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

arXiv: https://arxiv.org/abs/2408.02398 · HTML: https://mlsanity.com/paper/2408.02398/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 41 references that are in the map.
- First posted on arXiv 5 Aug 2024.

## Builds on (most cited first, 9 of 9)

- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Convolutional neural network architecture for geometric matching](https://mlsanity.com/paper/1703.05593/) (2017)
- [Positive-unlabeled convolutional neural networks for particle picking in cryo-electron micrographs](https://mlsanity.com/paper/1803.08207/) (2018)
- [Learning Accurate Template Matching with Differentiable Coarse-to-Fine Correspondence Refinement](https://mlsanity.com/paper/2303.08438/) (2023)
- [SHREC 2021: Classification in cryo-electron tomograms](https://mlsanity.com/paper/2203.10035/) (2022)
- [Fast Normalized Cross-Correlation for Template Matching with Rotations](https://mlsanity.com/paper/2311.07561/) (2023)
- [Principled Design and Implementation of Steerable Detectors](https://mlsanity.com/paper/1811.00863/) (2018)
- [Probabilistic bounds on best rank-one approximation ratio](https://mlsanity.com/paper/2201.02191/) (2022)
- [Complexity and computation for the spectral norm and nuclear norm of order three tensors with one fixed dimension](https://mlsanity.com/paper/2212.14775/) (2022)

## Built on by (most cited first, 1 of 1)

- [An Efficient Deep Template Matching and In-Plane Pose Estimation Method via Template-Aware Dynamic Convolution](https://mlsanity.com/paper/2510.01678/) (2025)

## Abstract (arXiv)

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