# LCM: Log Conformal Maps for Robust Representation Learning to Mitigate Perspective Distortion

arXiv: https://arxiv.org/abs/2410.03686 · HTML: https://mlsanity.com/paper/2410.03686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 31 references that are in the map.
- First posted on arXiv 20 Sep 2024.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [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)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [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)
- [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)
- [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)
- [Blind Geometric Distortion Correction on Images Through Deep Learning](https://mlsanity.com/paper/1909.03459/) (2019)
- [Camera Distortion-aware 3D Human Pose Estimation in Video with Optimization-based Meta-Learning](https://mlsanity.com/paper/2111.15056/) (2021)
- [PCLs: Geometry-aware Neural Reconstruction of 3D Pose with Perspective Crop Layers](https://mlsanity.com/paper/2011.13607/) (2020)
- [Learning Perspective Undistortion of Portraits](https://mlsanity.com/paper/1905.07515/) (2019)
- [Practical Wide-Angle Portraits Correction with Deep Structured Models](https://mlsanity.com/paper/2104.12464/) (2021)
- [CLIP-ReIdent: Contrastive Training for Player Re-Identification](https://mlsanity.com/paper/2303.11855/) (2023)
- [M"obius Transform for Mitigating Perspective Distortions in Representation Learning](https://mlsanity.com/paper/2405.02296/) (2024)

## Abstract (arXiv)

Perspective distortion (PD) leads to substantial alterations in the shape, size, orientation, angles, and spatial relationships of visual elements in images. Accurately determining camera intrinsic and extrinsic parameters is challenging, making it hard to synthesize perspective distortion effectively. The current distortion correction methods involve removing distortion and learning vision tasks, thus making it a multi-step process, often compromising performance. Recent work leverages the M"obius transform for mitigating perspective distortions (MPD) to synthesize perspective distortions without estimating camera parameters. M"obius transform requires tuning multiple interdependent and interrelated parameters and involving complex arithmetic operations, leading to substantial computational complexity. To address these challenges, we propose Log Conformal Maps (LCM), a method leveraging the logarithmic function to approximate perspective distortions with fewer parameters and reduced computational complexity. We provide a detailed foundation complemented with experiments to demonstrate that LCM with fewer parameters approximates the MPD. We show that LCM integrates well with supervised and self-supervised representation learning, outperform standard models, and matches the state-of-the-art performance in mitigating perspective distortion over multiple benchmarks, namely Imagenet-PD, Imagenet-E, and Imagenet-X. Further LCM demonstrate seamless integration with person re-identification and improved the performance. Source code is made publicly available at https://github.com/meenakshi23/Log-Conformal-Maps.