Journal of Zhejiang University SCIENCE C

, Volume 14, Issue 10, pp 777–784 | Cite as

Curve length estimation based on cubic spline interpolation in gray-scale images



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 

CLC number



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Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.College of Computer Science and TechnologyJilin UniversityChangchunChina
  2. 2.MOE Key Laboratory of Symbolic Computation and Knowledge EngineeringJilin UniversityChangchunChina

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