Anti-Forensics of Chromatic Aberration

Transcription

1 Anti-Foensics of Chomatic Abeation Owen Maye and Matthew C. Stamm Dept. of Electical and Compute Engineeing, Dexel Univesity, Philadelphia, PA, USA ABSTRACT Ove the past decade, a numbe of infomation foensic techniques have been developed to identify digital image manipulation and falsification. Recent eseach has shown, howeve, that an intelligent foge can use antifoensic countemeasues to disguise thei fogeies. In this pape, an anti-foensic technique is poposed to falsify the lateal chomatic abeation pesent in a digital image. Lateal chomatic abeation coesponds to the elative contaction o expansion between an image s colo channels that occus due to a lens s inability to focus all wavelengths of light on the same point. Pevious wok has used localized inconsistencies in an image s chomatic abeation to expose cut-and-paste image fogeies. The anti-foensic technique pesented in this pape opeates by estimating the expected lateal chomatic abeation at an image location, then emoving deviations fom this estimate caused by tampeing o falsification. Expeimental esults ae pesented that demonstate that ou anti-foensic technique can be used to effectively disguise evidence of an image fogey. Keywods: Infomation Foensics, Anti-Foensics, Copy-and-Move Fogey, Lateal Chomatic Abeation 1. INTRODUCTION In ode to detemine the authenticity, pocessing histoy, and souce of digital images, eseaches have developed a vaiety of infomation foensic techniques. 1 Recent eseach has shown, howeve, that an intelligent foge can ceate anti-foensic countemeasues capable of fooling seveal foensic algoithms. These anti-foensic attacks opeate by emoving o falsifying the taces that foensic techniques use as evidence of image pocessing o fogey. Anti-foensic attacks have been poposed to falsify an image s compession histoy, 2, 3 and hide evidence of common editing opeations such as esampling, 4 median filteing, 5 contast enhancement, 6 and copy-move fogeies. 7 Geneal appoaches have been developed to fool histogam-based foensic algoithms, 6, 8 along with methods of falsifying camea-specific taces such as senso noise 9 and both colo-filte aay pattens and demosaicking atifacts. 1 Additionally, anti-foensic attacks have been developed to hide evidence of fame deletion in digital videos. 11 One impotant foensic tace that has not yet been anti-foensically attacked is an image s lateal chomatic abeation. Lateal chomatic abeation is specific fom of colo distotion that occus because a camea s lens is unable to achieve the same focal point fo all wavelengths of light. This esults in a slight misalignment between an image s colo channels coesponding to a elative contaction o expansion about the image s optical cente. In pevious wok, Johnson and Faid showed that copying an object fom an image then pasting it elsewhee within the same image o a diffeent image will intoduce localized inconsistencies in an image s chomatic abeation. 12 Using this infomation, they developed a technique to detect copy-and-move fogeies by fist fitting an image s global lateal chomatic abeation patten to a model, then seaching fo image subegions whee the localized lateal chomatic abeation significantly deviates fom the global model. In this pape, we pesent a technique to disguise copy-and-paste fogeies by falsifying the lateal chomatic abeation within the inauthentic egion of an image. Ou anti-foensic attack woks by using a model to detemine the expected lateal chomatic abeation of pixels in the image egion whee a copied object is to be pasted. Next, the image that the object is copied fom is modified so that its lateal chomatic abeation within the object egion matches the expected lateal chomatic abeation of the egion of the image to whee it will be pasted. This is done by fist establishing a efeence colo channel, then mapping the pixel locations of the two emaining colo channels to new spatial locations that will match the desied lateal chomatic abeation. The authos can be eached by at om82@dexel.edu and mcstamm@coe.dexel.edu.

