Rst invariance of image watermarking algorithms and the framework of mathematical analysis

Abstract

In recent years, watermarking algorithms robust to the geometrical distortions have been the focus of research. Most of the proposed geometrical-transform-invariant algorithms are RST (Rotation, Scaling and Translation) invariant due to the fact that changing the image size or its orientation, even by slight amount, could dramatically deteriorate the performance of the watermark detection. Most of the existing RST invariant watermarking algorithms can be classified into several categories: RST invariant domain, salient feature, template, image decomposition and stochastic analysis based algorithms. An in-depth theoretical analysis of these algorithms is given in this thesis. With the detailed experimental results, the advantages and disadvantages of each algorithm are presented. This provides a solid basis for the further research in this field. Moreover, the clarification of the current algorithms' limitation can lead to new ideas of designing better algorithms. Based on the detailed analysis of the existing RST invariant watermarking algorithms, a novel feature-based RST invariant watermarking algorithm is proposed in this thesis. And, a framework is established to mathematically guide the watermark embedding process and analyze the performance of the watermarking algorithm like watermark embedding strength. Since it is difficult to model the entire image using a single mathematical model, the cover image is segmented into several homogeneous regions using the maximum a posteriority probability (MAP) segmentation. Each segmented-region of the image is modelled using a generalized Gaussian distribution model. Then the image can be approximated using a Gaussian mixture distribution model. And some rotation-invariant features are extracted from the cover image using the SIFT (Scale Invariant Feature) detection algorithm Image normalization is used to achieve scaling and translation invariance. Then, the user-defined disk regions centered at the well-selected feature points will be used for watermark embedding and extraction. In the watermark embedding process, the watermark is approximated as additive white Gaussian noise. And NVF (Noise Visibility Function) is used to adaptively adjust the watermark embedding strength. With the establishments of the stochastic models for the cover image and the watermark, it is easy to clarify the relation between the fidelity of the watermarked image and the embedding capacity in a more accurate mathematical way instead of the currently used empirical way. In the watermark extraction process, the linear correlation is used to detect the existence of the watermark. The experimental results demonstrate the proposed scheme is robust to RST transformation, noise pollution and JPEG compression. The established mathematical model for images provides a good analysis tool for watermarking algorithms, and can be further exploited and refined to give a better understanding of the various aspects of watermarking algorithms.