IAJIT First Online Publication

Size: px
Start display at page:

Download "IAJIT First Online Publication"

Transcription

1 Content Protecton n Vdeo Data Based on Robust Dgtal Watermarkng Resstant to Intentonal and Unntentonal Attacks Mad Masoum and Shervn Amr Department of Electrcal Engneerng, Islamc Azad Unversty Qazvn Branch, Iran Scentfc Member of electrcal engneerng Department, Iranan Research Organzaton for Scence and Technology, Iran IAJIT Frst Onlne Publcaton Abstract: Embeddng a dgtal watermark nto an electronc document s provng to be a feasble soluton for multmeda copyrght protecton and authentcaton purposes. In the present paper we propose a new dgtal vdeo watermarkng scheme based on scene change analyss. By detectng the moton scene of vdeo and usng CDMA technques the watermark s embedded nto md-frequency sub-bands of wavelet coeffcents. In ths experment n order to enhance the securty of our algorthm four keys are consdered. Three of them are formed n watermark encrypton process and one key s related to CDMA embeddng process. Also, wth the am of makng a good compatblty between the proposed scheme and Human Vsual System (HVS), the blue channel of RGB vdeo s utlzed to embed the watermark. Expermental results show the hgh robustness of the proposed method aganst both ntentonal and unntentonal attacks durng the transfer of vdeo data. The mplemented attacks are Gaussan nose, medan flterng, frame averagng, frame droppng, geometrc attacks and dfferent knds of lossy compressons ncludng MPEG-, MPEG-4, MJPEG and H.64/AVC. Keywords: Dgtal watermarkng, scene change analyss, geometrc attacks, nformaton securty, HVS. Receved May 3, ; accepted December 3,. Introducton In the past decade, the global rfe access of nternet technologes makes the communcaton and crculaton of dgtal multmeda contents lke mages, audo and vdeo very easy. However, ths convenence also causes substantal ncrease n llegal operatons such as duplcaton, modfcaton, forgery, copy-rght protecton and others n dgtal meda. Therefore, the protecton of dgtal meda has become an mperatve ssue. Recently, dgtal watermarkng has drawn much attenton of research communty to resolve these pressng problems [3, 6]. The basc procedure for dgtal watermarkng s to embed some hdden nformaton nto multmeda data, whle the qualty of the watermarked data s retaned, and the watermark can stll be detected under dfferent knds of ntentonal and unntentonal attacks. An effectve watermarkng scheme s dstngushed by three characterstcs, namely, mperceptblty, robustness and capacty. Also, n order to enhance the safety of algorthm another feature,.e., securty, can be added to the man necesstes of vdeo watermarkng. Imperceptblty: A degree that an embedded watermark remans unnotceable when a user vews the watermarked dgtal meda. The nformaton should embed the watermark n the regons of the vdeo frame n whch mperceptblty s least affected [3]. Robustness: The reslence of an embedded watermark aganst beng removed by ncdental and ntended attacks. Maor attacks on the vdeos are flterng, addng nose, compresson, scalng [3]. In some of the watermarkng technques, robustness s more a property and not a requrement []. Capacty: The amount of nformaton that can relably be hdden when the scheme provdes the ablty to change dgtal data [8,,, 9] These three requrements of watermarkng make a trangle. Improvement n any one of them, affects the other two negatvely. We have to fnd the correct balance between these conflctng requrements of watermarkng [3]. Securty: The ablty of the watermark to resst aganst attempts by a sophstcated attacker to remove t or destroy t va cryptanalyss, wthout modfyng the vdeo tself [6]. Applcatons of vdeo watermarkng contan fngerprntng, broadcast montorng, vdeo authentcaton and copyrght protecton. A varety of watermarkng algorthms have been proposed n the lterature. These algorthms can be broadly classfed n two categores accordng to the embeddng doman: spatal and transform doman. Spatal doman approaches [, ] are the smplest and the earlest algorthms based on the modfcaton of pxel ntenstes. These algorthms are less robust aganst the

2 attacks. On the other hand, transform doman approaches nsert the watermark nto transform coeffcents, such as Dscrete Fourer Transform (DFT) [9], Dscrete Cosne Transform (DCT) [], and Dscrete Wavelet Transform (DWT) [3, 5, 3]. L [5] proposed a scheme based on 3D-DWT and Artfcal Neural Network (ANN). Frst the average frame of the vdeo shot s computed. Then the resultng frame s transformed to the wavelet doman. Afterwards, the LL subband s dvded nto non overlappng 3 3 blocks. The blocks whch satsfy a relatonshp among the center of block, mean eght neghbors and standard devaton are selected as the tranng sets. The center of each block s the output whle the mean and standard devaton of the neghbor are the nputs. Consequently a traned network for watermark embeddng and extracton process s obtaned. So n the extracton stage, statstcal features of coeffcents and ther relatonshp are used whch means, ths scheme s not completely blnd; on the contrary, a large amount of data s requred to detect the watermark sequence. On the other hand embeddng the watermark nformaton n low frequency coeffcent enhances the robustness of system; however t severely destroys the qualty of vdeo and ts transparency. A DWT-based watermarkng scheme whch embeds the watermark n successve frames s proposed n [4]; ths scheme defned a general algorthm based on scene change detecton for embeddng the watermark by alterng the magntude of some wavelet coeffcents. In fact they nsert the watermark n both moton and motonless parts of vdeo. However, HVS s more senstve to motonless part of vdeo, so embeddng the watermark n ths part leads to the perceptblty of the watermark. On the other hand compresson algorthms used to destroy the motonless part of vdeo meanwhle mantan the moton part of t. Also, these motonless regons may be statstcally compared or averaged to remove the ndependent watermarks. From the other pont of vew, dvdng the vdeo based on scenechange detecton wll not be useful f the vdeo changes occur rapdly or contans too many dfferent short scenes, because t demands dfferent algorthms n each scene for embeddng and detectng the watermark n the watermarkng process. Furthermore they had no estmaton or dscusson about the acqurng of frame number based on a factor of n. Snce each algorthm whch has a 3D shape (e.g., 3D-DWT, 3D-DCT, ) should has a frame number of factor n for embeddng and extracton of watermark. Otherwse t faces problems n executng the nverse DWT, because f the number of frames s not a factor of n the coeffcents wll have zero values whch lead to maor damage n vdeo qualty and destructon of watermark nformaton. Among the delvered technques n recent years, the ones whch are based on the Dscrete Wavelet Transform (DWT) are ganng more popularty due to ther excellent spatal localzaton, frequency spread, and mult-resoluton characterstcs. The DWT s chosen because t s more computatonally effcent than other transform methods. The speed s faster than DCT and DFT as only sum or dfference of the pxel have to be calculated. From the other pont of vew, watermarkng n vdeo doman can be done on compressed or uncompressed vdeo. Generally the watermarkng n compressed vdeo has more compatblty for real-tme systems [4]. However, the goal of ths paper s to embed the watermark n uncompressed vdeo, because format conversons destroy the watermark whch s embedded n compressed watermarked vdeo. The huge memory requrement of the algorthms that compute the 3D- DWT s one of the man drawbacks n practcal mplementatons. Orgnally the algorthms whch are based on 3D-DWT and 3D-DCT, demand hgh computatonal complexty and have enormous memory usage. Also, f the 3D algorthms perform on all vdeo streams (contanng moton and motonless regons) they requre hgher computatonal complexty and are expensve for mplementaton and eventually cannot be useful for real-tme systems. The vdeo watermarkng methods whch have lower computatonal complexty (e.g. D based algorthms) are sutable for real-tme systems. Many of the exstent algorthms meet the mperceptblty necessty qute easly and survey robustness only aganst a subset of attacks not all knds of attacks, meanwhle robustness aganst dfferent attacks s the key challenge n watermarkng process. In ths study, a secure vdeo watermarkng scheme whch s robust aganst dfferent vdeo attacks and yet s sutable for real-tme systems s delvered. The rest of paper s planned as follows: The descrpton of used termnologes.e. Dscrete Wavelet Transform and watermark scramblng are explaned n Secton. Secton 3 llustrates the proposed watermarkng scheme n three sub-sectons. The expermental results are presented n Secton 4. Fnally, the concludng remarks are gven n Secton 5. IAJIT Frst Onlne Publcaton. Prelmnares In ths secton, we provde the man termnologes whch are used n the proposed algorthm to acheve the desred goal. These termnologes are as follows:.. Dscrete Wavelet Transform... One Dmensonal Dscrete Wavelet Transform A general -D dscrete wavelet transform can be wrtten as [9]:

