# M"obius Transform for Mitigating Perspective Distortions in Representation Learning

arXiv: https://arxiv.org/abs/2405.02296 · HTML: https://mlsanity.com/paper/2405.02296/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 64 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Builds on (most cited first, 30 of 43)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [FCOS: Fully Convolutional One-Stage Object Detection](https://mlsanity.com/paper/1904.01355/) (2019)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [Composition Loss for Counting, Density Map Estimation and Localization in Dense Crowds](https://mlsanity.com/paper/1808.01050/) (2018)
- [Bayesian Loss for Crowd Count Estimation with Point Supervision](https://mlsanity.com/paper/1908.03684/) (2019)
- [Rethinking Counting and Localization in Crowds:A Purely Point-Based Framework](https://mlsanity.com/paper/2107.12746/) (2021)
- [Context-Aware Crowd Counting](https://mlsanity.com/paper/1811.10452/) (2018)
- [Distribution Matching for Crowd Counting](https://mlsanity.com/paper/2009.13077/) (2020)
- [Pillar-based Object Detection for Autonomous Driving](https://mlsanity.com/paper/2007.10323/) (2020)
- [SPEC: Seeing People in the Wild with an Estimated Camera](https://mlsanity.com/paper/2110.00620/) (2021)
- [PixMix: Dreamlike Pictures Comprehensively Improve Safety Measures](https://mlsanity.com/paper/2112.05135/) (2021)
- [Perspective Fields for Single Image Camera Calibration](https://mlsanity.com/paper/2212.03239/) (2022)
- [From Open Set to Closed Set: Counting Objects by Spatial Divide-and-Conquer](https://mlsanity.com/paper/1908.06473/) (2019)
- [ImageNet-X: Understanding Model Mistakes with Factor of Variation Annotations](https://mlsanity.com/paper/2211.01866/) (2022)
- [Zolly: Zoom Focal Length Correctly for Perspective-Distorted Human Mesh Reconstruction](https://mlsanity.com/paper/2303.13796/) (2023)
- [DeepSportradar-v1: Computer Vision Dataset for Sports Understanding with High Quality Annotations](https://mlsanity.com/paper/2208.08190/) (2022)
- [Learning Spatial Awareness to Improve Crowd Counting](https://mlsanity.com/paper/1909.07057/) (2019)
- [NAS-Count: Counting-by-Density with Neural Architecture Search](https://mlsanity.com/paper/2003.00217/) (2020)
- [Surround-view Fisheye Camera Perception for Automated Driving: Overview, Survey and Challenges](https://mlsanity.com/paper/2205.13281/) (2022)
- [FishEyeRecNet: A Multi-Context Collaborative Deep Network for Fisheye Image Rectification](https://mlsanity.com/paper/1804.04784/) (2018)
- [ImageNet-E: Benchmarking Neural Network Robustness via Attribute Editing](https://mlsanity.com/paper/2303.17096/) (2023)

## Built on by (most cited first, 2 of 2)

- [AdapToPASS: Ambiguity-aware Adaptive Spherical Transformer for Panoramic Semantic Segmentation](https://mlsanity.com/paper/2608.29081/) (2026)
- [LCM: Log Conformal Maps for Robust Representation Learning to Mitigate Perspective Distortion](https://mlsanity.com/paper/2410.03686/) (2024)

## Abstract (arXiv)

Perspective distortion (PD) causes unprecedented changes in shape, size, orientation, angles, and other spatial relationships of visual concepts in images. Precisely estimating camera intrinsic and extrinsic parameters is a challenging task that prevents synthesizing perspective distortion. Non-availability of dedicated training data poses a critical barrier to developing robust computer vision methods. Additionally, distortion correction methods make other computer vision tasks a multi-step approach and lack performance. In this work, we propose mitigating perspective distortion (MPD) by employing a fine-grained parameter control on a specific family of M"obius transform to model real-world distortion without estimating camera intrinsic and extrinsic parameters and without the need for actual distorted data. Also, we present a dedicated perspectively distorted benchmark dataset, ImageNet-PD, to benchmark the robustness of deep learning models against this new dataset. The proposed method outperforms existing benchmarks, ImageNet-E and ImageNet-X. Additionally, it significantly improves performance on ImageNet-PD while consistently performing on standard data distribution. Notably, our method shows improved performance on three PD-affected real-world applications crowd counting, fisheye image recognition, and person re-identification and one PD-affected challenging CV task: object detection. The source code, dataset, and models are available on the project webpage at https://prakashchhipa.github.io/projects/mpd.