2 Figue 1. Lateal chomatic abeation though a lens. Finally, the modified image is esampled along the pixel gid, and the object is copied and pasted into the taget image. We expeimentally validate the pefomance of ou anti-foensic attack by ceating a set of anti-foensically modified copy-and-paste fogeies, then examining each image fo lateal chomatic abeation inconsistencies indicative of a falsified image. Ou esults demonstate that ou poposed anti-foensic attack can successfully disguise inconsistencies in an image s lateal chomatic abeation caused by copy-and-paste fogeies. 2. BACKGROUND In this section, we povide a bief oveview of lateal chomatic abeation, how it is estimated, and how it is used in infomation foensic to detect copy-and-paste image fogeies. When a digital camea captues an image, light is focused onto the camea s imaging senso using a photogaphic lens. Ideally, the lens accomplishes this by efacting all ays of light oiginating fom a single point in the scene onto a common focal point on the senso. In eality, howeve, the efactive index of the lens is dependent on the wavelength of the light that passes though it. This will cause a specific type of colo distotion known as lateal chomatic abeation. Lateal chomatic abeation occus when diffeent wavelengths of light oiginating fom the same souce point ae focused onto slightly diffeent points on the camea s senso, as is shown in Fig. 1. Since the amount of efaction is also dependent upon a light ay s angle of incidence with the lens, the distance between the focal points of two diffeent wavelengths tends to incease with the adial distance fom the optical axis. Because of this, lateal chomatic abeation can be viewed as a slight misalignment between an image s colo channels coesponding to a elative contaction o expansion about the image s optical cente. This visually manifests itself as colo finging aound edges and cones within an image. 2.1 Fogey Detection Using Lateal Chomatic Abeation The misalignment between two colo channels due to lateal chomatic abeation can be chaacteized by a mapping elating the spatial location (x, y ) of a point in a efeence colo channel to its location (x c, y c ) in a compaison colo channel. This mapping can be modeled as a paametic function f with paamete set θ, i.e. (x c, y c ) = f ( (x, y ), θ ). By adopting this appoach, the global lateal chomatic abeation patten between two colo channels can be detemined entiely by estimating the values of the paamete set θ. Johnson and Faid showed that significant localized deviations of the lateal chomatic abeation patten fom a global model can be used to expose copy-and-paste fogeies. 12 Copy-and-paste fogeies ae ceated by copying an object fom a souce image, then pasting it into a destination image. When this is done, the lateal chomatic abeation patten within the pasted egion will coespond to the lateal chomatic abeation at the location it was copied fom in the souce image. This is unlikely to match the lateal chomatic abeation patten at its pasted location in the destination image as pedicted by a global model. An example of this is shown in Fig. 2. To detect copy-and-paste fogeies, Johnson and Faid poposed examining an image using the following foensic algoithm. Fist, a global estimate of the image s lateal chomatic abeation mapping between two colo channels is estimated using the model ( x c y c ) (( x = f y ) ) (, α, x, y α(x = x ) + x α(y y ) + y ), (1)

3 Destination Image Souce Image Naively Falsified Image (a) (b) (c) Figue 2. Diagam of a copy-and-paste fogey. (a) Destination image with lateal chomatic abeation displacement vectos highlighted in the paste egion. (b) Souce image with lateal chomatic abeation displacement vectos highlighted in the copy egion. (c) Naively ceated copy-and-paste fogey with lateal chomatic abeation displacement vectos highlighted in the paste egion. Note that the displacement vectos in the paste egion of the naively falsified image ae inconsistent with those in the unalteed destination image. whee the paametes x and y coespond to the spatial location of the image s optical cente in the efeence colo channel, and α is a scaling paamete that chaacteizes the degee of expansion o contaction. The estimated paamete set θ = (α, x, y ) is used to calculate the lateal chomatic abeation displacement vecto field, defined as the diffeence between (x c, y c ) and (x, y ). Next, the image is divided into blocks, and a local estimate of the lateal chomatic abeation and its coesponding displacement vecto field is computed fo each block. A block is classified as inauthentic if the angula eo between the global and local lateal chomatic abeation displacement vectos exceeds a detection theshold. 