3 W(,k)= f ( x) ( x k ) M x () x.5 =.5 x otherwse. () Where W represents the wavelet coeffcents functon, and k denote the dlaton and translaton parameters respectvely, and M s the length of sequence f.... Two Dmensonal Dscrete Wavelet Transform The one-dmensonal wavelet transform can be easly extended to two-dmensonal functons lke mages. In two dmensons, a two-dmensonal scalng functon, ( x, y ) and three, two-dmensonal wavelets, H V D ( x, y ), ( x, y ), ( x, y ) are requred. Each s the product of a one-dmensonal scalng functon and correspondng wavelet. Excludng products that produce one-dmensonal results, lke ( x ) ( x ), the four remanng products produce the separable scalng functon: ( x, y) = ( x) ( y) (3) and separable, "drectonally senstve" wavelets : H ( x, y) = ( x) ( y) (4) W (, m, n) coeffcents add horzontal, vertcal, and dagonal detals for scales. Gven the W and W of equatons. (9) and (), f ( x, y) s obtaned va the nverse dscrete wavelet transform: IAJIT Frst Onlne Publcaton f(x,y)= W (, m, n), m, n( x, y) + MN m n W (, m, n), m, n( x, y) MN = H, V, D = m n ()..3 Three Dmensonal Dscrete Wavelet Transform In three dmenson, a three-dmensonal scalng functon, ( x, y, z ) and seven three-dmensonal LLH LHL wavelet functons, ( x, y, z), ( x, y, z), LHH HLL HLH ( x, y, z), ( x, y, z), ( x, y, z), HHL HHH ( x, y, z) and ( x, y, z) are requred. Each s the product of a one-dmensonal scalng functon and correspondng wavelet.excludng products that produce one-dmensonal results, lke ( x, y, z ) ( x, y, z), the eght resdual products produce the separable scalng functon: ( x, y, z) = ( x) ( y) ( z) () and separable, "drectonally senstve" wavelets : V ( x, y) = ( x) ( y) (5) D ( x, y) = ( x) ( y) (6) Gven separable two-dmensonal scalng and wavelet functons, extenson of the one-dmensonal DWT to two dmensons s straghtforward. The scaled and translated bass functons are:, m, n( x, y ) = ( x m, y n ) (7), m, n( x, y ) = ( x m, y n ) ={H,V,D} (8) Where ndex dentfes the drectonal wavelets n equatons (4) to (6). The dscrete wavelet transform of functon f ( x, y) of sze M N s then: M N W (, m, n) = f ( x, y ), m, n( x ) (9) MN x = y = M N W (, m, n) = f ( x, y), m, n( x ) MN x = y = ={H,V,D} () As n the one-dmensonal case, s an arbtrary startng scale and the W (, m, n) coeffcents defne an approxmaton of f ( x, y ) at scale. The LLH ( x, y, z) = ( x) ( y) ( z ) LHL ( x, y, z) = ( x) ( y) ( z) LHH ( x, y, z) = ( x) ( y) ( z) HLL ( x, y, z) = ( y) ( y) ( z) HLH ( x, y, z) = ( x) ( y) ( z) HHL ( x, y, z) = ( x) ( y) ( z ) HHH ( x, y, z) = ( x) ( y) ( z) (3) Gven separable three-dmensonal scalng and wavelet functons, extenson of the one-dmensonal DWT to three dmensons s smple. The scaled and translated bass functons are:,,, ( x, y, z) = ( x m, y n, z o) mno m n o z,,, ( x, y, z ) = ( x m, y n, o) ={LLH,LHL,LHH,HLL,HLH,HHL,HHH} (4) Where ndex dentfes the drectonal wavelets n equaton (3). The dscrete wavelet transform of functon f ( x, y, z) of sze M N O s then: O M N W(, m, n, o) = f ( xyz,, ), m, no, ( xyz MNO,, ) (5) z= x= y =

4 W(, m, n, o) = MNO ={LLH,LHL,LHH,HLL,HLH,HHL,HHH} O M N f ( x, y, z) mno,,, ( x, y, z) z= x= y = (6) As n the one-dmensonal case, s an arbtrary startng scale and the W (, m, n, o) coeffcents defne an approxmaton of f ( x, y, z) at scale. The W (, m, n, o) coeffcents add horzontal, vertcal, and dagonal detals for scales. Gven the W and W of equatons (5) and (6), f ( x, y, z ) s obtaned va the nverse dscrete wavelet transform: f(x,y)= MN MNO W (, m, n, o) ( x, y, z), m, n, o o m n HHH W ( mno,,, ), m, n, o( x, y, z) O = LLH = o m n.. Watermark Scramblng + (7) Usually scramblng transform s used n the pretreatment stage of the watermark as a way of encrypton. Generally, a meanngful watermark mage becomes meanngless and dsordered after scramblng. For mprovng the securty and confdentalty, a scramblng method [7] s used to encrypt the bnary watermark mage. After scramblng, human eyes cannot dstngush the shape of the orgnal watermark. Wthout the scramblng algorthm and the key, the attacker wll not recover the watermark at all even f t has been extracted from the watermarked vdeo. So shufflng the mage gves a secondary securty for the dgtal products. Ths method s defned as follows: x n+ α x n = mod( N ) y n + β αβ y + n (8) Where ( x n, y n) s the pxels poston n an N N mage; ( x n+, y n+ ) s the transformed poston after cat map; α and β are the system parameters and must be the postve ntegers. The determnant value s, so cat map s a map whch keepng area (no attractor). At the same tme, the cat map s one-to-one mappng; each pont n matrx can be transformed to another pont unquely. Cat map has two typcal factors, whch brng chaotc movement: tenson (multply matrx n order to enlarge x, y) and fold (takng mod n order to brng x, y n unt matrx). In fact, cat map s a chaotc map. Image poston can be scrambled va the teraton of cat map, by consderng ( α = 7, β = 3), consequently the encrypted mage wll be acheved. After a perod of teraton the watermark mage wll be attaned. So teraton tmes and system parameters (α, β ) can be used as the encrypton keys. By usng these three keys the securty of our scheme wll be enhanced. Fgure. Encryptng the watermark; Orgnal watermark Scrambled watermark (Iteraton tmes= 9). IAJIT Frst Onlne Publcaton 3. The Proposed Watermarkng Algorthm 3.. Preprocessng of Vdeo Applyng ndependent watermarks to each frame presents a problem, f regons n each vdeo frames reman lttle or no moton frame after frame. These motonless regons may be statstcally compared or averaged to remove the ndependent watermarks [4]. From the other pont of vew, dvdng the vdeo based on scene-change detecton wll not be useful f the vdeo changes occur rapdly or contans too many dfferent short scenes, because t demands dfferent algorthms of embeddng and detectng the watermark n a watermarkng process, especally f they use a 3Dbased watermarkng algorthm. Also, f the vdeo contans long motonless scenes, the algorthm wll face the same dffcultes. Therefore, n ths experment, we decded to nsert the watermark nto moton part of vdeo. In order to detect the moton part of vdeo, the followng crteron should be satsfed: n D (, + ) = H ( ) H ( ) (9) = + For ths purpose, only the hstograms of green components for all frames are utlzed. Ths s because of the ntended moton part of vdeo contans a large texture of green color whch dstngush t from the other scenes. In ths method s the number of frames, s the green component of frames and H s the calculated hstogram. So by meetng D (, + ) > thresholdt ( ) a scene change wll be occurred. Wth the purpose of obtanng the desred moton part of vdeo T s regarded as 535. In the consdered vdeo sequence.e. wldlfe sequence, we have chosen the scene that the brds start to fly, frames from the detected moton part are randomly shown n Fgure. Fgure. Two randomly frames from the detected moton scene. Two other reasons for choosng the moton scene of vdeo for embeddng the watermark can be llustrated as follows; Embeddng the watermark n moton scene

5 leads to less mperceptblty of the watermark, because HVS s less senstve to moton part of vdeo, on the other hand compresson algorthms used to destroy the motonless part of vdeo, at the same tme, mantan the moton part of t. In the Human Vsual System (HVS), there are three types of cones that react to the basc three colors: red, green and blue. The number of cones reacted to blue s 3 tmes smaller than the number of cones reacted to red or green, whch means the HVS has lack of sensblty to blue color []. Fgure 3 shows fracton of lght absorbed by each type of cone, here R, G, and B represent red, green and blue colors, respectvely. For ths reason, the proposed algorthm ntends to embed the watermark sgnal nto the blue channel; hence a good compatblty between the watermarkng and HVS wll be acheved. each frame and one dmensonal DWT wthn the temporal axs over frames. The three dmensonal coeffcents of HL, LH and HL3, LH3 are chosen for embeddng the watermark. Coeffcent of LL3 (.e. the low frequency sub-band) s not watermarked, as vdeo energy s concentrated on lower frequency wavelet coeffcent. If t s altered, t wll affect on perceptual qualty. Also the coeffcents of HH (.e. the hgh frequency sub-bands) are excluded from embeddng the watermark, as data loss usually occurs among the hgh frequency components due to lossy compresson [7]. Coeffcents of wavelet decomposton n three levels are shown n Fgure 4. IAJIT Frst Onlne Publcaton Fgure 4. Three levels of dscrete wavelet decomposton. Fgure 3. Sensblty of HVS to dfferent wavelength related to three basc colors. 3.. Watermark Inserton In ths secton n order to nsert the watermark a Code Dvson Multple Access (CDMA) technque s used. In ths technque watermarkng algorthm can be vewed n terms of a telecommuncaton system: a message (the watermark) has to be sent through a nose channel (the mage/vdeo) to a recever that has to recover the orgnal message []. Generally, n CDMA technque, the watermark nformaton s consdered as pseudo random numbers, then by usng an algorthm, each bt of watermark nformaton s scattered randomly throughout the vdeo frames, whch leads to ncrease n capacty of embeddng and mprovng the resstance of watermarkng system (specally aganst addng nose). Utlzng CDMA technque makes hard to detect the watermark because t uses wde-band, nose-lke sgnals. Also, by applyng pseudo-random numbers whch are ndependent from the data, both the band spread and securty of the system wll be provded. The process of embeddng the watermark s as follows: Frst of all, a three dmensonal wavelet n three levels s appled on the detected moton scene, namely two dmensonal DWT n terms of space on Embeddng process s followed by applyng CDMA technques n a way that pseudo random numbers based on Mersenne Twster algorthm whch s proposed by Nshmura and Matsumoto [6] are created. Ths method generates numbers wth a 9937 perod of ( - )/. By usng a key, four sets of pseudo random numbers whch W (,, k) {, + }, are acheved based on the adaptve sze of wavelet coeffcents. So ths key s consdered as our fourth key n the proposed algorthm whch guarantees the securty of the proposed watermarkng scheme. Accordng to magntudes of the 3D-DWT coeffcents, the scrambled watermark s adaptvely spread and embedded nto these coeffcents. Followng algorthm shows the embeddng process: C (,, k ) = C (,, k ) + QW. (,, k) f b = C (,, k ) = C (,, k ) f b = Where C (,, k) s the 3D wavelet coeffcent, C (,, k) s the watermarked 3D wavelet coeffcent, Q s the modulaton ndex, W (,, k) s the PRN matrx, b s bt of the scrambled watermark that has to be embedded and { HL, LH, HL3, LH 3}. Fnally by performng nverse 3D wavelet over the moton part of vdeo, the process of nsertng the watermark wll be accomplshed.

