Using fractional derivatives as a degree of symmetry to characterize natural shapes
Abstract/Contents
- Abstract
- The main pursuit of this thesis is to model shapes and features in natural data, such as interstellar neutral hydrogen images, in order to recognize the unusual, or novel, in the presence of the ordinary. The presented approach develops on an abstraction we call the degree of symmetry. We assert that any feature or shape decomposes into two orthogonal components: one signifies a fractional degree of symmetry, and the other a corresponding, fractional degree of anti-symmetry. This framework conflates measure of symmetry with fractional-order derivatives, such that every feature is an instantiation of a linear model consisting of the orthogonal components. Each component is a fractional derivative of a symmetric function. The parameters of our model induce a 3-D representation space for the purpose of detection, classification, and characterization of features. The Wavelet transform of the features, particularly the decay of the coefficients and the coefficients' footprint on the scale-translation plane, provides sufficient information to determine the parameters of the model. In a representative application of the method, analysis of 21-cm interstellar neutral hydrogen spectra collected synoptically by the 150-foot Stanford radio Telescope demonstrates the performance of the proposed method in search for unusual structures. Additional examples such as roughness analysis of silicon deposition surface images, using our fractional symmetry transformations, also illustrate the utility of the proposed approach.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2013 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Ilhan, Husrev Tolga |
|---|---|
| Associated with | Stanford University, Department of Electrical Engineering. |
| Primary advisor | Tyler, G. Leonard (George Leonard) |
| Thesis advisor | Tyler, G. Leonard (George Leonard) |
| Thesis advisor | Carlsson, Gunnar |
| Thesis advisor | Linscott, Ivan |
| Thesis advisor | Zebker, Howard A |
| Advisor | Carlsson, Gunnar |
| Advisor | Linscott, Ivan |
| Advisor | Zebker, Howard A |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Husrev Tolga Ilhan. |
|---|---|
| Note | Submitted to the Department of Electrical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2013. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by Husrev Tolga Ilhan
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
Also listed in
Loading usage metrics...