Fast numerical methods for image processing based on partial differential equations

• Main Author: Duan, Yuping
• Other Authors: Tai Xue-Cheng
• Format: Theses and Dissertations
• Language: English
• Published: 2012
• Subjects: DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis
• Online Access: https://hdl.handle.net/10356/47834
• Institution: Nanyang Technological University

Image processing is an important branch of computer vision, which includes many subfields such as denoising, segmentation and inpainting, etc.. This is a highly challenging issue, because images may be very diverse and the way we perceive them varies a lot according to individuals. This dissertation will focus on two specific branches of image processing called image denoising and image segmentation. Such problems are usually formulated by the minimizations of energies in mathematical language. There are mainly continuous and discrete methods for solving the energy minimizations numerically. The continuous approach pursues a function which takes values in a continuous set while the discrete approach seeks a variable at each discrete pixel in the discrete image domain. Although both kinds of methods have been successfully studied for image denoising and segmentation, they still remain most active areas of research in image processing and computer vision. This dissertation serves as some attempts to develop efficient algorithms based on the existing continuous and discrete approaches for well-known variational models in image denoising and segmentation.