Space-time metamorphosis
Andreas Bock, Colin Cotter

TL;DR
This paper introduces a novel space-time metamorphosis framework for image registration, formulating it as an infinite-dimensional optimization problem and solving it analytically with finite element methods and gradient descent.
Contribution
It develops a variational Eulerian space-time approach for image registration, including analytical solutions, finite element analysis, and a gradient descent algorithm for the control variable.
Findings
Analytical solutions to geodesic equations for registration.
Finite element method ensures well-posedness and convergence.
Numerical results demonstrate effectiveness of the proposed approach.
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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Taxonomy
TopicsCellular Automata and Applications · Algorithms and Data Compression
