Minimum-Length Polygons in Approximation Sausages

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. 1 School of Information Science, JAIST, Asahidai, Tatsunokuchi, 923-1292, Japan 2 CITR, University of Auckland Tamaki Campus, Building 731, Auckland, New Zealand. Minimum-Length Polygons in Approximation Sausages Tetsuo Asano, Yasuyuki Kawamura, Reinhard Klette, and Koji Obokata 1 School of Information Science, JAIST Asahidai, Tatsunokuchi, 923-1292 Japan [email protected] 2 CITR, University of Auckland, Tamaki Campus, Building 731 Auckland, New Zealand [email protected] Abstract. The paper introduces a new approximation scheme for planar digital curves. This scheme de nes 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 ner and ner 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 veri ed through experiments on various convex and non-convex curves. Experimental comparisons with two existing schemes have also been made. The paper introduces a new approximation scheme for planar digital curves. This scheme de nes 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 ner and ner 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 veri ed through experiments on various convex and non-convex curves. Experimental comparisons with two existing schemes have also been made.