Curve characterization with high-order tensor singular value decomposition

Oil has been found on what was once the banks of ancient rivers. As a consequence, there is an interest in identifying the locations of ancient rivers, which in turn motivates the need for criteria to identify river locations. To that end, we develop geometric descriptors to quantify river geometries and to observe their statistics. The river geometries are represented by curves which define their center lines. Curve descriptors are defined via Minkowski valuations and high-order singular value decomposition. The advantage of this method is that a large number of descriptors can be readily generated. The statistic study is conducted on a few groups of curves and a collection of rivers in Texas. To create the descriptors, high order Minkowski valuation tensors are generated based on the curves' position vectors, normal vectors and curvatures. Next, these tensors are decomposed via high-order singular-value decomposition into scalar descriptors derived from the eigenvalues of the tensors. Correlation amongst the descriptors are subsequently obtained and the independent ones are identified. At last, two sets of statistical analysis are conducted. The first analysis provides insights to the physics of the descriptors. Groups of curves are generated in this analysis, wherein specific geometric features are varied, and the change in the curve descriptors is observed. Thus we infer correlations between geometric features and descriptors. The second analysis evaluates a descriptors-based criterion to identify river-like curves. In this analysis, the descriptors of 1722 10-mile Texas river segments are obtained and a joint density probability function amongst the independent descriptors is created. The probability function is subsequently used as a criterion to identify river-like curves among randomly generated ones.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2016

Author dc:creator

• Cai, Muyun

Contributors dc:contributor

• Tortorelli, Daniel A.

• curve characterization
• Mikowski valuation

Statement dc:rights

• Copyright 2016 Muyun Cai

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/90683

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F90683