Detection of Outer Rotations on 3D-Vector Fields with Iterative Geometric Correlation

TL;DR

This paper demonstrates that iterative geometric correlation in Clifford algebras can effectively detect outer rotational misalignments in 3D vector fields, advancing techniques for image registration and pattern matching.

Contribution

It proves the effectiveness of iterative geometric correlation for detecting 3D rotational misalignments and introduces a new algorithm based on this theory.

Findings

Iterative geometric correlation detects outer rotations in 3D vector fields.

The developed algorithm successfully identifies rotational misalignments.

The method is applicable to image registration and pattern matching.

Abstract

Correlation is a common technique for the detection of shifts. Its generalization to the multidimensional geometric correlation in Clifford algebras has proven a useful tool for color image processing, because it additionally contains information about rotational misalignment. In this paper we prove that applying the geometric correlation iteratively can detect the outer rotational misalignment for arbitrary three-dimensional vector fields. Thus, it develops a foundation applicable for image registration and pattern matching. Based on the theoretical work we have developed a new algorithm and tested it on some principle examples.