6 3.3. Watermark Detecton Durng extracton process the orgnal vdeo s not needed, namely, blnd detecton. The detecton s the nverse process of watermark embeddng: Performng the 3D wavelet on moton part of vdeo, that s, D wavelet on each frame and D-DWT along temporal axs over frames. Selectng the three dmensonal coeffcents of HL, LH, HL3, and LH3 for extractng the watermark. Generatng four sets of pseudo random numbers based on Mersenne Twster algorthm by applyng the same key whch s used n nsertng process. Calculatng the correlaton between the extracted coeffcents and ther relatve pseudo-random numbers gves the hdden watermark: f ( ρ ( EC (,, k ), W (,, k ))) > th watermark s Avalabe end f Where { HL, LH, HL3,LH3} and EC (,, k ) s the extracted 3D wavelet coeffcents. It should be noted that th (threshold) s consdered by experence. Also the correlaton coeffcent between the extracted wavelet coeffcents and the pseudo random numbers s determned by [3]: ρωω (, ) = m n ( ω(, ) ϖ).( ω (, ) ϖ ) = = m n m n ω ϖ ω ϖ = = = = ( ( (, ) ) ).( ( (, ) ) ) () Where ϖ and ϖ are the mean of ω(, ) and ω (, ), respectvely. The value of ρ wll be equal to unty f the watermark s extracted wthout any error and ρ = for an error rate of 5%. 4. Expermental Results The mage whch s consdered as the watermark has a sze of whch s shown n Fgure. The watermarkng process s performed on true colour wldlfe vdeo sequence whch contans 33 frames and 5 fps wth CIF format. Generally, the accurate measurement of the mperceptblty as perceved by a human observer s a great challenge n mage/vdeo processng. The reason s that the amount and vsblty of the dstortons ntroduced by the watermarkng attacks strongly depend on the actual mage/vdeo content [8]. To measure the perceptual qualty, the Peak Sgnal-to- Nose Rato (PSNR) s calculated whch s used to estmate the qualty of the watermarked frames n comparson wth the orgnal ones. The PSNR [7] s defned as follows: PSNR max log ( ) MSE = () m m MSE = F Fˆ m = = where max max { ˆ,, } () = F m and the MSE s the mean squared error between the cover frame F and the watermarked frame ˆF.Ths parameter s declared as db. Based on [8] a PSNR value over 3 db wll be desrable. An example of watermarked frame s shown n Fgure 5. After extractng and refnng the watermark, a smlarty measurement between the extracted and reference watermark s used for obectve udgment of the extracton fdelty whch defned as: IAJIT Frst Onlne Publcaton W (, ). Wˆ (, ) NC = (3) [ W (, )] Whch s the cross-correlaton normalzed by the reference watermark energy to gve unty as the peak correlaton [5]. In the presented experment ths measurement s used to evaluate the robustness of the proposed scheme. In order to acheve a hgh vsual qualty for watermarked vdeo sequence, the modulaton ndex Q should be taken nto consderaton. In addton, for mplementng a good trade-off between the robustness and mperceptblty Q plays an mportant role. So, for ths sgnfcance, n ths experment Q s consdered as 3.5. By applyng ths value there wll be an acceptable PSNR of 36 db. Furthermore the extracted watermark has an admrable NC value of.9969 meanwhle th s consdered as.9. In all robustness evaluatons, the watermarked vdeos are analyzed usng possble watermark sgnals generated by dfferent keys; and the embedded watermark generated by the owner corresponds to the key equal to 5. Fgure 5. Watermarked frame Detector Response for In order to show the robustness of the presented scheme aganst ntentonal and unntentonal attacks dfferent knds of compresson methods lke MJEPG, MPEG-, MPEG-4 and H.64/AVC and also medan flterng and Gaussan nose, frame averagng, frame swappng, rotaton and rescalng are performed on the proposed watermarkng scheme, so the embedded watermark s retreved usng the proposed algorthm and the NC value of the recovered watermark s recorded for all knds of attacks. Compresson s one of the most basc attacks to

7 vdeo watermark. In most applcatons nvolvng storage and transmsson of dgtal vdeo, a lossy codng operaton s performed on the vdeo to reduce bt rates and ncrease effcency. For ths sgnfcance, the vdeo watermarkng scheme must be robust aganst lossy compresson. Any of aforementoned compressons have specfc method for compressng of vdeo frames. The mpact of these attacks over the watermarked vdeo s shown n Fgure 6. In order to show the robustness of the proposed algorthm aganst lossy compresson, watermarked vdeo s severely compressed wth hgh Compresson Rato (CR) for all knds of lossy compresson. As Fgure 6 shows the proposed algorthm has a good robustness aganst all of appled compresson methods. Furthermore, H.64/AVC lossy compresson whch recently s used as the most modern compresson codec n the worldwde s performed on our scheme. As Fgure 6(c) shows our approach has a very good robustness aganst ths wdely used knd of compresson, too. (c) (d) Fgure 6. Watermark robustness aganst lossy compresson; Detector response for MPEG-4 (CR=95:), MJPEG (CR=95:), (c) H.64/AVC (CR=93:), (d) MPEG- (CR=95:), respectvely. NC value. Fgure 7 shows the detector response for appled medan flterng and Gaussan nose attacks. IAJIT Frst Onlne Publcaton Fgure 7.Detector response for Gaussan nose (%), Medan flterng(3 3). Due to large amounts of data and nherent redundancy between frames, vdeo sgnals are hghly susceptble to prate attacks, ncludng frame averagng, frame droppng and generally statstcal analyss. In frame droppng, selected frames are removed from the watermarked vdeo and replaced by ther correspondng orgnal frames. Ths attack s often used as an effectve vdeo watermarkng attack, snce t leads lttle or no damage to the vdeo sgnal. For ths purpose 5% of the watermarked vdeo frames are dropped. Moreover, frame averagng s another sgnfcant vdeo watermarkng attack. It s clear that the average of multple frames wll remove the dynamc composton of the watermark. Frame averagng s the average of the current frame and ts two nearest neghbors to replace the current frame. Averagng s defned by: [ F (,) + F (,) + F (,)] F k n 3 k k k+ (, ),3,4,..., - k = = (4) Ths attack s also performed on 5% of the watermarked vdeo frames. The robustness of the presented algorthm aganst these two statstcal attacks s shown n Fgure 8. Addton of nose s another method to estmate the robustness of the watermark. Generally, addton of nose s responsble for the degradaton and dstorton of the vdeo. The watermark nformaton s also degraded by nose addton and results n dffculty n watermark extracton. So, n order to test the robustness of the proposed system % Gaussan nose wth zero mean s added to watermarked vdeo. As Fgure 7 depcts, the great acheved robustness aganst nose attack, declares the power of utlzed CDMA technque for watermarkng process. On the other hand, one of the most common manpulatons n dgtal vdeos s flterng. The extracted watermark, after applyng 3 3 medan flterng s retreved. By applyng ths flter, vdeo s sgnfcantly degraded and lots of data are lost but the extracted watermark can stll be recognzed wth hgh Fgure 8. Detector response for Frame averagng Frame droppng. For more showng the robustness of the proposed scheme another group of attacks n mage/vdeo processng doman.e. geometrc attack are tested over the presented algorthm. Rescalng and rotaton are two commonly geometrc attacks whch are wdely used n ths doman. As Fgure 9 shows these attacks have the least effects on the robustness of the proposed scheme.

