Tyler Seacrest

Harvey Mudd College Mathematics 2005

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Thesis Proposal: Matrix Perturbation Theory
Thesis Advisor: Prof. Weiqing Gu
Second Reader: Prof. Darryl Yong
E-Mail: tseacrest@hmc.edu
Midterm Report: Midterm Report: Mathematical Models of Image Processing
Thesis: Mathematical Models of Image Processing
Thesis Poster: Coloring Linear Algebra
Presentation days Presentation: Blurring Invariants

Mathematical Models of Image Processing

The purpose of this thesis is to develop various advanced linear algebra techniques in application to image processing. With the increasing use of computers and digital photography, the need to be able to manipulate digital images efficiently and with greater freedom is extremely important. By applying the tools of linear algebra, we hope to lend greater power in the ability to process such images.

We are especially interested in developing techniques that allow for computers to manipulate images requiring the least amount of human guidance. We demonstrate techniques that allow a computer to rotate an image to the correct orientation automatically, and similarly for the computer to correct a certain class of color distortion automatically. In both cases, certain properties of the eigenvalues of covariance matrices corresponding to the images are used. We develop theoretic techniques that specifiy a particular way to morph between two images that depends only on the content of the two images, with no human input.