Stochastic Metamorphosis with Template Uncertainties

Publikation: Bidrag til bog/antologi/rapportBidrag til bog/antologiForskningfagfællebedømt

In this paper, we investigate two stochastic perturbations of the metamorphosis equations of image analysis, in the geometrical context of the Euler-Poincaré theory. In the metamorphosis of images, the Lie group of diffeomorphisms deforms a template image that is undergoing its own internal dynamics as it deforms. This type of deformation allows more freedom for image matching and has analogies with complex uids when the template properties are regarded as order parameters. The first stochastic perturbation we consider corresponds to uncertainty due to random errors in the reconstruction of the deformation map from its vector field. We also consider a second stochastic perturbation, which compounds the uncertainty of the deformation map with the uncertainty in the reconstruction of the template position from its velocity field. We apply this general geometric theory to several classical examples, including landmarks, images, and closed curves, and we discuss its use for functional data analysis.

OriginalsprogEngelsk
TitelMathematics of Shapes and Applications
Antal sider22
Vol/bind37
ForlagWorld Scientific
Publikationsdato2019
Sider75-96
ISBN (Trykt)978-981-120-012-0
DOI
StatusUdgivet - 2019
NavnLecture Notes Series, Institute for Mathematical Sciences
Vol/bind37
ISSN1793-0758

ID: 237803867