Problems Of Medial Axis Of A Simple Polygon In GIS And Its Algorithm

The medial axis of a polygon is an important issue of geometry whose structure reflects the polygon's geometrical character. It has been used widely in the field of character recognition and computer vision, mean-while playing an important role in spatial analysis of GIS—road network detection, simplifying double-line-river into single-line-river in map generalization., delimitation and contour line interpolation etc.Domestic and oversea definitions of the axis of a simple polygon are compared in this paper, and their main characters are discussed respectively. Furthermore, it is pointed out that the medial axis is the locus of all centers of circles inside P that touch the boundary of P in two or more pints.For the raster format, the medial axis algorithm with the theory of inner distance transform of Map Algebra accounts for a perfect situation. For the vector format, the circumcenter and the barycenter methods based on constrained Delaunay Triangulations and the pure angle bisector method brought forward in the book named computation geometry -algorithm analysis and design are anatomized and it is found that the medial axes generated by the above methods are not the real axis/center line /distance isoline, but only alike them. It is conceptual mistake of axis of a polygon that brings great errors. Therefore the medial axis containing great errors is not qualified for those applications which need high precision.So, this paper puts forward a geometry method—double matching points algorithm which has rigorous theory and it is enough to satisfy many practical applications well.Generally, there are two goals in this subject: one is to escape from the pretty pass of the application of medial axis of polygon in GIS; another one is to study exact and efficient algorithm to fit for the use with high precision need.