Stochastic Shape Analysis

Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review

Standard

Stochastic Shape Analysis. / Arnaudon, Alexis; Holm, Darryl; Sommer, Stefan.

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision. Springer, 2023. p. 1325-1348.

Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review

Harvard

Arnaudon, A, Holm, D & Sommer, S 2023, Stochastic Shape Analysis. in Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision. Springer, pp. 1325-1348. https://doi.org/10.1007/978-3-030-98661-2_86

APA

Arnaudon, A., Holm, D., & Sommer, S. (2023). Stochastic Shape Analysis. In Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision (pp. 1325-1348). Springer. https://doi.org/10.1007/978-3-030-98661-2_86

Vancouver

Arnaudon A, Holm D, Sommer S. Stochastic Shape Analysis. In Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision. Springer. 2023. p. 1325-1348 https://doi.org/10.1007/978-3-030-98661-2_86

Author

Arnaudon, Alexis ; Holm, Darryl ; Sommer, Stefan. / Stochastic Shape Analysis. Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision. Springer, 2023. pp. 1325-1348

Bibtex

@inbook{43baac65ff9c43e181db841b1e2ef593,
title = "Stochastic Shape Analysis",
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.",
keywords = "Hamiltonian systems, Langevin equations, Shape analysis, Stochastic Euler-Poincar{\'e} equations, Stochastic geometric mechanics",
author = "Alexis Arnaudon and Darryl Holm and Stefan Sommer",
note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2023.",
year = "2023",
doi = "10.1007/978-3-030-98661-2_86",
language = "English",
isbn = "9783030986605",
pages = "1325--1348",
booktitle = "Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging",
publisher = "Springer",
address = "Switzerland",

}

RIS

TY - CHAP

T1 - Stochastic Shape Analysis

AU - Arnaudon, Alexis

AU - Holm, Darryl

AU - Sommer, Stefan

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2023.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Hamiltonian systems

KW - Langevin equations

KW - Shape analysis

KW - Stochastic Euler-Poincaré equations

KW - Stochastic geometric mechanics

UR - http://www.scopus.com/inward/record.url?scp=85161948752&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-98661-2_86

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

M3 - Book chapter

AN - SCOPUS:85161948752

SN - 9783030986605

SP - 1325

EP - 1348

BT - Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

PB - Springer

ER -

ID: 358550906