Abstract
We report here on the problem of estimating a smooth planar curve γ: [0, T] → ℝ2 and its derivatives from an ordered sample of interpolation points γ(t 0), γ(t 1),...,γ(t i -1),γ(t i ),...,γ(t m -1),γ(t m ), where 0 = t 0 < t 1 <... < t i - 1 < t i <...< t m - 1 < t m = T, and the t i are not known precisely for 0 < i < m. Such situtation may appear while searching for the boundaries of planar objects or tracking the mass center of a rigid body with no times available. In this paper we assume that the distribution of t i coincides with more-or-less uniform sampling. A fast algorithm, yielding quartic convergence rate based on 4-point piecewise-quadratic interpolation is analysed and tested. Our algorithm forms a substantial improvement (with respect to the speed of convergence) of piecewise 3-point quadratic Lagrange intepolation [19] and [20]. Some related work can be found in [7]. Our results may be of interest in computer vision and digital image processing [5], [8], [13], [14], [17] or [24], computer graphics [1], [4], [9], [10], [21] or [23], approximation and complexity theory [3], [6], [16], [22], [26] or [27], and digital and computational geometry [2] and [15].
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Noakes, L., Kozera, R. (2002). Interpolating Sporadic Data. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds) Computer Vision — ECCV 2002. ECCV 2002. Lecture Notes in Computer Science, vol 2351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47967-8_41
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DOI: https://doi.org/10.1007/3-540-47967-8_41
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