Examination Committee

Prof Huiwen LIAN, MGMT/HKUST (Chairperson)
Prof Weichuan YU, ECE/HKUST (Thesis Supervisor)
Prof Gene CHEUNG, ECE/HKUST (Thesis Co-supervisor)
Prof Soo-Chang PEI, Department of Electrical Engineering, National Taiwan University (External Examiner)
Prof Roger S K CHENG, ECE/HKUST
Prof Zhiyong FAN, ECE/HKUST
Prof Gary S H CHAN, CSE/HKUST

Abstract

To process discrete digital images, a straightforward approach is to view them as arrays of numbers then directly operate on the arrays. An alternative paradigm in the literature, however, is to regard them as samples from continuous signals. Hence, image processing problems can be analyzed and resolved with these continuous signals. By doing so, more mathematical tools become available and formal analysis can be performed, gaining profound insights to the problem being considered. This thesis focuses on two problems: graph-based image restoration and subpixel-based image scaling. Unlike existing works with the continuous-domain paradigm, it is non-trivial to analyze these two problems in the continuous domain. However, we manage to do so and answer/resolve several fundamental aspects of the two problems.
 
We first consider image restoration with the graph Laplacian regularizer, where the target pixel patch is assumed to be smooth with respect to an appropriate graph. However, the mechanisms and implications of imposing the graph Laplacian regularizer on the original problem are not well understood. In this work, we interpret neighborhood graphs of pixel patches as discrete counterparts of Riemannian manifolds and perform analysis in the continuous domain, bringing novel understandings to several key aspects of graph Laplacian regularization. Our proposed denoising algorithm performs competitively with the state-of-the-art methods.

In the second problem, we aim at re-scaling a given image for a color display by controlling the subpixels on it individually, so as to improve the luminance resolution of the displayed image. However, improved luminance resolution brings chrominance distortion. It is also challenging to develop a scheme applicable for various subpixel arrangements. We address these issues by considering the low-pass nature of the human visual system (HVS) and analyzing in the continuous domain. Our subpixel-based scaling method provides sharp images with negligible color distortions on displays with different subpixel arrangements.