katz, "Introduction to Geometrical Optics", WorldScientific Publishing Co. Pte. Ltd, Chapter 18, 2002.[9] Chih-Chung Chang and Chih-Jen Lin, "LIBSVM: a Library forSupport Vector Machines", 2001. Software available at

[10] R. G. Willson and S. A. Shafer, "Dynamic lens compensationfor active color imaging and constant magnification focusing,"Tech. Rep., Carnegie Mellon Univ., CMU-RI-TR-91, Oct. 1991.[11] S. Bayram, H. T. Sencar, and N. Memon, "Improvements onsource camera-model identification based on CFA interpolation,"Proc. of the WG 11.9 Intl. Conference on Digital Forensics,Orlando, FL, Jan. 2006.[12] A. Swaminathan, M. Wu, and K. J. Ray Liu, "Componentforensics of digital cameras: A non-intrusive approach," Proc. ofConference on Information Sciences and Systems, pp. 1194-1199,Princeton, NJ, Mar. 2006.[13] A. C. Popescu and H. Farid, "Exposing digital forgeries incolor filter array interpolated images," IEEE Trans. on SignalProcessing, vol. 53, no. 10, part 2, pp. 3948-3959, Oct. 2005.

*This work is carried out at the Centre for Multimedia and NetworkTechnology (CeMNet), Nanyang Technological University, Singapore.

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