2 results for Asano, Tetsuo

  • Minimum-Length Polygons In Approximation Sausages

    Asano, Tetsuo; Kawamura, Yasuyuki; Obokata, Koji (2001)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). The paper introduces a new approximation scheme for planar digital curves. This scheme defines an approximating sausage `around' the given digital curve, and calculates a minimum-length polygon in this approximating sausage. The length of the polygon is taken as an estimator for the length of the curve being the (unknown) preimage of the given digital curve. Assuming finer and finer grid resolution it is shown that this estimator converges to the true perimeter of an r-compact polygonal convex bounded set. This theorem provides theoretical evidence for practical convergence of the proposed method towards a `correct' estimation of the length of a curve. The validity of the scheme has been verified through experiments on various convex and non-convex curves. Experimental comparisons with two existing schemes have also been made.

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  • A New Approximation Scheme for Digital Objects and Curve Length Estimations

    Asano, Tetsuo; Kawamura, Yasuyuki; Obokata, Koji (2000)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). The paper introduces a new approximation scheme for planar digital curves. This scheme defines an approximating sausage 'around' the given digital curve, and calculates a minimum-length polygon in this approximating sausage. The length of this polygon is taken as an estimator for the length of the curve being the (unknown) preimage of the given digital curve. Assuming finer and finer grid resolution it is shown that this estimator converges to the true perimeter of an r-compact polygonal convex bounded set. This theorem provides theoretical evidence for practical convergence of the proposed method towards a `correct' estimation of the length of a curve.

    View record details