Tensorial template matching for fast cross-correlation with rotations and its application for tomography

TL;DR

This paper introduces tensorial template matching, a novel algorithm that efficiently detects objects with arbitrary rotations in large 3D images by representing all rotations with a tensor field, reducing computational complexity.

Contribution

The paper presents a new tensorial template matching algorithm that is faster and potentially more accurate than traditional methods, especially for large 3D tomograms.

Findings

Tensorial template matching is significantly faster than standard methods.

The algorithm's complexity is independent of rotation accuracy.

Demonstrated effectiveness on synthetic and real tomography data.

Abstract

Object detection is a main task in computer vision. Template matching is the reference method for detecting objects with arbitrary templates. However, template matching computational complexity depends on the rotation accuracy, being a limiting factor for large 3D images (tomograms). Here, we implement a new algorithm called tensorial template matching, based on a mathematical framework that represents all rotations of a template with a tensor field. Contrary to standard template matching, the computational complexity of the presented algorithm is independent of the rotation accuracy. Using both, synthetic and real data from tomography, we demonstrate that tensorial template matching is much faster than template matching and has the potential to improve its accuracy