Abstract

There are millions of people using social networking sites like Facebook, Google+, and Youtube every single day across the entire world for sharing photos and other digital media. Unfortunately, sometimes people publish content that does not belong to them. As a result, there is an increasing demand for quality software capable of providing maximum protection for copyrighted material. In addition, confidential content such as medical images and patient records require high level of security so that they can be protected from unintended disclosure, when transferred over the Internet. On the other hand, decreasing the size of an image without significant loss in quality is always highly desirable. Hence, the need for efficient compression algorithms.

This thesis introduces a robust method for image compression in the shearlet domain. Motivated by the outperformance of the Discrete Shearlet Transform (DST) compared to the Discrete Wavelet Transform (DWT) in encoding the directional information in images, we propose a DST-based compression algorithm that provides not only a better quality in terms of image approximation and compression ratio, but also increases the security of images via the Advanced Encryption Standard. Experimental results on a slew of medical images illustrate an improved performance in image quality of the proposed approximation approach in comparison to DWT, and also demonstrate its robustness against a variety of tests, including randomness, entropy, key sensitivity, and input sensitivity. We also present a 3D mesh hashing technique using spectral graph theory. The main idea is to partition a 3D model into sub-meshes, followed by the generation of the Laplace-Beltrami matrix of each sub-mesh, and the application of eigen-decomposition. This, in turn, is followed by the hashing of each sub-mesh using Tsallis entropy. The experimental results using a benchmark 3D models demonstrate the effectiveness of the proposed hashing scheme.