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|Title: ||Self-Similarity of Images and Non-local Image Processing|
|Authors: ||Glew, Devin|
|Keywords: ||SSIM Index|
Non-local means denoising
|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
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|
|Appears in Collections:||Electronic Theses and Dissertations (UW)|
Faculty of Mathematics Theses and Dissertations
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