8 Fgure 9. Detector response for Rescalng (-5-%), Rotaton (-.6º). 5. Conclusons In ths paper a novel watermarkng approach for mantanng the copyrght n dgtal vdeos was nvestgated. Because of embeddng the watermark n blue channel of vdeo, the delvered algorthm has a good compatblty wth HVS. Also, the securty of our scheme s guaranteed by addng four keys durng the embeddng process. Furthermore, the blnd retreval of watermark s the strength pont of the presented algorthm. So, t can be used for publc watermarkng applcatons, where the orgnal vdeo s not avalable for watermark extracton. As the expermental results showed the proposed method has a good robustness aganst dfferent knds of attacks ncludng ntentonal or unntentonal ones. References [] Al-Ha A.M., Advanced technques n multmeda watermarkng: mage, vdeo and audo applcatons, Hershey, New York,. [] Barn M., Bartoln F., Pva A., A DCT doman system for robust mage watermarkng, Sgnal Processng, vol. 66, no. 3, pp , 998. [3] Bhatnagar G., Jonathan Wu Q. M., Raman B., A new aspect n robust dgtal watermarkng, Multmeda Tools Applcaton,. [4] Chetan K.R., Raghavendra K., DWT based blnd dgtal vdeo watermarkng scheme for vdeo authentcaton, Internatonal Journal of Computer Applcaton,. [5] Chou-Tung H., Ja-Lng W., Dgtal watermarkng for vdeo, In Proc. 3th Internatonal Conf. on Dgtal Sgnal Processng (DSP 97), pp. 7-, 997. [6] Cox I.J., Mller M.L., Bloom J.A., Dgtal Watermarkng, Morgan Kaufmann, San Francsco,. [7] Cox J., Klan J., Leghton F.T., Shamoon T., Secure Spread Spectrum Watermarkng for Multmeda, IEEE Trans. Image Processng, vol. 6, no., 997. [8] Dutot T., Marqu es F., Appled sgnal processng, Sprnger, New York, 9. [9] Gonzalez R. C., Woods R. E., Dgtal Image Processng, thrd Edton, publshed by Pearson Educaton (Sngapore) Pte. Ltr., Indan Branch, 48 F.I.F. Patpargan, Delh 9, Inda, 4. [] Hartung F., Grod B., Watermarkng of uncompressed and compressed vdeo, Sgnal Processng, vol. 66, no. 3, pp. 83-3, 998. [] Hsu C.T., Wu J. L., Hdden dgtal watermarks n mages, IEEE Trans. Image Processng, vol. 8, no., pp , 999. [] Hwang M. S., Chang C. C., Hwang K. F., A watermarkng technque based on one-way hash functons, IEEE Trans. Consum Electron vol. 45, no., pp.86 94, 999. [3] Ishtaq M., Jaffar M. A., Khan M. A., Jan Z., Mrza A. M., Robust and mperceptble watermarkng of vdeo streams for low power devces, Communcaton Computer Informaton Scence, vol. 6, pp , 9. [4] langelaar G. C., Real-tme Watermarkng Technques for Compressed Vdeo Data, Ph.D thess,. [5] L., Wang R., A Vdeo Watermarkng Scheme based on 3D-DWT and Neural Network, Nnth IEEE Internatonal Symposum on Multmeda, Tachung, Tawan, December, pp. -5, 7. [6] Matsumoto M., Nshmura T., Mersenne Twster, A 63-dmensonally equlstrbuted unform pseudorandom number generator, ACM Trans. on Modelng and Computer Smulaton, vol. 8, pp. 3 3, 998. [7] Netraval A.N., Haskell B.G., Dgtal pctures: representaton, compresson, and standards, Plenum, 9ew York, 995. [8] Pettcolas F. A. P., Watermarkng schemes evaluaton, IEEE Sgnal Processng Magazne, vol. 7, no. 5, pp ,. [9] Pun C. M., A novel DFT-based dgtal watermarkng system for mages, In Proc. nternatonal, conference of sgnal processng, Venna, Austra, vol., pp 4, 6. [] Rosa L., Hgh Capacty Wavelet Watermarkng Usng CDMA Multlevel Codes, advancedsourcecode, 9 [] Sayood K., Introducton to Data Compresson, nd Edton, Morgan Kaufmann Publshers,. [] Schyndle R. G., Trkel A. Z., Osbrone C. F., A dgtal watermark, In Proc. IEEE nternatonal conference on mage processng, Austn, Texas, vol., pp. 86 9, 994. [3] Suatha S., Sathk M., Blnd Wavelet Based Watermarkng Technque for Image Authentcaton, Internatonal Arab Journal of Informaton Technology (IAJIT), vol., no. 3, 3, to be publshed. [4] Swanson M., Zhu B., Tewfk A., Multresoluton vdeo watermarkng usng perceptual models and scene segmentaton, In Proc. IAJIT Frst Onlne Publcaton

9 Internatonal Conference on Image Processng, Washngton, DC, pp , 997. [5] Wang Y., Doherty J. F., Van-dyck R. E., A wavelet based watermarkng algorthm for ownershp verfcaton of dgtal mages, IEEE Trans. Image Processng, vol., no. pp.77 88,. [6] Wang R., Hu L., u D., A Watermarkng Algorthm Based on the CABAC Entropy Codng for H.64/AVC, Journal of Computer Informaton System, vol. 7, no. 6 pp. 3-4,. [7] We Y., Hao Y., L Y., A Multpurpose Dgtal Watermarkng Algorthm of Color Image, In Proc. IEEE Internatonal Conf on Mechatroncs and Automaton, Changchun, Chna, pp. -7, 9. [8] Wnkler S., Gelasca E. D., Ebrahm T., Toward perceptual metrcs for vdeo watermark evaluaton, In Proc. SPIE, Applcatons of Dgtal Image Processng, pp , 3. [9] Wolfgang R. B., Podlchuk C. I., Delp E. J., Perceptual watermarks for dgtal mages and vdeo, In Proc. of IEEE, vol. 87, no. 7, pp. 8-6, 999. [3] a., Boncelet C. G., A multresoluton watermark for dgtal mages, In Proc IEEE nternatonal conference on mage processng,washngton, DC, USA, vol. 3, pp , 997. [3] Zhang F., Image watermarkng algorthm based on the code dvson multple access technque, Lecture Notes n Computer Scence, pp. 4, 6. Mad Masoum was born n Lahan, Iran, n 986. He s a Master student n electrcal engneerng at Azad Unversty of Qazvn. He receved hs B.Sc. degree n electrcal engneerng n 8. Hs prevously researches nclude audo watermarkng, opto-electroncs and photonc crystals. He s currently nterested n watermarkng, mage & vdeo processng, cryptography, optmzaton, and communcaton systems. Specally usng spread spectrum for makng secure the networks aganst attacks and ammers. He s presently workng at Iranan Research Organzaton for Scence and Technology (IROST) as a researcher. Shervn Amr was born n Tehran, Iran, n 966. He receved hs B.Sc., M.Sc. and Ph.D. from Iran Unversty of Scence & Technology (IUST) n communcaton systems. Now he s a Scentfc Member of electrcal engneerng department n Iranan Research Organzaton for Scence and Technology (IROST). He s supervsor of many PhD and MSc students n the felds of communcaton system and subsystems. IAJIT Frst Onlne Publcaton

Hybrid Non-Blind Color Image Watermarking

Hybrid Non-Blind Color Image Watermarking Hybrd Non-Blnd Color Image Watermarkng Ms C.N.Sujatha 1, Dr. P. Satyanarayana 2 1 Assocate Professor, Dept. of ECE, SNIST, Yamnampet, Ghatkesar Hyderabad-501301, Telangana 2 Professor, Dept. of ECE, AITS,

More information

Key-Selective Patchwork Method for Audio Watermarking

Key-Selective Patchwork Method for Audio Watermarking Internatonal Journal of Dgtal Content Technology and ts Applcatons Volume 4, Number 4, July 2010 Key-Selectve Patchwork Method for Audo Watermarkng 1 Ch-Man Pun, 2 Jng-Jng Jang 1, Frst and Correspondng

More information

A Fast Content-Based Multimedia Retrieval Technique Using Compressed Data

A Fast Content-Based Multimedia Retrieval Technique Using Compressed Data A Fast Content-Based Multmeda Retreval Technque Usng Compressed Data Borko Furht and Pornvt Saksobhavvat NSF Multmeda Laboratory Florda Atlantc Unversty, Boca Raton, Florda 3343 ABSTRACT In ths paper,

More information

A Hybrid Semi-Blind Gray Scale Image Watermarking Algorithm Based on DWT-SVD using Human Visual System Model

A Hybrid Semi-Blind Gray Scale Image Watermarking Algorithm Based on DWT-SVD using Human Visual System Model A Hybrd Sem-Blnd Gray Scale Image Watermarkng Algorthm Based on DWT-SVD usng Human Vsual System Model Rajesh Mehta r Scence & Engneerng, USICT Guru Gobnd Sngh Indrarprastha Unversty New Delh, Inda rajesh00ust@gmal.com

More information

Robust Watermarking for Text Images Based on Arnold Scrambling and DWT-DCT

Robust Watermarking for Text Images Based on Arnold Scrambling and DWT-DCT Internatonal Conference on Mechatroncs Electronc Industral and Control Engneerng (MEIC 015) Robust Watermarkng for Text Images Based on Arnold Scramblng and DWT-DCT Fan Wu College of Informaton Scence

More information

Robust Video Watermarking Using Image Normalization, Motion Vector and Perceptual Information

Robust Video Watermarking Using Image Normalization, Motion Vector and Perceptual Information Robust Vdeo Watermarkng Usng Image ormalzaton, Moton Vector and Perceptual Informaton Cedllo-Hernández Antono 1, Cedllo-Hernández Manuel 1, akano-myatake Marko 1, García-Vázquez Mreya S. 2 1 Postgraduate

More information

Content Based Image Retrieval Using 2-D Discrete Wavelet with Texture Feature with Different Classifiers

Content Based Image Retrieval Using 2-D Discrete Wavelet with Texture Feature with Different Classifiers IOSR Journal of Electroncs and Communcaton Engneerng (IOSR-JECE) e-issn: 78-834,p- ISSN: 78-8735.Volume 9, Issue, Ver. IV (Mar - Apr. 04), PP 0-07 Content Based Image Retreval Usng -D Dscrete Wavelet wth

More information

Enhanced Watermarking Technique for Color Images using Visual Cryptography

Enhanced Watermarking Technique for Color Images using Visual Cryptography Informaton Assurance and Securty Letters 1 (2010) 024-028 Enhanced Watermarkng Technque for Color Images usng Vsual Cryptography Enas F. Al rawashdeh 1, Rawan I.Zaghloul 2 1 Balqa Appled Unversty, MIS

More information

Improvement of Spatial Resolution Using BlockMatching Based Motion Estimation and Frame. Integration

Improvement of Spatial Resolution Using BlockMatching Based Motion Estimation and Frame. Integration Improvement of Spatal Resoluton Usng BlockMatchng Based Moton Estmaton and Frame Integraton Danya Suga and Takayuk Hamamoto Graduate School of Engneerng, Tokyo Unversty of Scence, 6-3-1, Nuku, Katsuska-ku,

More information

KEYWORDS: Digital Image Watermarking, Discrete Wavelet Transform, General Regression Neural Network, Human Visual System. 1.