2.2 Lateal Chomatic Abeation Estimation Fitting the lateal chomatic abeation to the model in (1) is a citical step in Johnson and Faid s fogey detection algoithm. To accomplish this, Johnson and Faid obseve that given the tue values of the paamete set θ = (α, x, y ), the lateal chomatic abeation distotion in the compaison channel can be compensated fo by applying the invese mapping f 1 (, θ) of (1). As a esult, they estimate the model paametes by finding the values θ that maximize the similaity, as measued by the mutual infomation I( ; ), between a coected vesion of the compaison colo channel C and the efeence colo channel R, i.e. θ = ag max I ( f 1 (C, θ); R ). (2) θ Because the mutual infomation between the coected compaison channel and the efeence channel is nonconvex in the paamete space, the optimal paamete values θ ae found though a bute-foce seach. While Johnson and Faid s appoach yields stong esults in tems of model fit fo global estimates of the lateal chomatic abeation, it is vey computationally expensive. Fo example, Gloe et al. epoted that when conducting expeiments with thei un-time optimized implementation of this appoach, it took appoximately 38 minutes to calculate the model paametes fo one pai of colo channels in a 6 megapixel image. 13 Futhemoe, this pocess must be pefomed on both pais of colo channels (i.e. (geen-to-ed) and (geen-to-blueblue) ), and epeated again fo each image block that is examined fo evidence of copy-and-past fogey. To addess this poblem, a moe computationally efficient method of estimating the model paametes was poposed by Gloe et al. 13 This method opeates by locally estimating lateal chomatic abeation displacement vectos at seveal locations thoughout the image, then fitting a global model to the local estimates. Locations suitable fo pefoming these local estimates ae chosen by using the Hais cone detection algoithm to identify cone points thoughout the efeence channel. 14 Next, a seach is pefomed in the compaison channel fo the W W pixel block B c that maximizes the similaity with an equivalently sized block B in the efeence channel centeed at each cone point. To enable a seach ove factional pixel displacements,

4 Destination Image Vitual Image Anti-Foensically Falsified Image (a) (b) (c) Figue 3. Diagam of an anti-foensically disguised copy-and-paste fogey. (a) Destination image with lateal chomatic abeation displacement vectos highlighted in the paste egion. (b) Vitual image whose lateal chomatic abeation displacement vectos in the copy egion have been modified to match those in the paste egion of the destination image. (c) Anti-foensically disguised copy-and-paste fogey with lateal chomatic abeation displacement vectos highlighted in the paste egion. Note that the displacement vectos in the paste egion of the naively falsified image ae consistent with those in the unalteed destination image. the window is upsampled by a facto of u using bicubic intepolation. The seach is limited to a maximum shift of, and the local displacement vecto is chosen to coespond to the shift that yields the maximum similaity between the blocks, i.e. ˆd(x, y) = ag max (m,n) {,..., } s(b (x, y), B c (x + m, y + n)) (3) whee the similaity s( ) between the two blocks is measued using the coelation coefficient. Finally, the model paametes ae found by using an iteative Gauss-Newton method to pefom a least squaes fit of the locally measued displacement vectos to the global model. This appoach to lateal chomatic abeation estimation yields significant gains in tems of un time without suffeing in tems of accuacy. As a esult, we use this appoach when estimating the lateal chomatic abeation displacement vectos and model paametes in ou expeiments. 3. ANTI-FORENSIC ATTACK In ode fo a copy-and-paste fogey to successfully avoid detection, local estimates of the lateal chomatic abeation obtained in the image egion coesponding to the pasted object must not significantly deviate fom the lateal chomatic abeation pedicted by a global model. In this section, we popose an anti-foensic attack that to accomplish this by falsifying the lateal chomatic abeation within the pasted object. When pefoming ou anti-foensic attack, we efe to the image containing the object to be copied as the souce image, and the image into which the object will be pasted as the destination image. Additionally, we constuct an intemediate image efeed to as the vitual image. The vitual image is ceated so that it contains visual infomation fom the souce image, while having a chomatic abeation patten that is consistent with the destination image. We then ceate ou anti-foensically disguised fogey by copying infomation fom the vitual and pasting into destination image. Figue 3 povides a diagam of the pocess. We adopt the notation convention that coodinates in the souce, destination, and vitual images ae denoted by the subscipts S, D, and V espectively. Fo a paticula image, coodinates in the efeence and compaison colo channels ae indicated by the supescipts and c. Futhemoe, the coodinates of optical cente of an image s compaison channel ae indicated by the supescipt. We begin ou attack by fist identifying the location of each pixel in the efeence channel of the souce image that coesponds to the object to be copied, along with the coesponding location that it will be pasted in the efeence channel of the destination image. Afte this, we choose a compaison channel, and estimate the lateal chomatic abeation model paametes fo both the souce and destination images using Gloe et al. s method descibed in Sec. 2.2.

