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- W4384111805 abstract "We study parameterisation-independent closed planar curve matching as a Bayesian inverse problem. The motion of the curve is modelled via a curve on the diffeomorphism group acting on the ambient space, leading to a large deformation diffeomorphic metric mapping (LDDMM) functional penalising the kinetic energy of the deformation. We solve Hamilton's equations for the curve matching problem using the Wu-Xu element [S. Wu, J. Xu, Nonconforming finite element spaces for $2m^text{th}$ order partial differential equations on $mathbb{R}^n$ simplicial grids when $m=n+1$, Mathematics of Computation 88 (316) (2019) 531-551] which provides mesh-independent Lipschitz constants for the forward motion of the curve, and solve the inverse problem for the momentum using Bayesian inversion. Since this element is not affine-equivalent we provide a pullback theory which expedites the implementation and efficiency of the forward map. We adopt ensemble Kalman inversion using a negative Sobolev norm mismatch penalty to measure the discrepancy between the target and the ensemble mean shape. We provide several numerical examples to validate the approach." @default.
- W4384111805 created "2023-07-13" @default.
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- W4384111805 date "2023-07-10" @default.
- W4384111805 modified "2023-09-24" @default.
- W4384111805 title "Planar Curve Registration using Bayesian Inversion" @default.
- W4384111805 doi "https://doi.org/10.48550/arxiv.2307.04909" @default.
- W4384111805 hasPublicationYear "2023" @default.
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