Abstract: This paper deals with a novel local arc length estimator for curves in gray-scale images. The method first estimates a cubic spline curve fit for the boundary points using the gray-level information of the nearby pixels, and then computes the sum of the spline segments’ lengths. In this model, the second derivatives and y coordinates at the knots are required in the computation; the spline polynomial coefficients need not be computed explicitly. We provide the algorithm pseudo code for estimation and preprocessing, both taking linear time. Implementation shows that the proposed model gains a smaller relative error than other state-of-the-art methods.

Key words: Arc length estimation, Cubic spline interpolation, Gray-scale image, Local algorithm

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