A new method of polyline approximation

Abstract

Many methods of a raw vectorization produce lines with redundant vertices. Therefore the results of vectorization usually need to be compressed. Approximating methods based on throwing out inessential vertices are widely disseminated. The result of using any of these methods is a polyline, the vertices of which are a subset of source polyline vertices. When the vertices of the source polyline contain noise, vertices of the result polyline will have the same noise. Reduction of vertices without noise filtering can disfigure the shape of the source polyline. We suggested a new optimal method of the piecewise linear approximation that produces noise filtering. Our method divides the source polyline into clusters and approximates each cluster with a straight line. Our optimal method of dividing polylines into clusters guarantees that the functional, which is the integral square error of approximation plus the penalty for each cluster, will be the minimum one. © Springer-Verlag 2004.