There are many people who deserve more than just an acknowledgement on this page. First, I would like to thank my supervisor, Professor Kai-Kuang Ma, who advised this thesis. It is a privilege to learn from him for five years where he gave me much freedom in doing research. He is very supportive and patient. Most importantly, he not only directed my research work, but also gave me precious suggestions and instructions on the research attitude and effective communications. These valuable experiences will greatly influence my future career and life. I would also like to thank my earlier teachers without whose support I might never come to this field for a PhD degree, in particular the advisor of my master degree, Professor Canhui Cai in Huaqiao University. They inspired my interests in thinking and learning. I would like to thank my labmates, Tian Jing, Zeng Huanqiang, Wang Chen and Ong Hui Ting for their valuable advices and discussions on my research. I would also like to thank all of my friends who have made my time at Nanyang Technological University enjoyable. Finally, I would like to thank my wife, my daughter, and my parents for their unselfish support all the time. Without their love, this work would be impossible. i Contents Acknowledgments i List of Figures v List of Tables xii Summary xiv the interpolation process through the developed contrast-guided decision map (CD-M), which is a binary map and generated by applying the diffusion process to the directional variation field. The generated CDM is used to guide the interpolation process, and the local contrasts are better preserved compared with that of using the edge map (or, edge-guided decision map) for guiding the image interpolation process. Simulation results have clearly shown that the proposed contrast-guided interpolation method significantly outperforms other state-of-the-art image interpolation methods with much reduced computational complexity.