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Subimage sensitive eigenvalue spectra for image comparison

Can one hear what’s painted on a drum?

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Abstract

This publication is a contribution to basic research in image comparison using eigenvalue spectra as features. The differential-geometric approach of eigenvalue spectrum-based descriptors is naturally applicable to shape data, but so far little work has been done to transfer it to the setting of image data painted on a rectangle or general curved surface. We present a new semi-global feature descriptor that also contains information about geometry of shapes visible in the image. This may not only improve the performance of the resulting distance measures, but may even enable us to approach the partial matching problem using eigenvalue spectra, which were previously only considered as global feature descriptors. We introduce some concepts that are useful in designing and understanding the behaviour of similar fingerprinting algorithms for images (and surfaces) and discuss some preliminary results.

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Notes

  1. This is also the Hamiltonian of the Schrödinger equation for a quantum particle moving in a potential. Motion is described by the Laplacian and the potential is given by the perturbation term.

  2. Represented by the value \(0\).

  3. Value \(1\).

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Acknowledgments

This research was partially supported by the National German Academic Foundation.

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Authors and Affiliations

  1. Leibniz University Hannover, Hannover, Germany

    Benjamin Berger, Alexander Vais & Franz-Erich Wolter

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  1. Benjamin Berger
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  2. Alexander Vais
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  3. Franz-Erich Wolter
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Correspondence to Benjamin Berger.

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Berger, B., Vais, A. & Wolter, FE. Subimage sensitive eigenvalue spectra for image comparison. Vis Comput 31, 205–221 (2015). https://doi.org/10.1007/s00371-014-1038-y

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