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.
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Acknowledgements
Research is never done in a vacuum. We are enormously grateful to our friends in the shape analysis community for their remarkable tradition of openness, inclusiveness and kind encouragement to each other in their many joint endeavours. The work is supported by the Villum Foundation grant 00022924 and the Novo Nordisk Foundation grant NNF18OC0052000.
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Arnaudon, A., Holm, D., Sommer, S. (2021). Stochastic Shape Analysis. In: Chen, K., Schönlieb, CB., Tai, XC., Younces, L. (eds) Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Cham. https://doi.org/10.1007/978-3-030-03009-4_86-1
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