Diffeomorphic Shape Matching Based on an Operator Splitting Method

Simple item page
dc.contributor.advisorAzencott, Robert
dc.contributor.committeeMemberHe, Jiwen
dc.contributor.committeeMemberMang, Andreas
dc.contributor.committeeMemberZoghbi, William A.
dc.creatorZhang, Peng 1989-
dc.date.accessioned2019-11-08T02:27:03Z
dc.date.createdAugust 2019
dc.date.issued2019-08
dc.date.submittedAugust 2019
dc.date.updated2019-11-08T02:27:04Z
dc.description.abstractIn order to study the valvular dynamic relying on a sequence of non-invasive echocardiographic 3D images of the mitral valve, one main goal is the reconstruction of shape deformations. In this dissertation, we use a spline technique to generate a static model of the mitral valve, which contains around 2000 points per snapshot. We find the optimal diffeomorphic matching of these mitral valves using an operator splitting method. To make the problem computationally accessible, we consider reproducing kernel Hilbert spaces using Gaussian kernels and weighted sums of Dirac measures. The objective function includes the kinetic energy of the velocity and a shape matching term. In order to efficiently optimize it, we apply an operator splitting method. Then based on the optimal diffeomorphism, the strain value of every point around the surface is calculated through a local surface strain tensor. A machine learning approach based on support vector machines is used to automatically classify patients into several subgroups.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginborn digital
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/10657/5326
dc.language.isoeng
dc.rightsThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).
dc.subjectOperator splitting method
dc.subjectGaussian kernels
dc.subjectShape Matching
dc.titleDiffeomorphic Shape Matching Based on an Operator Splitting Method
dc.type.dcmiText
dc.type.genreThesis
local.embargo.lift2021-08-01
local.embargo.terms2021-08-01
thesis.degree.collegeCollege of Natural Sciences and Mathematics
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

Files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
ZHANG-DISSERTATION-2019.pdf
Size:
3.66 MB
Format:
Adobe Portable Document Format
Download

License bundle

Now showing 1 - 2 of 2
No Thumbnail Available
Name:
PROQUEST_LICENSE.txt
Size:
4.43 KB
Format:
Plain Text
Description:
Download
No Thumbnail Available
Name:
LICENSE.txt
Size:
1.81 KB
Format:
Plain Text
Description:
Download

Collections

Published ETD Collection