# Tyler Seacrest

Harvey Mudd College Mathematics 2005

Thesis Proposal: | Matrix Perturbation Theory |
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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.