Brief paper: Gradient algorithms for polygonal approximation of convex contours

  • Authors:

  • Sara Susca;Francesco Bullo;Sonia Martínez

  • Affiliations:

  • Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, 93106-5070, USA;Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA, 93106-5070, USA;Mechanical and Aerospace Engineering Department, University of California at San Diego, 9500 Gilman Dr, La Jolla, CA, 92093-0411, USA

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2009

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Abstract

The subjects of this paper are descent algorithms to optimally approximate a strictly convex contour with a polygon. This classic geometric problem is relevant in interpolation theory and data compression, and has potential applications in robotic sensor networks. We design gradient descent laws for intuitive performance metrics such as the area of the inner, outer, and ''outer minus inner'' approximating polygons. The algorithms position the polygon vertices based on simple feedback ideas and on limited nearest-neighbor interaction.