KEYWORDS: Digital Image Watermarking, Discrete Wavelet Transform, General Regression Neural Network, Human Visual System. 1. An Adaptve Dgtal Image Watermarkng Based on Image Features n Dscrete Wavelet Transform Doman and General Regresson Neural Network Ayoub Taher Group of IT Engneerng, Payam Noor Unversty, Broujen, Iran ABSTRACT:

More information

Semi-Fragile Watermarking Scheme for Authentication of JPEG Images

Semi-Fragile Watermarking Scheme for Authentication of JPEG Images Tamkang Journal of Scence and Engneerng, Vol. 10, No 1, pp. 5766 (2007) 57 Sem-Fragle Watermarkng Scheme for Authentcaton of JPEG Images Chh-Hung n 1 *, Tung-Shh Su 2 and Wen-Shyong Hseh 2,3 1 Department

More information

A NEW AUDIO WATERMARKING METHOD BASED

A NEW AUDIO WATERMARKING METHOD BASED A NEW AUDIO WATERMARKING METHOD BASED ON DISCRETE COSINE TRANSFORM WITH A GRAY IMAGE Mohammad Ibrahm Khan 1, Md. Iqbal Hasan Sarker 2, Kaushk Deb 3 and Md. Hasan Furhad 4 1,2,3 Department of Computer Scence

More information

A Binarization Algorithm specialized on Document Images and Photos

A Binarization Algorithm specialized on Document Images and Photos A Bnarzaton Algorthm specalzed on Document mages and Photos Ergna Kavalleratou Dept. of nformaton and Communcaton Systems Engneerng Unversty of the Aegean kavalleratou@aegean.gr Abstract n ths paper, a

More information

Digital Video Watermarking using Discrete Wavelet Transform and Principal Component Analysis

Digital Video Watermarking using Discrete Wavelet Transform and Principal Component Analysis Internatonal Journal of Wsdom Based Computng, Vol. 1 (2), August 2011 7 Dgtal Vdeo Watermarkng usng Dscrete Wavelet Transform and Prncpal Component Analyss Sanjana Snha, Prajnat Bardhan, Swarnal Pramanck,

More information

An Optimal Algorithm for Prufer Codes *

An Optimal Algorithm for Prufer Codes * J. Software Engneerng & Applcatons, 2009, 2: 111-115 do:10.4236/jsea.2009.22016 Publshed Onlne July 2009 (www.scrp.org/journal/jsea) An Optmal Algorthm for Prufer Codes * Xaodong Wang 1, 2, Le Wang 3,

More information

FEATURE EXTRACTION. Dr. K.Vijayarekha. Associate Dean School of Electrical and Electronics Engineering SASTRA University, Thanjavur

FEATURE EXTRACTION. Dr. K.Vijayarekha. Associate Dean School of Electrical and Electronics Engineering SASTRA University, Thanjavur FEATURE EXTRACTION Dr. K.Vjayarekha Assocate Dean School of Electrcal and Electroncs Engneerng SASTRA Unversty, Thanjavur613 41 Jont Intatve of IITs and IISc Funded by MHRD Page 1 of 8 Table of Contents

More information

An Image Compression Algorithm based on Wavelet Transform and LZW

An Image Compression Algorithm based on Wavelet Transform and LZW An Image Compresson Algorthm based on Wavelet Transform and LZW Png Luo a, Janyong Yu b School of Chongqng Unversty of Posts and Telecommuncatons, Chongqng, 400065, Chna Abstract a cylpng@63.com, b y27769864@sna.cn

More information

Identify the Attack in Embedded Image with Steganalysis Detection Method by PSNR and RGB Intensity

Identify the Attack in Embedded Image with Steganalysis Detection Method by PSNR and RGB Intensity Internatonal Journal of Computer Systems (ISSN: 394-1065), Volume 03 Issue 07, July, 016 Avalable at http://www.jcsonlne.com/ Identfy the Attack n Embedded Image wth Steganalyss Detecton Method by PSNR

More information

Image Representation & Visualization Basic Imaging Algorithms Shape Representation and Analysis. outline

Image Representation & Visualization Basic Imaging Algorithms Shape Representation and Analysis. outline mage Vsualzaton mage Vsualzaton mage Representaton & Vsualzaton Basc magng Algorthms Shape Representaton and Analyss outlne mage Representaton & Vsualzaton Basc magng Algorthms Shape Representaton and

More information

Cluster Analysis of Electrical Behavior

Cluster Analysis of Electrical Behavior Journal of Computer and Communcatons, 205, 3, 88-93 Publshed Onlne May 205 n ScRes. http://www.scrp.org/ournal/cc http://dx.do.org/0.4236/cc.205.350 Cluster Analyss of Electrcal Behavor Ln Lu Ln Lu, School

More information

A Hybrid Digital Image Watermarking based on Discrete Wavelet Transform, Discrete Cosine Transform, and General Regression Neural Network

A Hybrid Digital Image Watermarking based on Discrete Wavelet Transform, Discrete Cosine Transform, and General Regression Neural Network A Hybrd Dgtal Image Watermarkng based on Dscrete Wavelet Transform, Dscrete Cosne Transform, and General Regresson Neural Network Ayoub Taher ; ABSTRACT In ths paper, a new hybrd dgtal watermarkng technque

More information

An Image Fusion Approach Based on Segmentation Region

An Image Fusion Approach Based on Segmentation Region Rong Wang, L-Qun Gao, Shu Yang, Yu-Hua Cha, and Yan-Chun Lu An Image Fuson Approach Based On Segmentaton Regon An Image Fuson Approach Based on Segmentaton Regon Rong Wang, L-Qun Gao, Shu Yang 3, Yu-Hua

More information

Information Hiding Watermarking Detection Technique by PSNR and RGB Intensity

Information Hiding Watermarking Detection Technique by PSNR and RGB Intensity www..org 3 Informaton Hdng Watermarkng Detecton Technque by PSNR and RGB Intensty 1 Neha Chauhan, Akhlesh A. Waoo, 3 P. S. Patheja 1 Research Scholar, BIST, Bhopal, Inda.,3 Assstant Professor, BIST, Bhopal,

More information

A Comparison between Digital Images Watermarking in Tow Different Color Spaces Using DWT2*

A Comparison between Digital Images Watermarking in Tow Different Color Spaces Using DWT2* A Comparson between Dgtal s ng n Tow Dfferent Color Spaces Usng DWT* Mehd Khall Natonal Academy of Scence of Armena Yerevan, Armena e-mal: khall.mehd@yahoo.com ABSTRACT A novel dgtal watermarkng for ownershp

More information

Shape-adaptive DCT and Its Application in Region-based Image Coding

Shape-adaptive DCT and Its Application in Region-based Image Coding Internatonal Journal of Sgnal Processng, Image Processng and Pattern Recognton, pp.99-108 http://dx.do.org/10.14257/sp.2014.7.1.10 Shape-adaptve DCT and Its Applcaton n Regon-based Image Codng Yamn Zheng,

More information

Edge Detection in Noisy Images Using the Support Vector Machines

Edge Detection in Noisy Images Using the Support Vector Machines Edge Detecton n Nosy Images Usng the Support Vector Machnes Hlaro Gómez-Moreno, Saturnno Maldonado-Bascón, Francsco López-Ferreras Sgnal Theory and Communcatons Department. Unversty of Alcalá Crta. Madrd-Barcelona

More information

Private Information Retrieval (PIR)

Private Information Retrieval (PIR) 2 Levente Buttyán Problem formulaton Alce wants to obtan nformaton from a database, but she does not want the database to learn whch nformaton she wanted e.g., Alce s an nvestor queryng a stock-market

More information

High Payload Reversible Data Hiding Scheme Using Difference Segmentation and Histogram Shifting

High Payload Reversible Data Hiding Scheme Using Difference Segmentation and Histogram Shifting JOURNAL OF ELECTRONIC SCIENCE AND TECHNOLOGY, VOL. 11, NO. 1, MARCH 2013 9 Hgh Payload Reversble Data Hdng Scheme Usng Dfference Segmentaton and Hstogram Shftng Yung-Chen Chou and Huang-Chng L Abstract

More information

A Lossless Watermarking Scheme for Halftone Image Authentication

A Lossless Watermarking Scheme for Halftone Image Authentication IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.6 No.2B, February 2006 147 A Lossless Watermarkng Scheme for Halftone Image Authentcaton Jeng-Shyang Pan, Hao Luo, and Zhe-Mng Lu,

More information

Adaptive digital watermarking of images using Genetic Algorithm

Adaptive digital watermarking of images using Genetic Algorithm Adaptve dgtal watermarkng of mages usng Genetc Algorthm Bushra Skander, Muhammad Ishtaq, M. Arfan Jaffar, Muhammad Tarq, Anwar M. Mrza Department of Computer Scence, Natonal Unversty of Computer and Emergng

