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Classification of Curves in 2D and 3D via Affine Integral Signatures

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Abstract

We propose new robust classification algorithms for planar and spatial curves subjected to affine transformations. Our motivation comes from the problems in computer image recognition. To each planar or spatial curve, we assign a planar signature curve. Curves, equivalent under an affine transformation, have the same signature. The signatures are based on integral invariants, which are significantly less sensitive to small perturbations of curves and noise than classically known differential invariants. Affine invariants are derived in terms of Euclidean invariants. We present two types of signatures: the global and the local signature. Both signatures are independent of curve parameterization. The global signature depends on a choice of the initial point and, therefore, cannot be used for local comparison. The local signature, albeit being slightly more sensitive to noise, is independent of the choice of the initial point and can be used to solve local equivalence problem. An experiment that illustrates robustness of the proposed signatures is presented.

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Authors and Affiliations

  1. ECE Department, North Carolina State University, Raleigh, NC, 27695-7914, USA

    Shuo Feng & Hamid Krim

  2. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695-8205, USA

    Irina Kogan

Authors
  1. Shuo Feng
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  2. Irina Kogan
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  3. Hamid Krim
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Correspondence to Shuo Feng.

Additional information

I.A. Kogan is supported in part by National Science Foundation (NSF) grant #0728801. H. Krim is supported in part by Air Force Office of Scientific Research (AFOSR) grant #F49620-98-1-0190.

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Feng, S., Kogan, I. & Krim, H. Classification of Curves in 2D and 3D via Affine Integral Signatures. Acta Appl Math 109, 903–937 (2010). https://doi.org/10.1007/s10440-008-9353-9

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  • DOI: https://doi.org/10.1007/s10440-008-9353-9

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