Detection of Total Rotations on 2D-Vector Fields with Geometric Correlation

TL;DR

This paper demonstrates that iterative geometric correlation can effectively detect total rotational misalignment in 2D vector fields, extending its application from linear to more general analytic fields using power series analysis.

Contribution

It proves that iterative geometric correlation can identify total rotations in 2D vector fields and provides a method to compute rotations from power series expansions.

Findings

Iterative geometric correlation detects total rotational misalignment in linear 2D vector fields.

The method extends to general analytic vector fields via power series.

Rotation angles can be calculated from the vector fields' power series expansions.

Abstract

Correlation is a common technique for the detection of shifts. Its generalization to the multidimensional geometric correlation in Clifford algebras additionally contains information with respect to rotational misalignment. It has been proven a useful tool for the registration of vector fields that differ by an outer rotation. In this paper we proof that applying the geometric correlation iteratively has the potential to detect the total rotational misalignment for linear two-dimensional vector fields. We further analyze its effect on general analytic vector fields and show how the rotation can be calculated from their power series expansions.