Smoothing a network of planar polygonal lines obtained with vectorization

Abstract

A new method of smoothing polygonal lines obtained as the result of vectorization and creating the network is suggested. This method performs not only smoothing but also filtering of vectorization errors taking into account that these errors appear not only as the errors of vertices but as errors of node coordinates as well. An important part of this algorithm is a technique of building piecewise polynomial base functions for local approximation of the polylines of the network. The suggested algorithm has a linear computational complexity for exponential weight functions. The necessity of using finite weight functions is shown. Algorithms of calculating tangents and curvatures are derived. Shrinking errors and errors of parameters are analyzed. A method of compensation of the shrinking errors is suggested and how to do smoothing with variable intensity is shown. © 2008 Springer-Verlag Berlin Heidelberg.