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Combinatorial Bounds and Algorithmic Aspects of Image Matching under Projective Transformations

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Mathematical Foundations of Computer Science 2008 (MFCS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5162))

Abstract

Image matching is an important problem in image processing and arises in such diverse fields as video compression, optical character recognition, medical imaging, watermarking etc. Given two images, image matching determines a transformation that changes the first image such that it most closely resembles the second. Common approaches require either exponential time, or find only an approximate solution, even when only rotations and scalings are allowed. This paper provides the first general polynomial time algorithm to find the exact solution to the image matching problem under projective, affine or linear transformations. Subsequently, nontrivial lower bounds on the number of different transformed images are given which roughly induce the complexity of image matching under the three classes of transformations.

Supported by DFG research grant RE 672/5-1.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Rostock, Germany

    Christian Hundt

  2. Institut für Theoretische Informatik, Universität zu Lübeck, Germany

    Maciej Liśkiewicz

Authors
  1. Christian Hundt
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  2. Maciej Liśkiewicz
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Edward Ochmański Jerzy Tyszkiewicz

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Hundt, C., Liśkiewicz, M. (2008). Combinatorial Bounds and Algorithmic Aspects of Image Matching under Projective Transformations. In: Ochmański, E., Tyszkiewicz, J. (eds) Mathematical Foundations of Computer Science 2008. MFCS 2008. Lecture Notes in Computer Science, vol 5162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85238-4_32

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  • DOI: https://doi.org/10.1007/978-3-540-85238-4_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85237-7

  • Online ISBN: 978-3-540-85238-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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