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.
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References
Cai, J., Walker, R., 2010. Height estimation from monocular image sequences using dynamic programming with explicit occlusions. IET Comput. Vis., 4(3):149–161. [doi:10.1049/iet-cvi.2009.0063]
Coeurjolly, D., Klette, R., 2004. A comparative evaluation of length estimators of digital curves. IEEE Trans. Pattern Anal. Mach. Intell., 26(2):252–258. [doi:10.1109/TPAMI.2004.1262194]
Deng, H., Himed, B., Wicks, M.C., 2006. Image feature based space-time processing for ground moving target detection. IEEE Signal Process. Lett., 13(4):216–219. [doi:10.1109/LSP.2005.863676]
Dyer, S.A., Dyer, J.S., 2001. Cubic-spline interpolation. 1. IEEE Instrum. Meas. Mag., 4(1):44–46. [doi:10.1109/5289.911175]
Foteinopoulos, P., 2009. Cubic spline interpolation to develop contours of large reservoirs and evaluate area and volume. Adv. Eng. Softw., 40(1):23–29. [doi:10.1016/j.advengsoft.2008.03.005]
Freeman, H., 1961. On the encoding of arbitrary geometric configurations. IRE Trans. Electron. Comput., 10(2):260–268. [doi:10.1109/TEC.1961.5219197]
Klette, R., Kovalevsky, V.V., Yip, B., 1999. Length estimation of digital curves. SPIE, 3811:117–128. [doi:10.1117/12.364118]
Lachaud, J.O., Provençal, X., 2011. Two linear-time algorithms for computing the minimum length polygon of a digital contour. Discr. Appl. Math., 159(18):2229–2250. [doi:10.1016/j.dam.2011.08.002]
Sladoje, N., Lindblad, J., 2009. High-precision boundary length estimation by utilizing gray-level information. IEEE Trans. Pattern Anal. Mach. Intell., 31(2):357–363. [doi:10.1109/TPAMI.2008.184]
Suhadolnik, A., Petrišič, J., Kosel, F., 2010. Digital curve length calculation by using B-spline. J. Math. Imag. Vis., 38(2):132–138. [doi:10.1007/s10851-010-0208-4]
Tadrous, P.J., 2010. On the concept of objectivity in digital image analysis in pathology. Pathology, 42(3):207–211. [doi:10.3109/00313021003641758]
Zhang, M., Mou, X., Zhang, L., 2011. Non-shift edge based ratio (NSER): an image quality assessment metric based on early vision features. IEEE Signal Process. Lett., 18(5):315–318. [doi:10.1109/LSP.2011.2127473]
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Project supported by the National Natural Science Foundation of China (Nos. 61170092, 61133011, 61272208, 61103091, and 61202308) and the Fundamental Research Funds for the Central Universities, China (Nos. 450060445674 and 450060481512)
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Wang, Zx., Ouyang, Jh. Curve length estimation based on cubic spline interpolation in gray-scale images. J. Zhejiang Univ. - Sci. C 14, 777–784 (2013). https://doi.org/10.1631/jzus.C1300056
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DOI: https://doi.org/10.1631/jzus.C1300056