Planar Curve Reconstruction from Unorganized Points through Field Representation

Curve reconstruction from a set of unorganized points plays an important role in the fields of reverse engineering and computer vision. In this paper, we assume that every point are charged, then the intensity of the electric field will reflect the distribution and shape of the point set. Projection of the main ridge curve of the field surface on plane can be taken as the reconstruction curve of the point set. To find the reconstruction curve, we can first choose an appropriate initial curve on the plane and move every point on this curve along the gradient direction of the field function. The limit position of this active curve is the reconstructed curve. This method is simple and easy to implement. Experiments show that the algorithm is an efficient way for curve reconstruction. It also does well when the data points are incomplete or a series of fixed points should be passed through by the reconstructed curve.