5 Next, we begin to constuct the vitual image by choosing its efeence channel to be equal to the efeence channel of the souce image. When we ceate ou fogey, we will copy a pixel fom location (x V, y V ) in the vitual image and paste it into location (x D, y D ) in the destination image. At the location (x D, y D ), the global model of the destination image s lateal chomatic abeation can be used to calculate the displacement between the efeence and compaison channels. This quantity, known as the displacement vecto d D, is given by the equation ( ) ( d D (x D, yd) x = D αd (x y D x D ) + ) ( x D (1 αd )(x D α D (yd y D ) + = D x D ) ) y D (1 α D )(yd y D ). (4) Similaly, fo a paticula choice of model paametes α V, x V, and y V vecto at location (x V, y V ) in the vitual image is given by ( ) ( d V (x V, x ) = V αv (x V x V ) + ) x V α V ( y V ) + = y V fo the vitual image, the displacement ( (1 αv )(x V x V ) ) (1 α V )( y V ). (5) To ensue that the lateal chomatic abeation inside the pasted object matches the destination image s global model, the displacement vectos of the vitual image and the destination image must be equal at locations coesponding to the same point in the object, i.e. d V (x V, y V ) = d D(x D, y D ). Fo this to occu, we note that by inspection of (4) and (5) the following is tue: ( ) ( ) ( ) ( ) x α V = α D, and V x V x = D x y D D y. (6) D Since the efeence channel of the vitual image is copied fom the efeence channel of the souce image, we know that (x V, y V ) = (x S, y S ). By substituting this into (6), we can deive the following equation fo the location of vitual image s optical cente ( ) ( ) ( ) ( ) x V x = S x ys D x y + D D y. (7) D Since the points (x S, y S ), (x D, y D ), and (x D y D ) ae known, this equation completely specifies the location of the vitual image s optical cente. We note that this location may lie outside of the bodes of the vitual image. Using the vitual image s model paametes, we can expess a location in its compaison channel in tems of a location in its efeence channel using the equation ( ) ( x c V αv (x = V x V ) + ) x V α V ( y V ) + (8) y V y c V Since (x V, y V ) = (x S, y S ), we can use the invese of the souce image s lateal chomatic abeation model to expess a location in the vitual image s efeence channel in tems of a location in the souce image s compaison channel as ( ) ( ) ( x V x 1 = S ys α = S (x c S x S ) + ) x S 1 α S (ys c y S ) + (9) y S Equations (6), (8), and (9) can be combined to expess a location in the vitual image s compaison channel in tems of the coesponding location in the souce image s compaison channel ( ( ) x c V c = α ( ) 1 D α S x c S xs) + x S x V + x V ( ( ) (1) 1 α D α S y c S ys) + y S + whee the optical cente of the vitual image is given by (7). This equation is used to map each pixel in the souce image s compaison channel to its coesponding location in the vitual image. The values of the vitual image s compaison channel ae then detemined at each pixel location though bicubic intepolation. This pocess is epeated again using the emaining compaison channel. Finally, we ceate ou anti-foensically disguised fogey by copying the desied object fom the vitual image and pasting it into the destination image. Ou entie anti-foensic algoithm can be summaized biefly as follows:

