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Edge detection by spherical separation

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  • A. Astorino
  • M. Gaudioso
  • W. Khalaf

Abstract

We describe an optimization-based method for tackling the classic image processing problem known as edge detection and we formulate it in the form of a classification one. The novelty of the approach is in the use of spherical separation as a classification tool in the image processing framework. Spherical separation consists in separating by means of a sphere two given discrete point-sets in a finite dimensional Euclidean space; in our context the two sets are the edge points and the non-edge points, respectively, in the digital representation of a given image. Assuming that the center of the sphere is fixed, the problem reduces to the minimization of a convex and nonsmooth function of just one variable, which can be effectively solved by means of an “ad hoc” bisection method. The results of our experiments on some edge detection benchmark images are provided. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • A. Astorino & M. Gaudioso & W. Khalaf, 2014. "Edge detection by spherical separation," Computational Management Science, Springer, vol. 11(4), pages 517-530, October.
    • Handle: RePEc:spr:comgts:v:11:y:2014:i:4:p:517-530
    DOI: 10.1007/s10287-013-0193-3
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    References listed on IDEAS

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    1. A. Astorino & M. Gaudioso, 2009. "A fixed-center spherical separation algorithm with kernel transformations for classification problems," Computational Management Science, Springer, vol. 6(3), pages 357-372, August.
    2. Peng Sun & Robert M. Freund, 2004. "Computation of Minimum-Volume Covering Ellipsoids," Operations Research, INFORMS, vol. 52(5), pages 690-706, October.
    3. A. Astorino & A. Fuduli & M. Gaudioso, 2010. "DC models for spherical separation," Journal of Global Optimization, Springer, vol. 48(4), pages 657-669, December.
    4. Annabella Astorino & Antonio Fuduli & Manlio Gaudioso, 2012. "Margin maximization in spherical separation," Computational Optimization and Applications, Springer, vol. 53(2), pages 301-322, October.
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