The Length of Digital Curves

The paper discusses one of the elementary subjects in image analysis: how to measure the length of a digital curve? A digital curve in the plane is defined to be a cycle given either as an alternating sequence of vertices and edges, or an alternating sequence of edges and squares. The paper reports about two length estimators, one based on the partition of a frontier of a simply-connected isothetic polygon into digital straight segments, and one based on calculating the minimum-length polygon within an open boundary of a simply-connected isothetic polygon. Both techniques are known to be implementations of convergent estimators of the perimeter of bounded, polygonal or smooth convex sets in the euclidean plane. For each technique a linear-time algorithm is specified, and both algorithms are compared with respect to convergence speed and number of generated segments. The experiments show convergent behavior also for perimeters of non-convex bounded subsets of the euclidean plane. 1 The University of Auckland, Computer Science Department, CITR, Tamaki Campus, Glen Innes, Auckland, New Zealand The Length of Digital Curves Reinhard Klette and Ben Yip CITR Tamaki, University of Auckland Tamaki Campus, Building 731, Auckland, New Zealand Abstract. The paper discusses one of the elementary subjects in image analysis: how to measure the length of a digital curve? A digital curve in the plane is de ned to be a cycle given either as an alternating sequence of vertices and edges, or an alternating sequence of edges and squares. The paper reports about two length estimators, one based on the partition of a frontier of a simply-connected isothetic polygon into digital straight segments, and one based on calculating the minimumlength polygon within an open boundary of a simply-connected isothetic polygon. Both techniques are known to be implementations of convergent estimators of the perimeter of bounded, polygonal or smooth convex sets in the euclidean plane. For each technique a linear-time algorithm is speci ed, and both algorithms are compared with respect to convergence speed and number of generated segments. The experiments show convergent behavior also for perimeters of non-convex bounded subsets of the euclidean plane. The paper discusses one of the elementary subjects in image analysis: how to measure the length of a digital curve? A digital curve in the plane is de ned to be a cycle given either as an alternating sequence of vertices and edges, or an alternating sequence of edges and squares. The paper reports about two length estimators, one based on the partition of a frontier of a simply-connected isothetic polygon into digital straight segments, and one based on calculating the minimumlength polygon within an open boundary of a simply-connected isothetic polygon. Both techniques are known to be implementations of convergent estimators of the perimeter of bounded, polygonal or smooth convex sets in the euclidean plane. For each technique a linear-time algorithm is speci ed, and both algorithms are compared with respect to convergence speed and number of generated segments. The experiments show convergent behavior also for perimeters of non-convex bounded subsets of the euclidean plane.