| Image transform is an important tool in image processing and machine vision research.Because of its strong robustness,strong decorrelation,and fast calculation,it has become more and more widely used in image processing.With the study of “fractional order” theory by many researchers,many image transforms have been generalized to fractional domain and introduced into the fields of image encryption and digital watermarking,resulting in better results than traditional image transforms.Discrete Tchebichef Transform(DTT),as a new excellent image transform technique proposed in recent years,whose investigations are still confined at the order of integers,which makes the study of the “spectrum” space of DTT not complete.What'more,the characteristics of DTT and its application in the field of image security need to be further studied.Based on this,this thesis mainly made some research work:1.This thesis deeply studies the characteristics of the core matrix of the DTT and the distribution of eigenvalues.A mathematical model of the Fractional Discrete Tchebichef Transform(FrDTT)is established using the eigendecomposition method by preserving the orthogonal basis of the eigenvectors and modifying the order of the eigenvalues.At the same time,Multiple-Parameter Fractional Discrete Tchebichef Transform(MFrDTT)is further obtained by extending the single fractional order to the fractional order vector.In addition,this thesis discusses the properties of the established fractional transform model,which promotes the further development of fractional theory.2.An image encryption method based on MFrDTT and generating sequence(GS)is proposed.The use of the fidelity and strong de-correlation of the fractional-order Tchebichef transform maks the encryption system meet real-value transmission and the encrypted images are confusing enough.The randomly generated row and column fractional vector and the generating sequence generated by the chaotic map are used as the keys to encrypt the images,which greatly expands the key space and has a good key sensitivity.Experimental results show that the method has sufficient security and good robustness.3.A digital watermarking algorithm based on FrDTT is proposed.First,the Arnold transform is used to scramble the watermark,then the watermark is embedded by the dither modulation method.Finally,the minimum distance decoder is used to extract the watermark.Experimental results show that by optimizing the fractional orders,the watermarking algorithm not only obtains better watermark imperceptibility than many classical watermarking algorithms,but also has better robustness under various image attacks.At the same time,the introduction of fractional order can be used as the keys of the watermarking algorithm together with the embedding positions,which further improves the security of the watermarking algorithm. |
