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ON RESAMPLING DETECTION AND ITS APPLICATION TO DETECT IMAGE TAMPERING

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ON RESAMPLING DETECTION AND ITS APPLICATION TO DETECT IMAGE TAMPERINGPrasad S.Department of Electrical EngineeringIndian Institute of Science, Bangalore, IndiaK. R. RamakrishnanDepartment of Electrical EngineeringIndian Institute of Science, Bangalore, IndiaABSTRACTUsually digital image forgeries are created by copy-pastinga portion of an image onto some other image. While doing so,it is often necessary to resize the pasted portion of the imageto suit the sampling grid of the host image. The resamplingoperation changes certain characteristics of the pasted por-tion, which when detected serves as a clue of tampering. Inthis paper, we present deterministic techniques to detect re-sampling, and localize the portion of the image that has beentampered with. Two of the techniques are in pixel domainand two others in frequency domain. We study the efficacyof our techniques against JPEG compression and subsequentresampling of the entire tampered image.1. INTRODUCTIONThe advent of digital cameras has made photography eas-ier, and the cheap availability of digital cameras in variousforms has made itself an essential household gadget acrossthe globe. As a result several millions of digital photographsare created every day. In addition to this, modern sophisti-cated photo editing softwares like Adobe Photoshop, GIMP,PaintShop Pro provide user friendly environments to edit dig-ital images. So, images can be easily tampered and can beused in various unethical ways. In this context, it becomesextremely important to validate the originality of digital im-ages.There are several techniques described in literature to dealwith different kinds of tampering. Popescu et. al [1] have no-ticed that the color images taken using a digital camera hasspecific kind of correlations among the pixels, due to the inter-polation in the color filter array. These correlations are likelyto be destroyed, when the image is tampered. Ng et. al [2]have described techniques to detect photomontaging. Theyhave a classifier based on the bi-coherence features of thenatural images and photomontaged images. They also haveproposed a mathematical model for image splicing [3]. Oneof the fundamental operations that needs to be done to createforgeries is resizing. It is an operation that is likely to be doneirrespective of the kind of forgery (copy move, photomon-tage, etc.). So, it is of interest to detect resampling in images.Popescu et. al. [4] have described a method to estimate theresampling parameters in a discrete sequence and have shownits applications to image forensics. They have shown that, fora certain type of resampling, some specific samples in a re-sampled sequence can be written as a linear combination oftheir neighbouring samples. Those samples are separated bya specific interval. Under certain assumptions, the scalars ofthe linear combination can be estimated using an expectation-maximization(EM) algorithm. It is this presence of periodiccorrelations, that gives the evidence of resampling.In this paper, we further investigate the properties of aresampled discrete sequence and present deterministic tech-niques to detect resampling.We call an image original, whenever it is acquired out of adigital camera and has not been altered, even in its resolutionor size. A tampered image is one which is deliberately alteredin its content. We call that portion of the image which hasbeen pasted from some other image as alien portion.2. RESAMPLINGAMNresampling of a 1-D discrete sequence x[k] involves thefollowing three steps [4]1. Up-sample: Create a new signal xu[k] by inserting M-1zeros after every x[k]2. Interpolate: Convolve xu[k] with a lowpass filter: xi[k]=xu[k] h[k]3. Decimate : Pick every Nthsample: y[k]=xi[Nk],k =0, 1, ...Resampling in two dimension is a straight forward applicationof the above mentioned operations in both spatial directions.In image processing applications, the most widely used inter-polation filters are bi-linear and bi-cubic. So, we carefully ex-amine the properties of a resampled signal, which uses thesetwo kind of filters.3. DETECTING RESAMPLING IN PIXEL DOMAINIn this section, we first describe t he techniques to detect re-sampling in one dimension and then its extension to two di-mensions.13251424403677/06/$20.00 ©2006 IEEE ICME 20063.1. Properties of the second differenceSuppose a sequence has been resampled with a factorMN≥ 2,then the following are observed. Every N samples in theoriginal sequence will get expanded to M samples, with afew original samples retained in the resulting sequence. WithMN≥ 2, we are assured of a condition that between everytwo original samples there are at least two more interpolatedsamples(Pigeon hole principle).Let us re-look the pigeon hole principle in our resamplingcontext. Suppose the original sequence had P samples, thenonce the resampling by a factor M/N has been done, then thereare totally (P*M)/N equally spaced samples. When M/N is≥ 2, this means we have to introduce at least one interpolatedsample between every pair of adjacent samples in the originalsequence. In case of linear and cubic interpolation kernels,the first difference of the samples between a pair of originalsamples are equal. So, the second difference will produce azero at that location. To be more specific, every Nthsamplein the original sequence will be the Mthsample in resampledsequence. Hence, the occurrence of zero is within that inter-val of M samples. Moreover, the positions at which a zerooccurs within the M sample interval is precisely fixed by thenumbers M and N. Hence, in every interval of M samples, thesecond difference produces zero in a periodic pattern. It is thisperiodicity that characterizes a resampled signal. It is highlyunlikely for a natural sequence to display this periodicity.To detect resampling, a binary sequence p[k] is constructedfrom the sequence of second differences x[k], as shown be-lowp[k]=1 ifx[k]=00 otherwise(1)The DFT magnitude of this binary sequence will displaydistinct peaks, showing the presence of periodic zeros in thesecond difference. This is shown in fig. 10 5 10 15 20 25 30050100150200250Original sequenceResampled sequence0 50 100 150 200 250 300 350 400050100150200250(i) (ii)Fig. 1. (i)Plot of the first few samples of a original and 5/2resampled sequence, and (ii)DFT magnitude of the binary se-quence constructed as per (1)3.2. Properties of the zero-crossings of the second


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