More information

Related-Mode Attacks on CTR Encryption Mode

Related-Mode Attacks on CTR Encryption Mode Internatonal Journal of Network Securty, Vol.4, No.3, PP.282 287, May 2007 282 Related-Mode Attacks on CTR Encrypton Mode Dayn Wang, Dongda Ln, and Wenlng Wu (Correspondng author: Dayn Wang) Key Laboratory

More information

Robust Blind Video Watermark Algorithm in Transform Domain Combining with 3D Video Correlation

Robust Blind Video Watermark Algorithm in Transform Domain Combining with 3D Video Correlation JOURNAL OF MULTIMEDIA, VOL. 8, NO. 2, APRIL 2013 161 Robust Blnd Vdeo Watermark Algorthm n Transform Doman Combnng wth 3D Vdeo Correlaton DING Ha-yang 1,3 1. Informaton Securty Center, Bejng Unversty of

More information

SLAM Summer School 2006 Practical 2: SLAM using Monocular Vision

SLAM Summer School 2006 Practical 2: SLAM using Monocular Vision SLAM Summer School 2006 Practcal 2: SLAM usng Monocular Vson Javer Cvera, Unversty of Zaragoza Andrew J. Davson, Imperal College London J.M.M Montel, Unversty of Zaragoza. josemar@unzar.es, jcvera@unzar.es,

More information

Detection of an Object by using Principal Component Analysis

Detection of an Object by using Principal Component Analysis Detecton of an Object by usng Prncpal Component Analyss 1. G. Nagaven, 2. Dr. T. Sreenvasulu Reddy 1. M.Tech, Department of EEE, SVUCE, Trupath, Inda. 2. Assoc. Professor, Department of ECE, SVUCE, Trupath,

More information

Problem Definitions and Evaluation Criteria for Computational Expensive Optimization

Problem Definitions and Evaluation Criteria for Computational Expensive Optimization Problem efntons and Evaluaton Crtera for Computatonal Expensve Optmzaton B. Lu 1, Q. Chen and Q. Zhang 3, J. J. Lang 4, P. N. Suganthan, B. Y. Qu 6 1 epartment of Computng, Glyndwr Unversty, UK Faclty

More information

Steganography System using Slantlet Transform

Steganography System using Slantlet Transform ISSN:43-6999 Journal of Inmaton Communcaton and Intellgence Systems (JICIS) Volume Issue February 06 Steganography System usng Slantlet Transm Ryadh Bassl Abduljabbar Abstract An approach hdng nmaton has

More information

S1 Note. Basis functions.

S1 Note. Basis functions. S1 Note. Bass functons. Contents Types of bass functons...1 The Fourer bass...2 B-splne bass...3 Power and type I error rates wth dfferent numbers of bass functons...4 Table S1. Smulaton results of type

More information

A Fast Visual Tracking Algorithm Based on Circle Pixels Matching

A Fast Visual Tracking Algorithm Based on Circle Pixels Matching A Fast Vsual Trackng Algorthm Based on Crcle Pxels Matchng Zhqang Hou hou_zhq@sohu.com Chongzhao Han czhan@mal.xjtu.edu.cn Ln Zheng Abstract: A fast vsual trackng algorthm based on crcle pxels matchng

More information

TN348: Openlab Module - Colocalization

TN348: Openlab Module - Colocalization TN348: Openlab Module - Colocalzaton Topc The Colocalzaton module provdes the faclty to vsualze and quantfy colocalzaton between pars of mages. The Colocalzaton wndow contans a prevew of the two mages

More information

Research and Application of Fingerprint Recognition Based on MATLAB

Research and Application of Fingerprint Recognition Based on MATLAB Send Orders for Reprnts to reprnts@benthamscence.ae The Open Automaton and Control Systems Journal, 205, 7, 07-07 Open Access Research and Applcaton of Fngerprnt Recognton Based on MATLAB Nng Lu* Department

More information

IMPLEMENTATION OF QIM BASED AUDIO WATERMARKING USING HYBRID TRANSFORM OF SWT-DCT-SVD METHODS OPTIMIZED WITH GENETIC ALORITHM

IMPLEMENTATION OF QIM BASED AUDIO WATERMARKING USING HYBRID TRANSFORM OF SWT-DCT-SVD METHODS OPTIMIZED WITH GENETIC ALORITHM IMPLEMENTATION OF QIM BASED AUDIO WATERMARKING USING HYBRID TRANSFORM OF SWT-DCT-SVD METHODS OPTIMIZED WITH GENETIC ALORITHM Ryan Amnullah 1, Gelar Budman 2, Irma Saftr 3 1, 2, 3 FakultasTeknk Elektro,

More information

Performance Analysis of Data Hiding in MPEG-4 AAC Audio *

Performance Analysis of Data Hiding in MPEG-4 AAC Audio * TSINGHUA SCIENCE AND TECHNOLOGY ISSNll1007-0214ll07/21llpp55-61 Volume 14, Number 1, February 2009 Performance Analyss of Data Hdng n MPEG-4 AAC Audo * XU Shuzheng ( ) **, ZHANG Peng ( ), WANG Pengjun

More information

A PATTERN RECOGNITION APPROACH TO IMAGE SEGMENTATION

A PATTERN RECOGNITION APPROACH TO IMAGE SEGMENTATION 1 THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Seres A, OF THE ROMANIAN ACADEMY Volume 4, Number 2/2003, pp.000-000 A PATTERN RECOGNITION APPROACH TO IMAGE SEGMENTATION Tudor BARBU Insttute

More information

Lecture 5: Multilayer Perceptrons

Lecture 5: Multilayer Perceptrons Lecture 5: Multlayer Perceptrons Roger Grosse 1 Introducton So far, we ve only talked about lnear models: lnear regresson and lnear bnary classfers. We noted that there are functons that can t be represented

More information

Research of Multiple Text Watermarks Technique in Electric Power System Texts

Research of Multiple Text Watermarks Technique in Electric Power System Texts Sensors & Transducers 203 by IFSA http://www.sensorsportal.com Research of Multple Text atermarks Technque n Electrc Power System Texts Xao-X XING, Qng CHEN, 2 Lan-X FU School of Optcal-Electrcal and Computer

More information

A Secured Method for Image Steganography Based On Pixel Values

A Secured Method for Image Steganography Based On Pixel Values A Secured Method for Image Steganography Based On Pxel Values Tarun Gulat #, Sanskrt Gupta * # Assocate Professor, Electroncs and Communcaton Engneerng Department, MMEC, M.M.U., Mullana, Ambala, Haryana,

More information

A Robust Webpage Information Hiding Method Based on the Slash of Tag

A Robust Webpage Information Hiding Method Based on the Slash of Tag Advanced Engneerng Forum Onlne: 2012-09-26 ISSN: 2234-991X, Vols. 6-7, pp 361-366 do:10.4028/www.scentfc.net/aef.6-7.361 2012 Trans Tech Publcatons, Swtzerland A Robust Webpage Informaton Hdng Method Based

More information

Learning the Kernel Parameters in Kernel Minimum Distance Classifier

Learning the Kernel Parameters in Kernel Minimum Distance Classifier Learnng the Kernel Parameters n Kernel Mnmum Dstance Classfer Daoqang Zhang 1,, Songcan Chen and Zh-Hua Zhou 1* 1 Natonal Laboratory for Novel Software Technology Nanjng Unversty, Nanjng 193, Chna Department

More information

Accounting for the Use of Different Length Scale Factors in x, y and z Directions

Accounting for the Use of Different Length Scale Factors in x, y and z Directions 1 Accountng for the Use of Dfferent Length Scale Factors n x, y and z Drectons Taha Soch (taha.soch@kcl.ac.uk) Imagng Scences & Bomedcal Engneerng, Kng s College London, The Rayne Insttute, St Thomas Hosptal,

More information

High-Boost Mesh Filtering for 3-D Shape Enhancement

High-Boost Mesh Filtering for 3-D Shape Enhancement Hgh-Boost Mesh Flterng for 3-D Shape Enhancement Hrokazu Yagou Λ Alexander Belyaev y Damng We z Λ y z ; ; Shape Modelng Laboratory, Unversty of Azu, Azu-Wakamatsu 965-8580 Japan y Computer Graphcs Group,

More information

Proper Choice of Data Used for the Estimation of Datum Transformation Parameters

Proper Choice of Data Used for the Estimation of Datum Transformation Parameters Proper Choce of Data Used for the Estmaton of Datum Transformaton Parameters Hakan S. KUTOGLU, Turkey Key words: Coordnate systems; transformaton; estmaton, relablty. SUMMARY Advances n technologes and

More information

A Background Subtraction for a Vision-based User Interface *

A Background Subtraction for a Vision-based User Interface * A Background Subtracton for a Vson-based User Interface * Dongpyo Hong and Woontack Woo KJIST U-VR Lab. {dhon wwoo}@kjst.ac.kr Abstract In ths paper, we propose a robust and effcent background subtracton

More information

An efficient method to build panoramic image mosaics

An efficient method to build panoramic image mosaics An effcent method to buld panoramc mage mosacs Pattern Recognton Letters vol. 4 003 Dae-Hyun Km Yong-In Yoon Jong-Soo Cho School of Electrcal Engneerng and Computer Scence Kyungpook Natonal Unv. Abstract

More information

Fuzzy Filtering Algorithms for Image Processing: Performance Evaluation of Various Approaches

Fuzzy Filtering Algorithms for Image Processing: Performance Evaluation of Various Approaches Proceedngs of the Internatonal Conference on Cognton and Recognton Fuzzy Flterng Algorthms for Image Processng: Performance Evaluaton of Varous Approaches Rajoo Pandey and Umesh Ghanekar Department of

