A robust image watermarking using DWT, SVD and Torus automorphism

Abstract

Digital watermarking is a process to provide authenticity by hiding a data into an image or audio or document. Hiding of data in an image can be done in frequency domain. Since frequency domain based techniques are more robust against signal processing and geometric attacks than time domain techniques. One such frequency domain technique is developed based on combination of discrete wavelet transform, singular value decomposition and torus automorphism and is presented in this paper. This results prove that this method robust against different attacks and has good PSNR ratio.

Cancelable Multimodal Biometrics Based on Chaotic Maps

“…However, designing a cancelable technique for an unordered set of features (i.e., minutia points) is still challenging. To overcome this issue, we suggest transforming the minutia points using Torus Automorphism, which is a type of spatial transformation that can be applied to plane region to increase chaos [19,20]. Torus Automorphism has been proven to be beneficial in the context of the encryption of images.…”

“…• First, Torus Automorphism is utilized to generate a chaotic sequence using the following definition [19,20]:…”

“…It uses a 2 × 2 matrix with fixed elements (a, b and N) to transform a point (x, y) to a new position (x , y ) in a space domain or to transform a state S t to S t+1 . In the context of Torus Automorphism, there is a value R that is referred to the recurrence time such that X 0 = X R [19,20]. Therefore, at time t R , the value of a state returns to the initial value at time t 0 .…”