Reconstructing Smooth Curve from Noise Sampled Data

Reconstructing smooth curve from 2D noise sampled data is a very important issue in many fields, such as data processing, reverse engineering, and so on. In this paper, we present a novel method to reconstruct smooth curve approximating sampled data in plane, at the same time filtering noise in the data. Our method is constructed on a set of local piecewise polynomial approximations associated with a monotone, decreasing and positive weight function. The method first generates a polynomial approximation for each point of sampled data based on the least squares method, and then constructs weighted blending to a set of polynomial curves. As a result, a global smooth curve approximation finally can be obtained from the noise sampled data by our weighted blending technique. Experiment results show that our method is quick, robust and stable, and it can be used in dealing with 2D noise sampled data with various resolutions in a well performance. Keywords-curve reconstruction, least square fitting, weighted blending, filtering noise