Varifold-Based Matching of Curves via Sobolev-Type Riemannian Metrics

被引：2

作者：

Bauer, Martin ^{[1
]}

Bruveris, Martins ^{[2
]}

Charon, Nicolas ^{[3
]}

Moller-Andersen, Jakob ^{[1
]}

机构：

[1] Florida State Univ, Dept Math, Tallahassee, FL 32306 USA

[2] Brunel Univ London, Dept Math, London, England

[3] Johns Hopkins Univ, CIS, Baltimore, MD USA

来源：

GRAPHS IN BIOMEDICAL IMAGE ANALYSIS, COMPUTATIONAL ANATOMY AND IMAGING GENETICS | 2017年 / 10551卷

关键词：

Curve matching; Sobolev metrics; Riemannian shape analysis; Varifold distance; Minimizing geodesics; LDDMM; SPACES; SHAPE;

D O I：

10.1007/978-3-319-67675-3_14

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Second order Sobolev metrics are a useful tool in the shape analysis of curves. In this paper we combine these metrics with varifold-based inexact matching to explore a new strategy of computing geodesics between unparametrized curves. We describe the numerical method used for solving the inexact matching problem, apply it to study the shape of mosquito wings and compare our method to curve matching in the LDDMM framework.

引用

页码：152 / 163

页数：12

共 15 条

[1] Riemannian metrics on ℝn and Sobolev-type Inequalities
A. V. Kolesnikov
E. Milman
[J]. Doklady Mathematics, 2016, 94 : 510 - 513
[2] Properties of Sobolev-type metrics in the space of curves
Mennucci, A. C. G.
Yezzi, A.
Sundaramoorthi, G.
[J]. INTERFACES AND FREE BOUNDARIES, 2008, 10 (04) : 423 - 445
[3] Riemannian metrics on a"e n and Sobolev-type Inequalities
Kolesnikov, A. V.
Milman, E.
[J]. DOKLADY MATHEMATICS, 2016, 94 (02) : 510 - 513
[4] Multiple Object Tracking via Prediction and Filtering with a Sobolev-Type Metric on Curves
Bardelli, Eleonora
Colombo, Maria
Mennucci, Andrea
Yezzi, Anthony
[J]. COMPUTER VISION - ECCV 2012: WORKSHOPS AND DEMONSTRATIONS, PT I, 2012, 7583 : 143 - 152
[5] Variational principles and Sobolev-type estimates for generalized interpolation on a Riemannian manifold
Dyn, N
Narcowich, FJ
Ward, JD
[J]. CONSTRUCTIVE APPROXIMATION, 1999, 15 (02) : 175 - 208
[6] SOBOLEV-TYPE INEQUALITIES AND COMPLETE RIEMANNIAN MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE
Abolarinwa, Abimbola
Adefolarin, Adekunle
Animasahun, Isaac A.
[J]. BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 11 (01): : 11 - 21
[7] Variational Principles and Sobolev-Type Estimates for Generalized Interpolation on a Riemannian Manifold
N. Dyn
F. J. Narcowich
J. D. Ward
[J]. Constructive Approximation, 1999, 15 : 175 - 208
[8] H°-type Riemannian metrics on the space of planar curves
Shah, Jayant
[J]. QUARTERLY OF APPLIED MATHEMATICS, 2008, 66 (01) : 123 - 137
[9] Heat Kernel Estimates, Sobolev-Type Inequalities and Riesz Transform on Noncompact Riemannian Manifolds
Coulhon, Thierry
[J]. ANALYSIS AND GEOMETRY OF METRIC MEASURE SPACES, 2013, 56 : 55 - 65
[10] Multiwavelet based moment method under discrete sobolev-type norm
Pan, G
Tong, MS
Gilbert, B
[J]. MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, 2004, 40 (01) : 47 - 50

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