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Scale-Covariant and Scale-Invariant Gaussian Derivative Networks

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Scale Space and Variational Methods in Computer Vision (SSVM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12679))

Abstract

This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the learnt parameters between multiple scale channels, and by using the transformation properties of the scale-space primitives under scaling transformations, the resulting network becomes provably scale covariant. By in addition performing max pooling over the multiple scale channels, a resulting network architecture for image classification also becomes provably scale invariant. We investigate the performance of such networks on the MNISTLargeScale dataset, which contains rescaled images from original MNIST over a factor of 4 concerning training data and over a factor of 16 concerning testing data. It is demonstrated that the resulting approach allows for scale generalization, enabling good performance for classifying patterns at scales not present in the training data.

The support from the Swedish Research Council (contract 2018-03586) is gratefully acknowledged.

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Authors and Affiliations

  1. Computational Brain Science Lab, Division of Computational Science and Technology, KTH Royal Institute of Technology, Stockholm, Sweden

    Tony Lindeberg

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  1. Tony Lindeberg
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Correspondence to Tony Lindeberg .

Editor information

Editors and Affiliations

  1. UNICAEN, GREYC – Normandy University, Caen, France

    Abderrahim Elmoataz

  2. ENSICAEN, GREYC – Normandy University, Caen, France

    Jalal Fadili

  3. CNRS, GREYC – Normandy University, Caen, France

    Yvain Quéau

  4. UNICAEN, GREYC – Normandy University, Caen, France

    Julien Rabin

  5. ENSICAEN, GREYC – Normandy University, Caen, France

    Loïc Simon

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Lindeberg, T. (2021). Scale-Covariant and Scale-Invariant Gaussian Derivative Networks. In: Elmoataz, A., Fadili, J., Quéau, Y., Rabin, J., Simon, L. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2021. Lecture Notes in Computer Science(), vol 12679. Springer, Cham. https://doi.org/10.1007/978-3-030-75549-2_1

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  • DOI: https://doi.org/10.1007/978-3-030-75549-2_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-75548-5

  • Online ISBN: 978-3-030-75549-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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