Self-Similarity of Images and Non-local Image Processing
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Date
2011-06-28T19:31:16Z
Authors
Glew, Devin
Journal Title
Journal ISSN
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Publisher
University of Waterloo
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.
Description
Keywords
SSIM Index, Non-local means denoising, Self-similarity, Wavelets, Image processing