6 1. Identify the location whee an object will be copied fom in the souce image and location whee it will be pasted in the destination image. 2. Estimate the lateal chomatic abeation model paametes fo the souce and destination images using Gloe et al. s method. 3. Set the efeence channel of the vitual image equal to the efeence channel of the souce image. 4. Fo each pixel in the souce image s compaison channel, find its coesponding location in the vitual image s compaison channel using (1). 5. Pefom intepolation to detemine the values of the vitual image s compaison channel at pixel locations. 6. Repeat this pocess fo the emaining compaison channel. 7. Copy the object fom the vitual image and paste it into the desied location in the destination image. 4. SIMULATION AND RESULTS In ode to veify ou anti-foensic attack s ability to disguise copy-and-paste fogeies, we conducted an expeimental evaluation of its pefomance. We began by ceating a database of 12 unalteed souce images of size pixels captued by a Sony CybeShot DSC-W8 camea, and a database of 12 unalteed destination images of size pixels captued by a Sony CybeShot DSC-V1 camea. The images in both databases wee captued and stoed as JPEGs using the default settings of each camea. We used these images to ceate a set of 12 anti-foensically disguised copy-and-paste fogeies. This was done by selecting a 3 4 pixel block fom each image in the souce image database, then copy-and-pasting it into an image in the destination image database using ou anti-foensic attack. We epeated this pocess without the use of ou anti-foensic attack to ceate an additional set of 12 naively constucted copy-and-paste fogeies. In pactice, a foge may copy fom any location in the souce image and paste into any location in the destination image. These locations have a significant impact on the pefomance of Johnson and Faid s fogey detection technique. A fogey will be difficult o impossible to detect if the displacement vectos in the copy and paste egions have simila angula oientations. This is likely to happen if these egions occu at simila locations with espect to the optical centes of the souce and destination images. When constucting the fogeies used in ou expeiment, the block copied fom each souce image was located halfway fom the image s top and 1 pixels fom its ight edge. It was pasted halfway fom the top and 1 pixels fom the left edge of its coesponding destination image. These locations wee chosen to povide the most favoable conditions fo Johnson and Faid s detection algoithm by maximizing the expected angle between the displacement vectos in the copy and paste egions. Since this coesponds to the least favoable expeimental setup fo a foge, ou esults can be intepeted as a minimax evaluation of ou anti-foensic attack, thus poviding a lowe bound on its pefomance. Next, using the geen channel as the efeence channel, we measued the geen-to-ed and geen-to-blue lateal chomatic abeation of each image in the set of anti-foensically disguised fogeies, naively constucted fogeies, and unalteed souce images. This was done using Gloe et al. s method to obtain a seies of locally estimated displacement vectos and global model paametes fo each image. Locally estimated displacement vectos wee obtained using seach blocks of size W = 64 pixels with an upsampling facto of u = 5 and a maximum seach displacement of = 3 pixels. Fig. 4 shows a typical example of the locally estimated and globally modeled displacement vecto fields fom a naively constucted fogey and an anti-foensically disguised fogey. The falsified image egion is maked with a dashed line, and locally measued displacement vectos in this egion ae shown in geen. We can easily see that in the falsified egion of the naively constucted fogey, thee ae lage angula eos between locally estimated displacement vectos and the global model. By contast, in the falsified egion of ou anti-foensically modified image, the locally estimated displacement vectos closely match the globally estimated model. These esults

