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

TL;DR

This paper introduces a novel M"obius transform-based method to mitigate perspective distortions in images, improving robustness of vision models without needing camera parameters or distorted training data.

Contribution

It proposes a new approach using a specific family of M"obius transforms for distortion correction, along with a benchmark dataset, enhancing model robustness against perspective distortions.

Findings

Outperforms existing benchmarks like ImageNet-E and ImageNet-X

Improves performance on real-world PD-affected applications

Enhances object detection under perspective distortions

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.