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

TL;DR

This paper introduces an iterative geometric correlation method in Clifford algebras to detect and correct arbitrary 3D outer rotations in vector fields, improving efficiency and practical applicability in color image processing.

Contribution

It proves that iterative geometric correlation can detect arbitrary 3D outer rotations and presents an explicit, efficient algorithm with acceleration techniques.

Findings

Effective detection of 3D outer rotations in vector fields.

Algorithm demonstrates high efficiency and practical success.

Acceleration methods significantly improve performance.

Abstract

Correlation is a common technique for the detection of shifts. Its generalization to the multidimensional geometric correlation in Clifford algebras has been proven a useful tool for color image processing, because it additionally contains information about a rotational misalignment. But so far the exact correction of a three-dimensional outer rotation could only be achieved in certain special cases. In this paper we prove that applying the geometric correlation iteratively has the potential to detect the outer rotational misalignment for arbitrary three-dimensional vector fields. We further present the explicit iterative algorithm, analyze its efficiency detecting the rotational misalignment in the color space of a color image. The experiments suggest a method for the acceleration of the algorithm, which is practically tested with great success.