Stochastic Shape Analysis

Alexis Arnaudon; Darryl Holm; Stefan Sommer

doi:10.1007/978-3-030-98661-2_86

Stochastic Shape Analysis

Alexis Arnaudon, Darryl Holm, Stefan Sommer^*

^*Corresponding author for this work

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Abstract

The chapter describes stochastic models of shapes from a Hamiltonian viewpoint, including Langevin models, Riemannian Brownian motions and stochastic variational systems. Starting from the deterministic setting of outer metrics on shape spaces and transformation groups, we discuss recent approaches to introducing noise in shape analysis from a physical or Hamiltonian point of view. We furthermore outline important applications and statistical uses of stochastic shape models, and we discuss perspectives and current research efforts in stochastic shape analysis.

Original language	English
Title of host publication	Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging : Mathematical Imaging and Vision
Publisher	Springer
Publication date	2023
Pages	1325-1348
ISBN (Print)	9783030986605
ISBN (Electronic)	9783030986612
DOIs	https://doi.org/10.1007/978-3-030-98661-2_86
Publication status	Published - 2023

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2023.

Keywords

Hamiltonian systems
Langevin equations
Shape analysis
Stochastic Euler-Poincaré equations
Stochastic geometric mechanics

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10.1007/978-3-030-98661-2_86

Cite this

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KW - Hamiltonian systems

KW - Langevin equations

KW - Shape analysis

KW - Stochastic Euler-Poincaré equations

KW - Stochastic geometric mechanics

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ER -

Stochastic Shape Analysis

Abstract

Bibliographical note

Keywords

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