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Stochastic Shape Analysis

In: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author

Listed:
  • Alexis Arnaudon

    (Imperial College, Department of Mathematics
    École polytechnique fédéral de Lausanne (EPFL), Blue Brain Project)

  • Darryl Holm

    (Imperial College, Department of Mathematics)

  • Stefan Sommer

    (University of Copenhagen, Department of Computer Science (DIKU))

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.

Suggested Citation

  • Alexis Arnaudon & Darryl Holm & Stefan Sommer, 2023. "Stochastic Shape Analysis," Springer Books, in: Ke Chen & Carola-Bibiane Schönlieb & Xue-Cheng Tai & Laurent Younes (ed.), Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, chapter 38, pages 1325-1348, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98661-2_86
    DOI: 10.1007/978-3-030-98661-2_86
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