Stochastic Metamorphosis with Template Uncertainties
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Stochastic Metamorphosis with Template Uncertainties. / Arnaudon, Alexis; Holm, Darryl D.; Sommer, Stefan.
Mathematics of Shapes and Applications. Bind 37 World Scientific, 2019. s. 75-96 (Lecture Notes Series, Institute for Mathematical Sciences, Bind 37).Publikation: Bidrag til bog/antologi/rapport › Bidrag til bog/antologi › Forskning › fagfællebedømt
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TY - CHAP
T1 - Stochastic Metamorphosis with Template Uncertainties
AU - Arnaudon, Alexis
AU - Holm, Darryl D.
AU - Sommer, Stefan
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
U2 - 10.1142/9789811200137_0004
DO - 10.1142/9789811200137_0004
M3 - Book chapter
AN - SCOPUS:85075752299
SN - 978-981-120-012-0
VL - 37
T3 - Lecture Notes Series, Institute for Mathematical Sciences
SP - 75
EP - 96
BT - Mathematics of Shapes and Applications
PB - World Scientific
ER -
ID: 237803867