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A Flexible Scheme for Constructing (Quasi-)Invariant Signal Representations

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Excursions in Harmonic Analysis, Volume 5

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

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Abstract

We describe a generic scheme for constructing signal representations that are (quasi-)invariant to perturbations of the domain. It is motivated from first principles and based on the preservation of topology under homeomorphisms. Under certain assumptions the resulting models can be used as direct plug ins to render an existing signal processing algorithm invariant. We show one concretization of the general scheme and develop it into a computational procedure that leads to applications in image processing and computer vision. The latter factorizes the n−dimensional problem into an ensemble of one-dimensional problems, which in turn can be reduced to proving the existence of paths in a graph. We show empirical results on real-world data in two important problems in computer vision, template matching and online tracking.

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Author information

Authors and Affiliations

  1. Siemens Corporate Technology, 755 College Road East, Princeton, NJ, USA

    Jan Ernst

Authors
  1. Jan Ernst
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Correspondence to Jan Ernst .

Editor information

Editors and Affiliations

  1. Norbert Wiener Center, University of Maryland, College Park, Maryland, USA

    Radu Balan

  2. Norbert Wiener Center, University of Maryland, College Park, Maryland, USA

    John J. Benedetto

  3. Norbert Wiener Center, University of Maryland, College Park, Maryland, USA

    Wojciech Czaja

  4. Norbert Wiener Center, University of Maryland, College Park, Maryland, USA

    Matthew Dellatorre

  5. Norbert Wiener Center, University of Maryland, College Park, Maryland, USA

    Kasso A. Okoudjou

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Ernst, J. (2017). A Flexible Scheme for Constructing (Quasi-)Invariant Signal Representations. In: Balan, R., Benedetto, J., Czaja, W., Dellatorre, M., Okoudjou, K. (eds) Excursions in Harmonic Analysis, Volume 5. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-54711-4_11

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