Robust reconstruction of 2D curves from scattered noisy point data

• We propose a robust 2D reconstruction method from unorganized noisy point data.
• The outliers and noise of data can be effectively detected and smoothed.
• Sharp corners are preserved properly in the output curves with our method.

In this paper, a robust algorithm is proposed for reconstructing 2D curve from unorganized point data with a high level of noise and outliers. By constructing the quadtree of the input point data, we extract the “grid-like” boundaries of the quadtree, and smooth the boundaries using a modified Laplacian method. The skeleton of the smoothed boundaries is computed and thereby the initial curve is generated by circular neighboring projection. Subsequently, a normal-based processing method is applied to the initial curve to smooth jagged features at low curvatures areas, and recover sharp features at high curvature areas. As a result, the curve is reconstructed accurately with small details and sharp features well preserved. A variety of experimental results demonstrate the effectiveness and robustness of our method.