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Affine Steerers for Structured Keypoint Description

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Computer Vision – ECCV 2024 (ECCV 2024)

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Abstract

We propose a way to train deep learning based keypoint descriptors that makes them approximately equivariant for locally affine transformations of the image plane. The main idea is to use the representation theory of GL(2) to generalize the recently introduced concept of steerers from rotations to affine transformations. Affine steerers give high control over how keypoint descriptions transform under image transformations. We demonstrate the potential of using this control for image matching. Finally, we propose a way to finetune keypoint descriptors with a set of steerers on upright images and obtain state-of-the-art results on several standard benchmarks. Code will be published at github.com/georg-bn/affine-steerers.

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Notes

  1. 1.

    In practice, image warps corresponding to camera motions are piecewise continuous and piecewise differentiable. The discontinuities stem from motion boundaries, which we will ignore in the theoretical part of this paper.

  2. 2.

    An irrep on V is a representation that does not leave any proper subspace \(W\subset V\) invariant. Irreps can be thought of as fundamental building blocks of representations as many general representations can be decomposed into irreps. However, for \(\textrm{GL}(2)\), not all representations can be built out of its irreps. The standard counterexample is  [63, Example 4.11].

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Acknowledgements

This work was supported by the Wallenberg Artificial Intelligence, Autonomous Systems and Software Program (WASP), funded by the Knut and Alice Wallenberg Foundation and by the strategic research environment ELLIIT, funded by the Swedish government. The computational resources were provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) at C3SE, partially funded by the Swedish Research Council through grant agreement no. 2022-06725, and by the Berzelius resource, provided by the Knut and Alice Wallenberg Foundation at the National Supercomputer Centre.

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Authors and Affiliations

  1. Chalmers University of Technology, Gothenburg, Sweden

    Georg Bökman & Fredrik Kahl

  2. Linköping University, Linköping, Sweden

    Johan Edstedt & Michael Felsberg

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  1. Georg Bökman
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  2. Johan Edstedt
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  3. Michael Felsberg
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  4. Fredrik Kahl
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Correspondence to Georg Bökman .

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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, Hessen, Germany

    Stefan Roth

  4. Princeton University, Palo Alto, CA, 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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Bökman, G., Edstedt, J., Felsberg, M., Kahl, F. (2025). Affine Steerers for Structured Keypoint Description. 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 15144. Springer, Cham. https://doi.org/10.1007/978-3-031-73016-0_26

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