More information

A New Feature of Uniformity of Image Texture Directions Coinciding with the Human Eyes Perception 1

A New Feature of Uniformity of Image Texture Directions Coinciding with the Human Eyes Perception 1 A New Feature of Unformty of Image Texture Drectons Concdng wth the Human Eyes Percepton Xng-Jan He, De-Shuang Huang, Yue Zhang, Tat-Mng Lo 2, and Mchael R. Lyu 3 Intellgent Computng Lab, Insttute of Intellgent

More information

Local Quaternary Patterns and Feature Local Quaternary Patterns

Local Quaternary Patterns and Feature Local Quaternary Patterns Local Quaternary Patterns and Feature Local Quaternary Patterns Jayu Gu and Chengjun Lu The Department of Computer Scence, New Jersey Insttute of Technology, Newark, NJ 0102, USA Abstract - Ths paper presents

More information

Skew Angle Estimation and Correction of Hand Written, Textual and Large areas of Non-Textual Document Images: A Novel Approach

Skew Angle Estimation and Correction of Hand Written, Textual and Large areas of Non-Textual Document Images: A Novel Approach Angle Estmaton and Correcton of Hand Wrtten, Textual and Large areas of Non-Textual Document Images: A Novel Approach D.R.Ramesh Babu Pyush M Kumat Mahesh D Dhannawat PES Insttute of Technology Research

More information

A Modified Median Filter for the Removal of Impulse Noise Based on the Support Vector Machines

A Modified Median Filter for the Removal of Impulse Noise Based on the Support Vector Machines A Modfed Medan Flter for the Removal of Impulse Nose Based on the Support Vector Machnes H. GOMEZ-MORENO, S. MALDONADO-BASCON, F. LOPEZ-FERRERAS, M. UTRILLA- MANSO AND P. GIL-JIMENEZ Departamento de Teoría

More information

Enhanced AMBTC for Image Compression using Block Classification and Interpolation

Enhanced AMBTC for Image Compression using Block Classification and Interpolation Internatonal Journal of Computer Applcatons (0975 8887) Volume 5 No.0, August 0 Enhanced AMBTC for Image Compresson usng Block Classfcaton and Interpolaton S. Vmala Dept. of Comp. Scence Mother Teresa

More information

A Clustering Algorithm for Key Frame Extraction Based on Density Peak

A Clustering Algorithm for Key Frame Extraction Based on Density Peak Journal of Computer and Communcatons, 2018, 6, 118-128 http://www.scrp.org/ournal/cc ISSN Onlne: 2327-5227 ISSN Prnt: 2327-5219 A Clusterng Algorthm for Key Frame Extracton Based on Densty Peak Hong Zhao

More information

Subspace clustering. Clustering. Fundamental to all clustering techniques is the choice of distance measure between data points;

Subspace clustering. Clustering. Fundamental to all clustering techniques is the choice of distance measure between data points; Subspace clusterng Clusterng Fundamental to all clusterng technques s the choce of dstance measure between data ponts; D q ( ) ( ) 2 x x = x x, j k = 1 k jk Squared Eucldean dstance Assumpton: All features

More information

Grading Image Retrieval Based on DCT and DWT Compressed Domains Using Low-Level Features

Grading Image Retrieval Based on DCT and DWT Compressed Domains Using Low-Level Features Journal of Communcatons Vol. 0 No. January 0 Gradng Image Retreval Based on DCT and DWT Compressed Domans Usng Low-Level Features Chengyou Wang Xnyue Zhang Rongyang Shan and Xao Zhou School of echancal

More information

Load Balancing for Hex-Cell Interconnection Network

Load Balancing for Hex-Cell Interconnection Network Int. J. Communcatons, Network and System Scences,,, - Publshed Onlne Aprl n ScRes. http://www.scrp.org/journal/jcns http://dx.do.org/./jcns.. Load Balancng for Hex-Cell Interconnecton Network Saher Manaseer,

More information

Brushlet Features for Texture Image Retrieval

Brushlet Features for Texture Image Retrieval DICTA00: Dgtal Image Computng Technques and Applcatons, 1 January 00, Melbourne, Australa 1 Brushlet Features for Texture Image Retreval Chbao Chen and Kap Luk Chan Informaton System Research Lab, School

More information

Lecture 13: High-dimensional Images

Lecture 13: High-dimensional Images Lec : Hgh-dmensonal Images Grayscale Images Lecture : Hgh-dmensonal Images Math 90 Prof. Todd Wttman The Ctadel A grayscale mage s an nteger-valued D matrx. An 8-bt mage takes on values between 0 and 55.

More information

The Research of Ellipse Parameter Fitting Algorithm of Ultrasonic Imaging Logging in the Casing Hole

The Research of Ellipse Parameter Fitting Algorithm of Ultrasonic Imaging Logging in the Casing Hole Appled Mathematcs, 04, 5, 37-3 Publshed Onlne May 04 n ScRes. http://www.scrp.org/journal/am http://dx.do.org/0.436/am.04.584 The Research of Ellpse Parameter Fttng Algorthm of Ultrasonc Imagng Loggng

More information

COMPLEX WAVELET TRANSFORM-BASED COLOR INDEXING FOR CONTENT-BASED IMAGE RETRIEVAL

COMPLEX WAVELET TRANSFORM-BASED COLOR INDEXING FOR CONTENT-BASED IMAGE RETRIEVAL COMPLEX WAVELET TRANSFORM-BASED COLOR INDEXING FOR CONTENT-BASED IMAGE RETRIEVAL Nader Safavan and Shohreh Kasae Department of Computer Engneerng Sharf Unversty of Technology Tehran, Iran skasae@sharf.edu

More information

Shape Representation Robust to the Sketching Order Using Distance Map and Direction Histogram

Shape Representation Robust to the Sketching Order Using Distance Map and Direction Histogram Shape Representaton Robust to the Sketchng Order Usng Dstance Map and Drecton Hstogram Department of Computer Scence Yonse Unversty Kwon Yun CONTENTS Revew Topc Proposed Method System Overvew Sketch Normalzaton

More information

Parallelism for Nested Loops with Non-uniform and Flow Dependences

Parallelism for Nested Loops with Non-uniform and Flow Dependences Parallelsm for Nested Loops wth Non-unform and Flow Dependences Sam-Jn Jeong Dept. of Informaton & Communcaton Engneerng, Cheonan Unversty, 5, Anseo-dong, Cheonan, Chungnam, 330-80, Korea. seong@cheonan.ac.kr

More information

Face Recognition University at Buffalo CSE666 Lecture Slides Resources:

Face Recognition University at Buffalo CSE666 Lecture Slides Resources: Face Recognton Unversty at Buffalo CSE666 Lecture Sldes Resources: http://www.face-rec.org/algorthms/ Overvew of face recognton algorthms Correlaton - Pxel based correspondence between two face mages Structural

More information

Data Hiding and Image Authentication for Color-Palette Images

Data Hiding and Image Authentication for Color-Palette Images Data Hdng and Image Authentcaton for Color-Palette Images Chh-Yang Yn ( 殷志揚 ) and Wen-Hsang Tsa ( 蔡文祥 ) Department of Computer & Informaton Scence Natonal Chao Tung Unversty 00 Ta Hsueh Rd., Hsnchu, Tawan

More information

Corner-Based Image Alignment using Pyramid Structure with Gradient Vector Similarity

Corner-Based Image Alignment using Pyramid Structure with Gradient Vector Similarity Journal of Sgnal and Informaton Processng, 013, 4, 114-119 do:10.436/jsp.013.43b00 Publshed Onlne August 013 (http://www.scrp.org/journal/jsp) Corner-Based Image Algnment usng Pyramd Structure wth Gradent

More information

MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION

MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION Paulo Quntlano 1 & Antono Santa-Rosa 1 Federal Polce Department, Brasla, Brazl. E-mals: quntlano.pqs@dpf.gov.br and

More information

User Authentication Based On Behavioral Mouse Dynamics Biometrics

User Authentication Based On Behavioral Mouse Dynamics Biometrics User Authentcaton Based On Behavoral Mouse Dynamcs Bometrcs Chee-Hyung Yoon Danel Donghyun Km Department of Computer Scence Department of Computer Scence Stanford Unversty Stanford Unversty Stanford, CA

More information

Tsinghua University at TAC 2009: Summarizing Multi-documents by Information Distance

Tsinghua University at TAC 2009: Summarizing Multi-documents by Information Distance Tsnghua Unversty at TAC 2009: Summarzng Mult-documents by Informaton Dstance Chong Long, Mnle Huang, Xaoyan Zhu State Key Laboratory of Intellgent Technology and Systems, Tsnghua Natonal Laboratory for

More information

PCA Based Gait Segmentation

PCA Based Gait Segmentation Honggu L, Cupng Sh & Xngguo L PCA Based Gat Segmentaton PCA Based Gat Segmentaton Honggu L, Cupng Sh, and Xngguo L 2 Electronc Department, Physcs College, Yangzhou Unversty, 225002 Yangzhou, Chna 2 Department

More information

Using Fuzzy Logic to Enhance the Large Size Remote Sensing Images

Using Fuzzy Logic to Enhance the Large Size Remote Sensing Images Internatonal Journal of Informaton and Electroncs Engneerng Vol. 5 No. 6 November 015 Usng Fuzzy Logc to Enhance the Large Sze Remote Sensng Images Trung Nguyen Tu Huy Ngo Hoang and Thoa Vu Van Abstract

More information

X- Chart Using ANOM Approach

X- Chart Using ANOM Approach ISSN 1684-8403 Journal of Statstcs Volume 17, 010, pp. 3-3 Abstract X- Chart Usng ANOM Approach Gullapall Chakravarth 1 and Chaluvad Venkateswara Rao Control lmts for ndvdual measurements (X) chart are

More information

Classifier Selection Based on Data Complexity Measures *

Classifier Selection Based on Data Complexity Measures * Classfer Selecton Based on Data Complexty Measures * Edth Hernández-Reyes, J.A. Carrasco-Ochoa, and J.Fco. Martínez-Trndad Natonal Insttute for Astrophyscs, Optcs and Electroncs, Lus Enrque Erro No.1 Sta.

