# Learning Continuous Rotation Canonicalization with Radial Beam Sampling

arXiv: https://arxiv.org/abs/2206.10690 · HTML: https://mlsanity.com/paper/2206.10690/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 42 references that are in the map.
- First posted on arXiv 21 Jun 2022.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [A Kernel Theory of Modern Data Augmentation](https://mlsanity.com/paper/1803.06084/) (2018)
- [Rotation equivariant vector field networks](https://mlsanity.com/paper/1612.09346/) (2016)
- [On Robustness and Transferability of Convolutional Neural Networks](https://mlsanity.com/paper/2007.08558/) (2020)
- [Meta-Learning Symmetries by Reparameterization](https://mlsanity.com/paper/2007.02933/) (2020)
- [Covariant Compositional Networks For Learning Graphs](https://mlsanity.com/paper/1801.02144/) (2018)
- [Data augmentation in Bayesian neural networks and the cold posterior effect](https://mlsanity.com/paper/2106.05586/) (2021)
- [A rotation-equivariant convolutional neural network model of primary visual cortex](https://mlsanity.com/paper/1809.10504/) (2018)
- [A Group-Theoretic Framework for Data Augmentation](https://mlsanity.com/paper/1907.10905/) (2019)
- [Exploring Weight Symmetry in Deep Neural Networks](https://mlsanity.com/paper/1812.11027/) (2018)
- [Deep Reinforcement Learning for Dexterous Manipulation with Concept Networks](https://mlsanity.com/paper/1709.06977/) (2017)
- [Symmetry-driven graph neural networks](https://mlsanity.com/paper/2105.14058/) (2021)

## Built on by (most cited first, 4 of 4)

- [Tilt your Head: Activating the Hidden Spatial-Invariance of Classifiers](https://mlsanity.com/paper/2405.03730/) (2024)
- [Geometrically Constrained and Token-Based Probabilistic Spatial Transformers](https://mlsanity.com/paper/2509.11218/) (2025)
- [Saccadic Vision for Fine-Grained Visual Classification](https://mlsanity.com/paper/2509.15688/) (2025)
- [Robust Canonicalization through Bootstrapped Data Re-Alignment](https://mlsanity.com/paper/2510.08178/) (2025)

## Abstract (arXiv)

Nearly all state of the art vision models are sensitive to image rotations. Existing methods often compensate for missing inductive biases by using augmented training data to learn pseudo-invariances. Alongside the resource demanding data inflation process, predictions often poorly generalize. The inductive biases inherent to convolutional neural networks allow for translation equivariance through kernels acting parallely to the horizontal and vertical axes of the pixel grid. This inductive bias, however, does not allow for rotation equivariance. We propose a radial beam sampling strategy along with radial kernels operating on these beams to inherently incorporate center-rotation covariance. Together with an angle distance loss, we present a radial beam-based image canonicalization model, short BIC. Our model allows for maximal continuous angle regression and canonicalizes arbitrary center-rotated input images. As a pre-processing model, this enables rotation-invariant vision pipelines with model-agnostic rotation-sensitive downstream predictions. We show that our end-to-end trained angle regressor is able to predict continuous rotation angles on several vision datasets, i.e. FashionMNIST, CIFAR10, COIL100, and LFW.