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

Source: [M\\"obius Transform for Mitigating Perspective Distortions in Representation Learning](<https://www.sota2.com/research/paper/68fa74251e209131cea5ffe6>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T03:02:53.994Z

Authors: Prakash Chandra Chhipa, Meenakshi Subhash Chippa, Kanjar De, Rajkumar Saini, Marcus Liwicki, Mubarak Shah

Published: 2024-03-07T15:39:00.000Z

## Abstract

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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2405.02296>)

[PDF](<https://arxiv.org/pdf/2405.02296.pdf>)