Measuring linearity of open planar curve segments

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Žunić, J. ; Rosin, Paul L. (2011)

In this paper we define a new linearity measure for open planar curve segments. We start with the integral of the squared distances between all the pairs of points belonging to the measured curve segment, and show that, for curves of a fixed length, such an integral reaches its maximum for straight line segments. We exploit this nice property to define a new linearity measure for open curve segments. The new measure ranges over the interval (0, 1], and produces the value 1 if and only if the measured open line is a straight line segment. The new linearity measure is invariant with respect to translations, rotations and scaling transformations. Furthermore, it can be efficiently and simply computed using line moments. Several experimental results are provided in order to illustrate the behaviour of the new measure.
  • References (37)
    37 references, page 1 of 4

    [1] S. Benhamou. How to reliably estimate the tortuosity of an animal's path: Straightness, sinuosity, or fractal dimension. Journal of Theoretical Biology, 229(2):209-220, 2004.

    [2] E. Bullitt, G. Gerig, S.M. Pizer, W. Lin, and S.R. Aylward. Measuring tortuosity of the intracerebral vasculature. IEEE Trans. Med. Imaging, 22(9):1163-1171, 2003.

    [3] C.-C. Chen. Improved moment invariants for shape discrimination. Pattern Recognition, 26(5):683-686, 1993.

    [4] D. Coeurjolly and R. Klette. A comparative evaluation of length estimators of digital curves. IEEE Trans. on Patt. Anal. and Mach. Intell., 26(2):252-257, 2004.

    [5] A. El-ghazal, O. Basir, and S. Belkasim. Farthest point distance: A new shape signature for Fourier descriptors. Signal Processing: Image Communication, 24(7):572-586, 2009.

    [6] S. Escalera, A. Forn´es, O. Pujol, J. Llad´os, and P. Radeva. Circular blurred shape model for multiclass symbol recognition. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 41(2):497-506, 2011.

    [7] T. Gautama, D.P. Mandi´c, and M.M. Van Hull. A novel method for determining the nature of time series. IEEE Transactions on Biomedical Engineering, 51(5):728-736, 2004.

    [8] T. Gautama, D.P. Mandi´c, and M.M. Van Hulle. Signal nonlinearity in fMRI: A comparison between BOLD and MION. IEEE Transactions on Medical Images, 22(5):636-644, 2003.

    [9] E. Grisan, M. Foracchia, and A. Ruggeri. A novel method for the automatic grading of retinal vessel tortuosity. IEEE Trans. Med. Imaging, 27(3):310-319, 2008.

    [10] M. Hu. Visual pattern recognition by moment invariants. IRE Trans. Inf. Theory, 8(2):179-187, 1962.

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