Transportation techniques for geometric data processing
Abstract/Contents
- Abstract
- Modeling and understanding low- and high-dimensional data is a recurring theme in graphics, optimization, learning, and vision. Abstracting away application domains reveals common threads using geometric constructs like distances, similarities, and curvatures. This shared structure suggests the possibility of developing geometric data processing as a discipline in itself. To this end, this thesis introduces optimal transportation (OT) as a versatile component of the geometric data processing toolkit. Originally proposed for minimizing the cost of shipping products from producers to consumers, OT links probability and geometry using distributions to encode geometric features and developing metric machinery to quantify their relationships. To transition OT from theory to practice, we show how to solve previously intractable OT problems efficiently on discretized domains and demonstrate a wide range of applications enabled by this new machinery. We illustrate the advantages and challenges of OT for geometric data processing by outlining my recent work in geometry processing, computer graphics, and machine learning. In each case, we consider optimization aspects of the OT problem for relevant geometric domains---including triangulated surfaces, graphs, and subsets of Euclidean space---and then show how the resulting machinery can be used to approach outstanding problems in surface correspondence, modeling, and semi-supervised learning.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2015 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Solomon, Justin |
|---|---|
| Associated with | Stanford University, Department of Computer Science. |
| Primary advisor | Guibas, Leonidas J |
| Thesis advisor | Guibas, Leonidas J |
| Thesis advisor | Fedkiw, Ronald P, 1968- |
| Thesis advisor | Savarese, Silvio |
| Advisor | Fedkiw, Ronald P, 1968- |
| Advisor | Savarese, Silvio |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Justin Solomon. |
|---|---|
| Note | Submitted to the Department of Computer Science. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2015. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2015 by Justin Moore Solomon
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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