Topology of spaces of micro-images, and an application to texture discrimination
Abstract/Contents
- Abstract
- Using the fact that most 3-by-3 pixel high-contrast patches from natural images accumulate around a space with the topology of a Klein bottle, we present in this thesis a novel method for texture representation and discrimination. Given a texture image, most of its high-contrast patches can be projected onto the aforementioned Klein bottle. We analyze this sample in terms of its underlying probability density function, which we show can be represented via Fourier-like coefficients. These coefficients in turn, can be estimated with high confidence from the sample. Dissimilarity measures are defined on the set of estimated coefficients, and performance of the method is tested on a large collection of texture images.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2011 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Perea Benitez, Jose Andres |
|---|---|
| Associated with | Stanford University, Department of Mathematics |
| Primary advisor | Carlsson, G. (Gunnar), 1952- |
| Thesis advisor | Carlsson, G. (Gunnar), 1952- |
| Thesis advisor | Papanicolaou, George |
| Thesis advisor | Vasy, András |
| Advisor | Papanicolaou, George |
| Advisor | Vasy, András |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Jose Andres Perea Benitez. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Ph.D. Stanford University 2011 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2011 by Jose Andres Perea Benitez
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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