Image forgery is a crucial part of the transmission of misinformation,which may be illegal in some jurisdictions.The powerful image editing software has made it nearly impossible to detect altered images with the nake...Image forgery is a crucial part of the transmission of misinformation,which may be illegal in some jurisdictions.The powerful image editing software has made it nearly impossible to detect altered images with the naked eye.Images must be protected against attempts to manipulate them.Image authentication methods have gained popularity because of their use in multimedia and multimedia networking applications.Attempts were made to address the consequences of image forgeries by creating algorithms for identifying altered images.Because image tampering detection targets processing techniques such as object removal or addition,identifying altered images remains a major challenge in research.In this study,a novel image texture feature extraction model based on the generalized k-symbolWhittaker function(GKSWF)is proposed for better image forgery detection.The proposed method is divided into two stages.The first stage involves feature extraction using the proposed GKSWF model,followed by classification using the“support vector machine”(SVM)to distinguish between authentic and manipulated images.Each extracted feature from an input image is saved in the features database for use in image splicing detection.The proposed GKSWF as a feature extraction model is intended to extract clues of tampering texture details based on the probability of image pixel.When tested on publicly available image dataset“CASIA”v2.0(ChineseAcademy of Sciences,Institute of Automation),the proposed model had a 98.60%accuracy rate on the YCbCr(luminance(Y),chroma blue(Cb)and chroma red(Cr))color spaces in image block size of 8×8 pixels.The proposed image authentication model shows great accuracy with a relatively modest dimension feature size,supporting the benefit of utilizing the k-symbol Whittaker function in image authentication algorithms.展开更多
This paper deals with an integral transformation involving Whittaker function Mk,m（X） into a multiple hypergeometric series of Lauricella function FA（n） of n variables. A number of known and new transformation and...This paper deals with an integral transformation involving Whittaker function Mk,m（X） into a multiple hypergeometric series of Lauricella function FA（n） of n variables. A number of known and new transformation and reduction formulae for a hypergeometric function 2F1, Appell function F2, Lauricella function FA（3） and a hypergeometric function of four variables Fp（4） are derived as special cases.展开更多
We solve the one-dimensionai time-independent Schrodinger equation in the presence of the modified Cusp potential and report the solutions in terms of the Whittaker functions. We obtain the reflection and transmission...We solve the one-dimensionai time-independent Schrodinger equation in the presence of the modified Cusp potential and report the solutions in terms of the Whittaker functions. We obtain the reflection and transmission coefficients as well as the bound-state solutions in terms of the Whittaker functions. We comment on the solutions and discuss them in terms of the engaged parameters.展开更多
文摘Image forgery is a crucial part of the transmission of misinformation,which may be illegal in some jurisdictions.The powerful image editing software has made it nearly impossible to detect altered images with the naked eye.Images must be protected against attempts to manipulate them.Image authentication methods have gained popularity because of their use in multimedia and multimedia networking applications.Attempts were made to address the consequences of image forgeries by creating algorithms for identifying altered images.Because image tampering detection targets processing techniques such as object removal or addition,identifying altered images remains a major challenge in research.In this study,a novel image texture feature extraction model based on the generalized k-symbolWhittaker function(GKSWF)is proposed for better image forgery detection.The proposed method is divided into two stages.The first stage involves feature extraction using the proposed GKSWF model,followed by classification using the“support vector machine”(SVM)to distinguish between authentic and manipulated images.Each extracted feature from an input image is saved in the features database for use in image splicing detection.The proposed GKSWF as a feature extraction model is intended to extract clues of tampering texture details based on the probability of image pixel.When tested on publicly available image dataset“CASIA”v2.0(ChineseAcademy of Sciences,Institute of Automation),the proposed model had a 98.60%accuracy rate on the YCbCr(luminance(Y),chroma blue(Cb)and chroma red(Cr))color spaces in image block size of 8×8 pixels.The proposed image authentication model shows great accuracy with a relatively modest dimension feature size,supporting the benefit of utilizing the k-symbol Whittaker function in image authentication algorithms.
文摘This paper deals with an integral transformation involving Whittaker function Mk,m（X） into a multiple hypergeometric series of Lauricella function FA（n） of n variables. A number of known and new transformation and reduction formulae for a hypergeometric function 2F1, Appell function F2, Lauricella function FA（3） and a hypergeometric function of four variables Fp（4） are derived as special cases.
文摘We solve the one-dimensionai time-independent Schrodinger equation in the presence of the modified Cusp potential and report the solutions in terms of the Whittaker functions. We obtain the reflection and transmission coefficients as well as the bound-state solutions in terms of the Whittaker functions. We comment on the solutions and discuss them in terms of the engaged parameters.
