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B-spline Curve Fitting by Diagonal Approximation BFGS Methods

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Abstract

Fitting of data points by a B-spline curve is demanded in many applications in computer graphics, computer vision, CAD/CAM, and image processing. In this paper, we use approximation BFGS Methods to solve the associated nonlinear least square optimization problem and present an approach for inserting further control points of the B-spline curve. Differently from the traditional methods, the proposed technique optimizes the l control points and the N foot points simultaneously, as in Zheng et al. (Comput Aided Geometr Des 29(7):448–462, 2012), Speer et al. (Comput Aided Geometr Des 15(9):869–877, 1998). The complexity per step of our technique is O(n), where \(n=l+N\), and it requires only O(n) memory allocations. Our experimental results show the usefulness of the method for complicated shapes with a large number of data points, confirming the theoretical results.

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Acknowledgements

The authors would like to thanks anonymous referees for their helpful comments and useful suggestions.

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Authors and Affiliations

  1. Computer Geometry and Dynamical Systems Laboratory, Faculty of Mathematical Sciences, Yazd University, Yazd, Iran

    A. Ebrahimi & G. B. Loghmani

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  1. A. Ebrahimi
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  2. G. B. Loghmani
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Correspondence to G. B. Loghmani.

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Ebrahimi, A., Loghmani, G.B. B-spline Curve Fitting by Diagonal Approximation BFGS Methods. Iran J Sci Technol Trans Sci 43, 947–958 (2019). https://doi.org/10.1007/s40995-017-0347-1

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  • DOI: https://doi.org/10.1007/s40995-017-0347-1

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