# Scale Equivariance Improves Siamese Tracking

arXiv: https://arxiv.org/abs/2007.09115 · HTML: https://mlsanity.com/paper/2007.09115/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2020.

## Built on by (most cited first, 30 of 32)

- [TCTrack: Temporal Contexts for Aerial Tracking](https://mlsanity.com/paper/2203.01885/) (2022)
- [Unsupervised Domain Adaptation for Nighttime Aerial Tracking](https://mlsanity.com/paper/2203.10541/) (2022)
- [DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detection](https://mlsanity.com/paper/2207.10758/) (2022)
- [Approximation-Generalization Trade-offs under (Approximate) Group Equivariance](https://mlsanity.com/paper/2305.17592/) (2023)
- [DISCO: accurate Discrete Scale Convolutions](https://mlsanity.com/paper/2106.02733/) (2021)
- [LieGG: Studying Learned Lie Group Generators](https://mlsanity.com/paper/2210.04345/) (2022)
- [Towards Real-World Visual Tracking with Temporal Contexts](https://mlsanity.com/paper/2308.10330/) (2023)
- [Exploiting Redundancy: Separable Group Convolutional Networks on Lie Groups](https://mlsanity.com/paper/2110.13059/) (2021)
- [SGDViT: Saliency-Guided Dynamic Vision Transformer for UAV Tracking](https://mlsanity.com/paper/2303.04378/) (2023)
- [SAM-DA: UAV Tracks Anything at Night with SAM-Powered Domain Adaptation](https://mlsanity.com/paper/2307.01024/) (2023)
- [On genuine invariance learning without weight-tying](https://mlsanity.com/paper/2308.03904/) (2023)
- [Siamese Object Tracking for Unmanned Aerial Vehicle: A Review and Comprehensive Analysis](https://mlsanity.com/paper/2205.04281/) (2022)
- [Progressive Representation Learning for Real-Time UAV Tracking](https://mlsanity.com/paper/2409.16652/) (2024)
- [Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networks](https://mlsanity.com/paper/2409.11772/) (2024)
- [Prompt-Driven Temporal Domain Adaptation for Nighttime UAV Tracking](https://mlsanity.com/paper/2409.18533/) (2024)
- [Implicit Equivariance in Convolutional Networks](https://mlsanity.com/paper/2111.14157/) (2021)
- [Empowering Networks With Scale and Rotation Equivariance Using A Similarity Convolution](https://mlsanity.com/paper/2303.00326/) (2023)
- [BACTrack: Building Appearance Collection for Aerial Tracking](https://mlsanity.com/paper/2312.06136/) (2023)
- [Rotationally Equivariant Super-Resolution of Velocity Fields in Two-Dimensional Fluids Using Convolutional Neural Networks](https://mlsanity.com/paper/2202.11099/) (2022)
- [Continuity-Aware Latent Interframe Information Mining for Reliable UAV Tracking](https://mlsanity.com/paper/2303.04525/) (2023)
- [Multi-step Temporal Modeling for UAV Tracking](https://mlsanity.com/paper/2403.04363/) (2024)
- [Capacity of Group-invariant Linear Readouts from Equivariant Representations: How Many Objects can be Linearly Classified Under All Possible Views?](https://mlsanity.com/paper/2110.07472/) (2021)
- [Mutual-Learning Knowledge Distillation for Nighttime UAV Tracking](https://mlsanity.com/paper/2312.07884/) (2023)
- [Current Symmetry Group Equivariant Convolution Frameworks for Representation Learning](https://mlsanity.com/paper/2409.07327/) (2024)
- [Symmetry-aware Neural Architecture for Embodied Visual Navigation](https://mlsanity.com/paper/2112.09515/) (2021)
- [Siamese Object Tracking for Vision-Based UAM Approaching with Pairwise Scale-Channel Attention](https://mlsanity.com/paper/2211.14564/) (2022)
- [DaDiff: Domain-aware Diffusion Model for Nighttime UAV Tracking](https://mlsanity.com/paper/2410.12270/) (2024)
- [On the VC dimension of deep group convolutional neural networks](https://mlsanity.com/paper/2410.15800/) (2024)
- [CGTrack: Cascade Gating Network with Hierarchical Feature Aggregation for UAV Tracking](https://mlsanity.com/paper/2505.05936/) (2025)
- [Built-in Elastic Transformations for Improved Robustness](https://mlsanity.com/paper/2107.09391/) (2021)

## Abstract (arXiv)

Siamese trackers turn tracking into similarity estimation between a template and the candidate regions in the frame. Mathematically, one of the key ingredients of success of the similarity function is translation equivariance. Non-translation-equivariant architectures induce a positional bias during training, so the location of the target will be hard to recover from the feature space. In real life scenarios, objects undergoe various transformations other than translation, such as rotation or scaling. Unless the model has an internal mechanism to handle them, the similarity may degrade. In this paper, we focus on scaling and we aim to equip the Siamese network with additional built-in scale equivariance to capture the natural variations of the target a priori. We develop the theory for scale-equivariant Siamese trackers, and provide a simple recipe for how to make a wide range of existing trackers scale-equivariant. We present SE-SiamFC, a scale-equivariant variant of SiamFC built according to the recipe. We conduct experiments on OTB and VOT benchmarks and on the synthetically generated T-MNIST and S-MNIST datasets. We demonstrate that a built-in additional scale equivariance is useful for visual object tracking.