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Abstract

Image symmetrization may be cast as a nonrigid image registration problem
with symmetry constraints imposed in the registration target as well as in the
subsequent parameter tuning. An effective use case of image symmetrization is
found in electronic band structure mapping by multidimensional photoemission
spectroscopy, which employs a 3D time-of-flight detector to measure electrons
sorted into the momentum (k_x, k_y) and energy (E) coordinates. Stray
magnetic fields due to instrument imperfections perturb the photoelectron
trajectories and distort the symmetry in the measured band structure, which
hinders the full understanding and use of the volumetric datasets. To restore
symmetry in the measured data, we formulate registration-based symmetrization
in an iterative framework, incorporating the symmetry properties of materials
as physical constraints, in order to minimize the landmark localization error.
Using proposed symmetry metrics, we show quantitatively that our iterative
approach outperforms its non-iterative counterpart in the restored symmetry of
the outcome while preserving the average shape of the image pattern. Our
approach is generalizable to distortion corrections in different types of
symmetries and should also find applications in other experimental methods that
produce images with similar features.