- Title Information
- Title
- Conformal Shape Representation
- Name:
Personal
- Name Part
- Feiszli, Matthew D.
- Role
- Role Term:
Text
- creator
- Origin Information
- Copyright Date
(keyDate="yes", encoding="w3cdtf")
- 2008
- Physical Description
- Extent
- ix, 152 p.
- digitalOrigin
- born digital
- Note
- Thesis (Ph.D.) -- Brown University (2008)
- Name:
Personal
- Name Part
- Mumford, David
- Role
- Role Term:
Text
- director
- Name:
Personal
- Name Part
- Brock, Jeffrey
- Role
- Role Term:
Text
- reader
- Name:
Personal
- Name Part
- Geman, Stuart
- Role
- Role Term:
Text
- reader
- Name:
Corporate
- Name Part
- Brown University. Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Genre (aat)
- theses
- Abstract
- Representation and comparison of shapes is a central problem in computer vision. In this dissertation, we continue investigation of a relatively recent approach, based on
conformal mapping, which was first introduced by Mumford and Sharon in 2006. We first study the way this representation encodes the geometry. One perceptually salient attribute of a shape is its
medial axis. By careful study of the boundary derivatives of conformal maps, we demonstrate how our representation encodes a sort of continuous version of the medial axis. This line of work
provides medial-axis-based variants of results like the Ahlfors distortion theorem, and also provides a new proof and refinement of the conjecture, attributed to Thurston and first proven by V.
Markovic, that the nearest-point retraction map is 2-Lipschitz in the hyperbolic metrics. In addition, we obtain explicit estimates demonstrating how conformal maps encode the local Euclidean
curvature of the boundary. The machinery involved in making our geometric estimates comes both from classical function theory and hyperbolic geometry. We next investigate the differential of the
isomorphism between quasisymmetric circle maps and shapes; we obtain explicit formulas for the differential in terms of the Hilbert transform. We then apply our results to develop an adaptive
compressor for plane curves based on the ``fingerprint'' construction explored by Sharon and Mumford. We demonstrate that our compressor is optimal on certain classes of
functions.
- Subject (Local)
- Topic
- conformal
- Subject (Local)
- Topic
- medial axis
- Subject (Local)
- Topic
- teichmuller
- Subject (Local)
- Topic
- quasiconformal
- Subject (Local)
- Topic
- compression
- Subject (Local)
- Topic
- hyperbolic
- Subject (FAST)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/875029")
- Topic
- Conformal geometry
- Subject (FAST)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/1115245")
- Topic
- Shapes
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20091218
- Language
- Language Term:
Code (ISO639-2B)
- eng
- Language Term:
Text
- English
- Identifier:
DOI
- 10.7301/Z0JS9NQN
- Access Condition:
rights statement
(href="http://rightsstatements.org/vocab/InC/1.0/")
- In Copyright
- Access Condition:
restriction on access
- Collection is open for research.
- Type of Resource (primo)
- dissertations