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Žunić, J.; Rosin, Paul L. (2011)
Publisher: Elsevier
Languages: English
Types: Article
Subjects: QA75
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.
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    • [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.
    • [11] M.N. Huxley. Exponential sums and lattice points III. Proc. London Math. Soc., 87(3):591-609, 2003.
    • [12] A.R. Imre. Fractal dimension of time-indexed paths. Applied Mathematics and Computation, 207(1):221-229, 2009.
    • [13] R. Kakarala. Testing for convexity with Fourier descriptors. Electronics Letters, 34(14):1392-1393, 1998.
    • [14] R. Klette and A. Rosenfeld. Digital Geometry. Morgan Kaufmann, San Francisko, 2004.
    • [15] R. Klette and J. Zˇuni´c. Digital approximation of moments of convex regions. Graphical Models and Image Processing, 61(5):274-298, 1999.
    • [16] S. Manay, D. Cremers, B.-W. Hong, A. Yezzi, and S. Soatto. Integral invariants for shape matching. IEEE Trans. on Patt. Anal. and Mach. Intell., 28(10):1602-1618, 2006.
    • [17] R. Melter, I. Stojmenovi´c, and J. Zˇuni´c. A new characterization of digital lines by least square fits. Pattern Recognition Letters, 14(2):83-88, 1993.
    • [18] W. Mio, A. Srivastava, and S.H. Joshi. On shape of plane elastic curves. Int. Journal of Computer Vision, 73(3):307-324, 2007.
    • [19] M.E. Munich and P. Perona. Visual identification by signature tracking. IEEE Trans. on Patt. Anal. and Mach. Intell., 25(2):200-217, 2003.
    • [20] J.C. Perez and E. Vidal. Optimum polygonal approximation of digitized curves. Pattern Recognition Letters, 15(3):743-750, 1994.
    • [21] E. Rahtu, M. Salo, and J. Heikkil¨a. A new convexity measure based on a probabilistic interpretation of images. IEEE Trans. on Patt. Anal. and Mach. Intell., 28(9):1501- 1512, 2006.
    • [22] P.L. Rosin. Techniques for assessing polygonal approximations of curves. IEEE Trans. on Patt. Anal. and Mach. Intell., 19(6):659-666, 1997.
    • [23] P.L. Rosin and G.A.W. West. Non-parametric segmentation of curves into various representations. IEEE Trans. on Patt. Anal. and Mach. Intell., 17:1140-1153, 1995.
    • [24] C. Di Ruberto and A. Dempster. Circularity measures based on mathematical morphology. Electronics Letters, 36(20):1691-1693, 2000.
    • [25] M.P. Segundo, L. Silva, O.R.P. Bellon, and C.C. Queirolo. Automatic face segmentation and facial landmark detection in range images. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 40(5):1319-1330, 2010.
    • [26] X. Shu and X.-J. Wu. A novel contour descriptor for 2d shape matching and its application to image retrieval. Image and Vision Computing, 20(4):286-294, 2011.
    • [27] N. Sladoje and J. Lindblad. High precision boundary length estimation by utilizing gray-level information. IEEE Trans. on Patt. Anal. and Mach. Intell., 31(2):357-363, 2009.
    • [28] M. Sonka, V. Hlavac, and R. Boyle. Image Processing, Analysis, and Machine Vision. PWS, 1998.
    • [29] M. Stojmenovi´c and A. Nayak. Measuring linearity of ordered point sets. PSIVT 2007, Lecture Notes in Computer Science, 4872:274-288, 2007.
    • [30] M. Stojmenovi´c, A. Nayak, and J. Zˇuni´c. Measuring linearity of planar point sets. Pattern Recognition, 41(8):2503-2511, 2008.
    • [31] M. Stojmenovi´c and J. Zˇuni´c. Measuring elongation from shape boundary. Journal Mathematical Imaging and Vision, 30(1):73-85, 2008.
    • [32] V. Venkatraghavan, M. Agarwal, and A.K. Roy. Shape orientation pattern. IEEE Signal Processing Letters, 16(8):711-714, 2009.
    • [33] J. Zˇuni´c, K. Hirota, and P.L. Rosin. A Hu moment invariant as a shape circularity measure. Pattern Recognition, 43(1):47-57, 2010.
    • [34] J. Zˇuni´c, L. Kopanja, and P.L. Rosin. On the orientability of shapes. IEEE Transactions on Image Processing, 15(11):3478-3487, 2006.
    • [35] J. Zˇuni´c and C. Martinez-Ortiz. Linearity measure for curve segments. Applied Mathematics and Computation, 215(8):3098-3105, 2009.
    • [36] J. Zˇuni´c and P.L. Rosin. Rectilinearity meaurements for polygons. IEEE Trans. on Patt. Anal. and Mach. Intell., 25(9):1193-3200, 2003.
    • [37] D. Zhang and G. Lu. Study and evaluation of different Fourier methods for image retrieval. Image and Vision Computing, 23(1):3349, 2005.
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