More information

A Novel Adaptive Descriptor Algorithm for Ternary Pattern Textures

A Novel Adaptive Descriptor Algorithm for Ternary Pattern Textures A Novel Adaptve Descrptor Algorthm for Ternary Pattern Textures Fahuan Hu 1,2, Guopng Lu 1 *, Zengwen Dong 1 1.School of Mechancal & Electrcal Engneerng, Nanchang Unversty, Nanchang, 330031, Chna; 2. School

More information

Face Detection with Deep Learning

Face Detection with Deep Learning Face Detecton wth Deep Learnng Yu Shen Yus122@ucsd.edu A13227146 Kuan-We Chen kuc010@ucsd.edu A99045121 Yzhou Hao y3hao@ucsd.edu A98017773 Mn Hsuan Wu mhwu@ucsd.edu A92424998 Abstract The project here

More information

High resolution 3D Tau-p transform by matching pursuit Weiping Cao* and Warren S. Ross, Shearwater GeoServices

High resolution 3D Tau-p transform by matching pursuit Weiping Cao* and Warren S. Ross, Shearwater GeoServices Hgh resoluton 3D Tau-p transform by matchng pursut Wepng Cao* and Warren S. Ross, Shearwater GeoServces Summary The 3D Tau-p transform s of vtal sgnfcance for processng sesmc data acqured wth modern wde

More information

Assignment # 2. Farrukh Jabeen Algorithms 510 Assignment #2 Due Date: June 15, 2009.

Assignment # 2. Farrukh Jabeen Algorithms 510 Assignment #2 Due Date: June 15, 2009. Farrukh Jabeen Algorthms 51 Assgnment #2 Due Date: June 15, 29. Assgnment # 2 Chapter 3 Dscrete Fourer Transforms Implement the FFT for the DFT. Descrbed n sectons 3.1 and 3.2. Delverables: 1. Concse descrpton

More information

An Application of the Dulmage-Mendelsohn Decomposition to Sparse Null Space Bases of Full Row Rank Matrices

An Application of the Dulmage-Mendelsohn Decomposition to Sparse Null Space Bases of Full Row Rank Matrices Internatonal Mathematcal Forum, Vol 7, 2012, no 52, 2549-2554 An Applcaton of the Dulmage-Mendelsohn Decomposton to Sparse Null Space Bases of Full Row Rank Matrces Mostafa Khorramzadeh Department of Mathematcal

More information

Feature Reduction and Selection

Feature Reduction and Selection Feature Reducton and Selecton Dr. Shuang LIANG School of Software Engneerng TongJ Unversty Fall, 2012 Today s Topcs Introducton Problems of Dmensonalty Feature Reducton Statstc methods Prncpal Components

More information

Research Article High Capacity Reversible Watermarking for Audio by Histogram Shifting and Predicted Error Expansion

Research Article High Capacity Reversible Watermarking for Audio by Histogram Shifting and Predicted Error Expansion e Scentfc World Journal, Artcle ID 656251, 7 pages http://dx.do.org/1.1155/214/656251 Research Artcle Hgh Capacty Reversble Watermarkng for Audo by Hstogram Shftng and Predcted Error Expanson Fe Wang,

More information

Improved H.264 Rate Control by Enhanced MAD-Based Frame Complexity Prediction

Improved H.264 Rate Control by Enhanced MAD-Based Frame Complexity Prediction Journal of Vsual Communcaton and Image Representaton (Specal Issue on Emergng H.64/AVC Vdeo Codng Standard), Elsever Scence, May 005 Improved H.64 Rate Control by Enhanced -Based Frame Complexty Predcton

More information

Constructing Minimum Connected Dominating Set: Algorithmic approach

Constructing Minimum Connected Dominating Set: Algorithmic approach Constructng Mnmum Connected Domnatng Set: Algorthmc approach G.N. Puroht and Usha Sharma Centre for Mathematcal Scences, Banasthal Unversty, Rajasthan 304022 usha.sharma94@yahoo.com Abstract: Connected

More information

Novel Pattern-based Fingerprint Recognition Technique Using 2D Wavelet Decomposition

Novel Pattern-based Fingerprint Recognition Technique Using 2D Wavelet Decomposition Mathematcal Methods for Informaton Scence and Economcs Novel Pattern-based Fngerprnt Recognton Technque Usng D Wavelet Decomposton TUDOR BARBU Insttute of Computer Scence of the Romanan Academy T. Codrescu,,

More information

Modular PCA Face Recognition Based on Weighted Average

Modular PCA Face Recognition Based on Weighted Average odern Appled Scence odular PCA Face Recognton Based on Weghted Average Chengmao Han (Correspondng author) Department of athematcs, Lny Normal Unversty Lny 76005, Chna E-mal: hanchengmao@163.com Abstract

More information

An Improved Image Segmentation Algorithm Based on the Otsu Method

An Improved Image Segmentation Algorithm Based on the Otsu Method 3th ACIS Internatonal Conference on Software Engneerng, Artfcal Intellgence, Networkng arallel/dstrbuted Computng An Improved Image Segmentaton Algorthm Based on the Otsu Method Mengxng Huang, enjao Yu,

More information

Available online at Available online at Advanced in Control Engineering and Information Science

Available online at   Available online at   Advanced in Control Engineering and Information Science Avalable onlne at wwwscencedrectcom Avalable onlne at wwwscencedrectcom Proceda Proceda Engneerng Engneerng 00 (2011) 15000 000 (2011) 1642 1646 Proceda Engneerng wwwelsevercom/locate/proceda Advanced

More information

Using Counter-propagation Neural Network for Digital Audio Watermarking

Using Counter-propagation Neural Network for Digital Audio Watermarking Usng Counter-propagaton Neural Network for Dgtal Audo Watermarkng Chuan-Yu Chang and Wen-Chh Shen Graduate School of Computer Scence and Informaton Engneerng Natonal Yunln Unversty of Scence & Technology

More information

CHAPTER 3 ENCODING VIDEO SEQUENCES IN FRACTAL BASED COMPRESSION. Day by day, the demands for higher and faster technologies are rapidly

CHAPTER 3 ENCODING VIDEO SEQUENCES IN FRACTAL BASED COMPRESSION. Day by day, the demands for higher and faster technologies are rapidly 65 CHAPTER 3 ENCODING VIDEO SEQUENCES IN FRACTAL BASED COMPRESSION 3.1 Introducton Day by day, the demands for hgher and faster technologes are rapdly ncreasng. Although the technologes avalable now are

More information

Comparison Study of Textural Descriptors for Training Neural Network Classifiers

Comparison Study of Textural Descriptors for Training Neural Network Classifiers Comparson Study of Textural Descrptors for Tranng Neural Network Classfers G.D. MAGOULAS (1) S.A. KARKANIS (1) D.A. KARRAS () and M.N. VRAHATIS (3) (1) Department of Informatcs Unversty of Athens GR-157.84

More information

Efficient Content Representation in MPEG Video Databases

Efficient Content Representation in MPEG Video Databases Effcent Content Representaton n MPEG Vdeo Databases Yanns S. Avrths, Nkolaos D. Doulams, Anastasos D. Doulams and Stefanos D. Kollas Department of Electrcal and Computer Engneerng Natonal Techncal Unversty

More information

Robust and Reversible Relational Database Watermarking Algorithm Based on Clustering and Polar Angle Expansion

Robust and Reversible Relational Database Watermarking Algorithm Based on Clustering and Polar Angle Expansion Robust and Reversble Relatonal Database Watermarkng Algorthm Based on Clusterng and Polar Angle Expanson Zhyong L, Junmn Lu and Wecheng Tao College of Informaton Scence and Engneerng, Hunan Unversty, Changsha,

More information

Smoothing Spline ANOVA for variable screening

Smoothing Spline ANOVA for variable screening Smoothng Splne ANOVA for varable screenng a useful tool for metamodels tranng and mult-objectve optmzaton L. Rcco, E. Rgon, A. Turco Outlne RSM Introducton Possble couplng Test case MOO MOO wth Game Theory

More information

NAG Fortran Library Chapter Introduction. G10 Smoothing in Statistics

NAG Fortran Library Chapter Introduction. G10 Smoothing in Statistics Introducton G10 NAG Fortran Lbrary Chapter Introducton G10 Smoothng n Statstcs Contents 1 Scope of the Chapter... 2 2 Background to the Problems... 2 2.1 Smoothng Methods... 2 2.2 Smoothng Splnes and Regresson

More information

R s s f. m y s. SPH3UW Unit 7.3 Spherical Concave Mirrors Page 1 of 12. Notes

R s s f. m y s. SPH3UW Unit 7.3 Spherical Concave Mirrors Page 1 of 12. Notes SPH3UW Unt 7.3 Sphercal Concave Mrrors Page 1 of 1 Notes Physcs Tool box Concave Mrror If the reflectng surface takes place on the nner surface of the sphercal shape so that the centre of the mrror bulges

More information