7 (a) Naively Constucted Fogey (b) Anti-Foensically Disguised Fogey Figue 4. Geen-to-ed lateal chomatic abeation displacement field of (a) a naively constucted fogey and (b) an anti-foensically disguised fogey. Displacement vectos detemined using the global model ae shown in blue. Locally measued estimated displacement vectos ae shown in geen within the falsified egion and ed elsewhee. Fo display puposes, vectos have been scaled by a facto of 2. indicate that ou anti-foensic attack can successfully pevent localized inconsistencies in the lateal chomatic abeation of cut-and-paste fogeies. We used Johnson and Faid s technique to seach each image in the set of anti-foensically disguised fogeies, naively constucted fogeies, and unalteed destination images fo evidence of falsification by computing the angula eo between the locally estimated displacement vectos and the global model. The eos wee then aggegated and used to empiically estimate the distibution of angula eos within the paste egion of each set of images. These distibutions ae shown in Fig 5. By examining this figue, we can clealy see a high occuence ate of lage angula eos in the paste egion of the naively constucted fogeies. Fo fogeies constucted using ou anti-foensic attack, lage angula eos occu fa less fequently. Futhemoe, the distibution of angula eos in the set of anti-foensically disguised fogeies closely matches the distibution of angula eos in the set of unalteed images. This indicates that ou anti-foensic attack can successfully fool Johnson and Faid s fogey detection technique. To futhe veify this esult, we statistically chaacteized the pefomance of Johnson and Faid s detecto unde ou anti-foensic attack. This was done by classifying an image as a fogey if the angula eo within the paste egion exceeded a detection theshold. The detection theshold was vaied ove a ange of values, and the esults wee ecoded. The pobabilities of detection P D and false alam P F A wee detemined fo each theshold by espectively calculating the pecentage of fogeies that wee coectly classified, and the pecentage of unalteed destination images that wee incoectly classified. These esults wee used to geneate the eceive opeating chaacteistic (ROC) cuves shown in Fig. 6. In these ROC cuves, the blue line epesents the pefomance of a decision ule that andomly classifies an image as a fogey with pobability P F A, i.e. making a andom guess. As we can see fom Fig. 6, ou anti-foensic attack is able to educe the pefomance of Johnson and Faid s fogey detection technique to a simila o equivalent level fo both the geen-to-ed and geen-to-blue lateal chomatic abeation. Additionally, we used this data to compute the anti-foensic susceptibility of Johnson and Faid s detection technique to ou anti-foensic attack. The anti-foensic susceptibility S α is a measue of the decease in effectiveness of a foensic detecto caused by an anti-foensic attack. 15 A susceptibility of S α = 1 indicates that the attack was able to ende the foensic technique completely ineffective, while a susceptibility of S α = indicates that the attack had no effect. Ou esults, which ae shown in Fig. 7, show that Johnson and Faid s foensic technique was completely susceptible to ou attack fo geen-to-blue lateal chomatic abeation, and susceptible with a ate

8 .35.3 Unalteed Image Naive Fogey Anti Foensic Fogey.3.25 Unalteed Image Naive Fogey Anti Foensic Fogey Empiical Distibution Empiical Distibution Angle (in adians) Angle (in adians) (a) Geen-to-Red Angula Eo Distibution (b) Geen-to-Blue Angula Eo Distibution Figue 5. Empiical estimates of the angula eo distibution within the paste egion of anti-foensically disguised fogeies, naively constucted fogeies, and unalteed destination images fo (a) geen-to-ed and (b) blue-to-ed lateal chomatic abeation measuements P D.5 P D Naive Fogey Anti Foensic Fogey P FA (a) Geen to Red LCA.2.1 Naive Fogey Anti Foensic Fogey P FA (b) Geen to Blue LCA Figue 6. Receive opeating chaacteistic cuves fo Johnson and Faid s copy-and-paste fogey detecto when tested against naively constucted fogeies and anti-foensically disguised fogeies. of at least.8 fo geen-to-ed lateal chomatic abeation. The esults in Figs. 6 and 7 clealy show the success of ou anti-foensic attack. 