Interpolating Sporadic Data

• Authors: Lyle Noakes;Ryszard Kozera
• Venue: ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
• Year: 2002

We report here on the problem of estimating a smooth planar curve 驴 : [0, T] 驴 R2 and its derivatives from an ordered sample of interpolation points {驴(t0), 驴(t1),..., 驴(ti-1), 驴(ti),..., 驴(tm-1), 驴(tm)}, where 0 = t0 t1 ti-1 ti tm-1 tm = T, and the ti 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 ti 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].