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http://hdl.handle.net/10012/6019
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| Title: | Self-Similarity of Images and Non-local Image Processing |
| Authors: | Glew, Devin |
| Keywords: | SSIM Index
Non-local means denoising
Self-similarity
Wavelets
Image processing |
| Approved Date: | 28-Jun-2011 |
| Date Submitted: | 2011 |
| Abstract: | This thesis has two related goals: the first involves the concept of self-similarity
of images. Image self-similarity is important because it forms the basis for many
imaging techniques such as non-local means denoising and fractal image coding.
Research so far has been focused largely on self-similarity in the pixel domain.
That is, examining how well different regions in an image mimic each other. Also,
most works so far concerning self-similarity have utilized only the mean squared
error (MSE).
In this thesis, self-similarity is examined in terms of the pixel and wavelet representations
of images. In each of these domains, two ways of measuring similarity
are considered: the MSE and a relatively new measurement of image fidelity called
the Structural Similarity (SSIM) Index. We show that the MSE and SSIM Index
give very different answers to the question of how self-similar images really are.
The second goal of this thesis involves non-local image processing. First, a
generalization of the well known non-local means denoising algorithm is proposed
and examined. The groundwork for this generalization is set by the aforementioned
results on image self-similarity with respect to the MSE. This new method is then
extended to the wavelet representation of images. Experimental results are given
to illustrate the applications of these new ideas. |
| Program: | Applied Mathematics |
| Department: | Applied Mathematics |
| Degree: | Master of Mathematics |
| URI: | http://hdl.handle.net/10012/6019 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
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