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arXiv · 2005.08743

Space-time metamorphosis

Andreas Bock·Colin Cotter
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Abstract

We study the problem of registering images. The framework we use is metamorphosis and we construct a variational Eulerian space-time setting and pose the registration problem as an infinite-dimensional optimisation problem. The geodesic equations correspond to a system of advection and continuity equations and are solved analytically. Well-posedness of a primal conforming finite element method is established and its convergence is investigated numerically. This provides a discrete forward operator for the matching parameterized by a space-time velocity field. We propose a gradient descent method on this control variable and show several promising numerical results for this approach.

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Andreas Bock, Colin Cotter. 2020-05-18. Space-time metamorphosis. https://arxiv.org/abs/2005.08743

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