Volume 60, Nº 4 (2017)

In this paper a new invisible watermarking algorithm using vector quantization (VQ) approach for image content authentication application is proposed. At the first stage, a robust verification watermark is embedded using properties of indices of vector quantized image using key based approach. At the second stage, the semi-fragile watermark is embedded by using modified index key based (MIKB) method. Robust watermark andVQenhance the security of the system by providing its double protection. The semi-fragile watermark is utilized for the authentication of the received image. Blind extraction of the watermark is performed independently in two successive steps i.e. in the order of embedding. Further, in oder to classify quantitatively an incidental or intentional attack, which at present is not being followed, a quantitative threshold approach using pixel neighborhood clustering is suggested. The existing methods employ the qualitative approach of identifying incidental or intentional attacks. Imperceptibility of watermarked image is 41 dB on the average, and it is also possible to detect and locate tamper with very high sensitivity. The present scheme is compared with the existing algorithms. The performance of proposed algorithm has been tested on various practical images. It outperforms in distinguishing malicious tampering from content preserving changes and the tampered regions are accurately localized.

In this paper it is obtained the distribution of absolute maximum of mean square differentiable stationery Gaussian process by means of integration of the results of the second Kolmogorov equation solution. It is shown the way simplifying integration and its interrelation to integro-differential equation obtained before. The second Kolmogorov equation is solved first for the boundary conditions allowing to obtain the results in form of infinite series with coefficients obtained by means of solution of Sturm–Liouville problem and reducing to the simple expression. It is analyzed the correlation of obtained results with known before. It is carried out a comparative analysis of correlation functions and expressions for distribution of absolute maximums of mean square differentiable and single-component Markov processes. In spite of correlation function of single-component Markov process can be considered as limit expression for correlation function of mean square differentiable process, the expression for distribution of their absolute maximums are essentially different. It shows practical meaning of the results since real processes in radio engineering systems can be mean square differentiable only.