Teichmuller Mapping (T-Map) and Its Applications to Landmark Matching Registration

2014 ◽  
Vol 7 (1) ◽  
pp. 391-426 ◽  
Author(s):  
Lok Ming Lui ◽  
Ka Chun Lam ◽  
Shing-Tung Yau ◽  
Xianfeng Gu
Keyword(s):  
Teichmüller Mapping ◽  
Landmark Matching

scholarly journals Planar morphometrics using Teichmüller maps

2018 ◽  
Vol 474 (2217) ◽  
pp. 20170905 ◽  
Author(s):  
Gary P. T. Choi ◽  
L. Mahadevan
Keyword(s):  
Functional Data Analysis ◽  
Functional Data ◽  
Complex Analysis ◽  
Computational Approach ◽  
Similarity Matrix ◽  
Physical Systems ◽  
Developmental Progression ◽  
Planar Shapes ◽  
Teichmüller Mapping ◽  
Landmark Matching

Inspired by the question of quantifying wing shape, we propose a computational approach for analysing planar shapes. We first establish a correspondence between the boundaries of two planar shapes with boundary landmarks using geometric functional data analysis and then compute a landmark-matching curvature-guided Teichmüller mapping with uniform quasi-conformal distortion in the bulk. This allows us to analyse the pair-wise difference between the planar shapes and construct a similarity matrix on which we deploy methods from network analysis to cluster shapes. We deploy our method to study a variety of Drosophila wings across species to highlight the phenotypic variation between them, and Lepidoptera wings over time to study the developmental progression of wings. Our approach of combining complex analysis, computation and statistics to quantify, compare and classify planar shapes may be usefully deployed in other biological and physical systems.

Teichmuller Geometry

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Uniqueness Theorem ◽  
Existence Theorems ◽  
Quadratic Differentials ◽  
Complex Structures ◽  
Metric Geometry ◽  
Quasiconformal Maps ◽  
Hyperbolic Structures ◽  
Teichmüller Metric ◽  
Uniqueness And Existence ◽  
Teichmüller Mapping

This chapter focuses on the metric geometry of Teichmüller space. It first explains how one can think of Teich(Sɡ) as the space of complex structures on Sɡ. To this end, the chapter defines quasiconformal maps between surfaces and presents a solution to the resulting Teichmüller's extremal problem. It also considers the correspondence between complex structures and hyperbolic structures, along with the Teichmüller mapping, Teichmüller metric, and the proof of Teichmüller's uniqueness and existence theorems. The fundamental connection between Teichmüller's theorems, holomorphic quadratic differentials, and measured foliations is discussed as well. Finally, the chapter describes the Grötzsch's problem, whose solution is tied to the proof of Teichmüller's uniqueness theorem.

Optimized Conformal Surface Registration with Shape-based Landmark Matching

2010 ◽  
Vol 3 (1) ◽  
pp. 52-78 ◽  
Author(s):  
Lok Ming Lui ◽  
Sheshadri Thiruvenkadam ◽  
Yalin Wang ◽  
Paul M. Thompson ◽  
Tony F. Chan
Keyword(s):  
Surface Registration ◽  
Landmark Matching

Landmark Matching via Large Deformation Diffeomorphisms on the Sphere

2004 ◽  
Vol 20 (1/2) ◽  
pp. 179-200 ◽  
Author(s):  
Joan Glaunès ◽  
Marc Vaillant ◽  
Michael I. Miller
Keyword(s):  
Large Deformation ◽  
Landmark Matching

Ten-fold Improvement in Visual Odometry Using Landmark Matching

2007 ◽  
Author(s):  
Zhiwei Zhu ◽  
Taragay Oskiper ◽  
Supun Samarasekera ◽  
Rakesh Kumar ◽  
Harpreet S. Sawhney
Keyword(s):  
Visual Odometry ◽  
Landmark Matching

scholarly journals SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS

2009 ◽  
Vol 87 (2) ◽  
pp. 275-288 ◽  
Author(s):  
C. ZHANG
Keyword(s):  
Riemann Surface ◽  
Finite Type ◽  
Quadratic Differential ◽  
Quadratic Differentials ◽  
Closed Geodesics ◽  
Dehn Twists ◽  
Holomorphic Quadratic Differential ◽  
Simple Closed Geodesics ◽  
Disk Component ◽  
Teichmüller Mapping

AbstractLet S be a Riemann surface of finite type. Let ω be a pseudo-Anosov map of S that is obtained from Dehn twists along two families {A,B} of simple closed geodesics that fill S. Then ω can be realized as an extremal Teichmüller mapping on a surface of the same type (also denoted by S). Let ϕ be the corresponding holomorphic quadratic differential on S. We show that under certain conditions all possible nonpuncture zeros of ϕ stay away from all closures of once punctured disk components of S∖{A,B}, and the closure of each disk component of S∖{A,B} contains at most one zero of ϕ. As a consequence, we show that the number of distinct zeros and poles of ϕ is less than or equal to the number of components of S∖{A,B}.

A novel visual landmark matching for a biologically inspired homing

2001 ◽  
Vol 22 (13) ◽  
pp. 1371-1378 ◽  
Author(s):  
A. Rizzi ◽  
D. Duina ◽  
S. Inelli ◽  
R. Cassinis
Keyword(s):  
Biologically Inspired ◽  
Visual Landmark ◽  
Landmark Matching
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