5. CONCLUSIONS In this pape, we have poposed an anti-foensic method to disguise lateal chomatic abeation inconsistencies in copy-and-paste image fogeies. Ou anti-foensic attack woks by fist estimating the lateal chomatic abeation in the copy egion of a souce image and the paste egion of a destination image. The colo layes of the souce image ae then manipulated so that the falsified lateal chomatic abeation in the copy egion matches the expected lateal chomatic abeation in the paste egion of the destination image. Finally, the modified image is esampled along the pixel gid, and the object is copied and pasted into the taget image. We evaluated the effectiveness of ou anti-foensic attack by ceating a seies of anti-foensically falsified image fogeies and compaing thei lateal chomatic abeation pattens to those fom authentic images. Ou expeimental esults

9 S α Geen to Red LCA Geen to Blue LCA P FA Figue 7. Plot of the anti-foensic susceptibility of Johnson and Faid s detecto to ou anti-foensic attack. demonstate that ou poposed anti-foensic attack can successfully fool the state-of-the-at foensic technique to detect copy-and-move fogeies using lateal chomatic abeation. REFERENCES [1] Stamm, M. C., Wu, M., and Liu, K. J. R., Infomation foensics: An oveview of the fist decade, IEEE Access 1, (213). [2] Stamm, M. C. and Liu, K. J. R., Anti-foensics of digital image compession, IEEE Tans. on Infomation Foensics and Secuity 6(3), (211). [3] Chu, X., Stamm, M. C., Chen, Y., and Liu, K. J. R., On anti-foensic concealability with ate-distotion tadeoff, IEEE Tans. on Image Pocessing (215, in pess). [4] Kichne, M. and Böhme, R., Hiding taces of esampling in digital images, IEEE Tans. on Infomation Foensics and Secuity 3(4), (28). [5] Wu, Z.-H., Stamm, M. C., and Liu, K. J. R., Anti-foensics of median filteing, in [Poc. IEEE Int. Conf. Acoust., Speech, Signal Pocess.], (213). [6] Bani, M., Fontani, M., and Tondi, B., A univesal technique to hide taces of histogam-based image manipulations, in [Poceedings of the ACM Wokshop on Multimedia and Secuity], 97 14, ACM, New Yok, NY, USA (212). [7] Costanzo, A., Ameini, I., Caldelli, R., and Bani, M., Foensic analysis of SIFT keypoint emoval and injection, IEEE Tans. on Infomation Foensics and Secuity 9(9), (214). [8] Comesana-Alfao, P. and Peez-Gonzalez, F., Optimal countefoensics fo histogam-based foensics, in [Poc. IEEE Int. Conf. Acoust., Speech, Signal Pocess.], (213). [9] Gloe, T., Kichne, M., Winkle, A., and Böhme, R., Can we tust digital image foensics?, in [Poc. Int. Confeence on Multimedia], 78 86, ACM, New Yok, NY, USA (27). [1] Kichne, M. and Böhme, R., Synthesis of colo filte aay patten in digital images, in [Poc. SPIE-IS&T Electonic Imaging: Media Foensics and Secuity], 7254 (29). [11] Stamm, M., Lin, W., and Liu, K., Tempoal foensics and anti-foensics fo motion compensated video, IEEE Tans. on Infomation Foensics and Secuity 7(4), (212). [12] Johnson, M. K. and Faid, H., Exposing digital fogeies though chomatic abeation, in [Poceedings of the 8th Wokshop on Multimedia and Secuity], 48 55, ACM, New Yok, NY, USA (26). [13] Gloe, T., Boowka, K., and Winkle, A., Efficient estimation and lage-scale evaluation of lateal chomatic abeation fo digital image foensics, Poc. SPIE-IS&T Electonic Imaging: Media Foensics and Secuity 7541, (21).

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