# Equivalence of Correlation Filter and Convolution Filter in Visual Tracking

arXiv: https://arxiv.org/abs/2105.00158 · HTML: https://mlsanity.com/paper/2105.00158/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 50 references that are in the map.
- First posted on arXiv 1 May 2021.

## Builds on (most cited first, 25 of 25)

- [Object Detection with Deep Learning: A Review](https://mlsanity.com/paper/1807.05511/) (2018)
- [SiamRPN++: Evolution of Siamese Visual Tracking with Very Deep Networks](https://mlsanity.com/paper/1812.11703/) (2018)
- [Fast Online Object Tracking and Segmentation: A Unifying Approach](https://mlsanity.com/paper/1812.05050/) (2018)
- [ECO: Efficient Convolution Operators for Tracking](https://mlsanity.com/paper/1611.09224/) (2016)
- [Probabilistic Regression for Visual Tracking](https://mlsanity.com/paper/2003.12565/) (2020)
- [A Survey of the Recent Architectures of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1901.06032/) (2019)
- [Siamese Box Adaptive Network for Visual Tracking](https://mlsanity.com/paper/2003.06761/) (2020)
- [A Review on Deep Learning Techniques Applied to Semantic Segmentation](https://mlsanity.com/paper/1704.06857/) (2017)
- [Know Your Surroundings: Exploiting Scene Information for Object Tracking](https://mlsanity.com/paper/2003.11014/) (2020)
- [Deformable Siamese Attention Networks for Visual Object Tracking](https://mlsanity.com/paper/2004.06711/) (2020)
- [Beyond Correlation Filters: Learning Continuous Convolution Operators for Visual Tracking](https://mlsanity.com/paper/1608.03773/) (2016)
- [Learning Spatially Regularized Correlation Filters for Visual Tracking](https://mlsanity.com/paper/1608.05571/) (2016)
- [Learning Background-Aware Correlation Filters for Visual Tracking](https://mlsanity.com/paper/1703.04590/) (2017)
- [Learning Spatial-Temporal Regularized Correlation Filters for Visual Tracking](https://mlsanity.com/paper/1803.08679/) (2018)
- [AutoTrack: Towards High-Performance Visual Tracking for UAV with Automatic Spatio-Temporal Regularization](https://mlsanity.com/paper/2003.12949/) (2020)
- [Learning Aberrance Repressed Correlation Filters for Real-Time UAV Tracking](https://mlsanity.com/paper/1908.02231/) (2019)
- [Discriminative Correlation Filter with Channel and Spatial Reliability](https://mlsanity.com/paper/1611.08461/) (2016)
- [GradNet: Gradient-Guided Network for Visual Object Tracking](https://mlsanity.com/paper/1909.06800/) (2019)
- [Object Tracking by Reconstruction with View-Specific Discriminative Correlation Filters](https://mlsanity.com/paper/1811.10863/) (2018)
- [Learning Residue-Aware Correlation Filters and Refining Scale Estimates with the GrabCut for Real-Time UAV Tracking](https://mlsanity.com/paper/2104.03114/) (2021)
- [Training-Set Distillation for Real-Time UAV Object Tracking](https://mlsanity.com/paper/2003.05326/) (2020)
- [Keyfilter-Aware Real-Time UAV Object Tracking](https://mlsanity.com/paper/2003.05218/) (2020)
- [ROI Pooled Correlation Filters for Visual Tracking](https://mlsanity.com/paper/1911.01668/) (2019)
- [Augmented Memory for Correlation Filters in Real-Time UAV Tracking](https://mlsanity.com/paper/1909.10989/) (2019)
- [Towards Robust Visual Tracking for Unmanned Aerial Vehicle with Tri-Attentional Correlation Filters](https://mlsanity.com/paper/2008.00528/) (2020)

## Built on by (most cited first, 3 of 3)

- [Towards Discriminative Representations with Contrastive Instances for Real-Time UAV Tracking](https://mlsanity.com/paper/2308.11450/) (2023)
- [Learning Disentangled Representation with Mutual Information Maximization for Real-Time UAV Tracking](https://mlsanity.com/paper/2308.10262/) (2023)
- [Dynamic Semantic-Aware Correlation Modeling for UAV Tracking](https://mlsanity.com/paper/2510.21351/) (2025)

## Abstract (arXiv)

(Discriminative) Correlation Filter has been successfully applied to visual tracking and has advanced the field significantly in recent years. Correlation filter-based trackers consider visual tracking as a problem of matching the feature template of the object and candidate regions in the detection sample, in which correlation filter provides the means to calculate the similarities. In contrast, convolution filter is usually used for blurring, sharpening, embossing, edge detection, etc in image processing. On the surface, correlation filter and convolution filter are usually used for different purposes. In this paper, however, we proves, for the first time, that correlation filter and convolution filter are equivalent in the sense that their minimum mean-square errors (MMSEs) in visual tracking are equal, under the condition that the optimal solutions exist and the ideal filter response is Gaussian and centrosymmetric. This result gives researchers the freedom to choose correlation or convolution in formulating their trackers. It also suggests that the explanation of the ideal response in terms of similarities is not essential.