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Möbius Transform for Mitigating Perspective Distortions in Representation Learning

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Computer Vision – ECCV 2024 (ECCV 2024)

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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 Möbius 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.

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Acknowledgment

The authors thank Sumit Rakesh, Luleå University of Technology, for his support with the Lotty Bruzelius cluster. We also thank the National Supercomputer Centre at Linköping University for the Berzelius supercomputing, supported by the Knut and Alice Wallenberg Foundation.

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Authors and Affiliations

  1. Luleå Tekniska Universitet, Luleå, Sweden

    Prakash Chandra Chhipa, Meenakshi Subhash Chippa, Rajkumar Saini & Marcus Liwicki

  2. Fraunhofer Heinrich-Hertz-Institut, Berlin, Germany

    Kanjar De

  3. University of Central Florida, Orlando, USA

    Mubarak Shah

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  1. Prakash Chandra Chhipa
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  2. Meenakshi Subhash Chippa
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  3. Kanjar De
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  4. Rajkumar Saini
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  5. Marcus Liwicki
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  6. Mubarak Shah
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Corresponding author

Correspondence to Prakash Chandra Chhipa .

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Editors and Affiliations

  1. University of Birmingham, Birmingham, UK

    Aleš Leonardis

  2. University of Trento, Trento, Italy

    Elisa Ricci

  3. Technical University of Darmstadt, Darmstadt, Germany

    Stefan Roth

  4. Princeton University, Princeton, NJ, USA

    Olga Russakovsky

  5. Czech Technical University in Prague, Prague, Czech Republic

    Torsten Sattler

  6. École des Ponts ParisTech, Marne-la-Vallée, France

    Gül Varol

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Chhipa, P.C., Chippa, M.S., De, K., Saini, R., Liwicki, M., Shah, M. (2025). Möbius Transform for Mitigating Perspective Distortions in Representation Learning. In: Leonardis, A., Ricci, E., Roth, S., Russakovsky, O., Sattler, T., Varol, G. (eds) Computer Vision – ECCV 2024. ECCV 2024. Lecture Notes in Computer Science, vol 15131. Springer, Cham. https://doi.org/10.1007/978-3-031-73464-9_21

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