# Data augmentation with Mobius transformations

arXiv: https://arxiv.org/abs/2002.02917 · HTML: https://mlsanity.com/paper/2002.02917/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2020.

## Built on by (most cited first, 9 of 9)

- [Direct Differentiable Augmentation Search](https://mlsanity.com/paper/2104.04282/) (2021)
- [OmniZoomer: Learning to Move and Zoom in on Sphere at High-Resolution](https://mlsanity.com/paper/2308.08114/) (2023)
- [3D Human Pose Estimation Using M"obius Graph Convolutional Networks](https://mlsanity.com/paper/2203.10554/) (2022)
- [Rigidity Preserving Image Transformations and Equivariance in Perspective](https://mlsanity.com/paper/2201.13065/) (2022)
- [M"obius Transform for Mitigating Perspective Distortions in Representation Learning](https://mlsanity.com/paper/2405.02296/) (2024)
- [Learning High-Quality Navigation and Zooming on Omnidirectional Images in Virtual Reality](https://mlsanity.com/paper/2405.00351/) (2024)
- [AdapToPASS: Ambiguity-aware Adaptive Spherical Transformer for Panoramic Semantic Segmentation](https://mlsanity.com/paper/2608.29081/) (2026)
- [Empowering the trustworthiness of ML-based critical systems through engineering activities](https://mlsanity.com/paper/2209.15438/) (2022)
- [Image augmentation with conformal mappings for a convolutional neural network](https://mlsanity.com/paper/2212.05258/) (2022)

## Abstract (arXiv)

Data augmentation has led to substantial improvements in the performance and generalization of deep models, and remain a highly adaptable method to evolving model architectures and varying amounts of data---in particular, extremely scarce amounts of available training data. In this paper, we present a novel method of applying Mobius transformations to augment input images during training. Mobius transformations are bijective conformal maps that generalize image translation to operate over complex inversion in pixel space. As a result, Mobius transformations can operate on the sample level and preserve data labels. We show that the inclusion of Mobius transformations during training enables improved generalization over prior sample-level data augmentation techniques such as cutout and standard crop-and-flip transformations, most notably in low data regimes.