**Symmetry-guided nonrigid registration: the case for distortion correction in multidimensional photoemission spectroscopy **

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.

*The original publication is available by link DOI:
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10.1016/j.ultramic.2019.04.004