Date of Award

Fall 2014

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Computer Science

First Advisor

Jan P. Allebach

Committee Chair

Jan P. Allebach

Committee Member 1

Mikhail J. Atallah

Committee Member 2

Greg N. Frederickson

Committee Member 3

Yi Wu


In the last two decades, the increasing popularity of information technology has led to a dramatic increase in the amount of visual data. Many applications are developed by processing, analyzing and understanding such increasing data; and modelling the relation among images is fundamental to success of many of them. Examples include image classification, content-based image retrieval and face recognition. Given signatures of images, there are many ways to depict the relation among them, such as pairwise distance, kernel function and factor analysis. However, existing methods are still insufficient as they suffer from many real factors such as misalignment of images and inefficiency from nonlinearity. This dissertation focuses on improving the relation modelling, its applications and related optimization. In particular, three aspects of relation modelling are addressed: 1. Integrate image alignment into the relation modelling methods, including image classification and factor analysis, to achieve stability in real applications. 2. Model relation when images are on multiple manifolds. 3. Develop nonlinear relation modelling methods, including tapering kernels for sparsification of kernel-based relation models and developing piecewise linear factor analysis to enjoy both the efficiency of linear models and the flexibility of nonlinear ones. We also discuss future directions of relation modelling in the last chapter from both application and methodology aspects.