Different non-linear diffusion filters combined with triangle method used for noise removal from polygonal shapes

A two-step process for removing noise from polygonal shapes is presented in this study. The authors present a polygonal shape as its turning function and then apply a non-linear diffusion filter and a triangle method on it. In the first step the authors apply several different non-linear diffusion filters on the turning function and compare the performance of these filters later. Non-linear diffusion filters identify dominant vertices in a polygon and remove those vertices that are identified as noise or irrelevant features. The vertices in the turning function which diffuse until the sides that immediately surround them approach the same turning function are identified as noise and removed. The vertices that are enhanced are preserved without changing their coordinates and they are identified as dominant ones. After the authors carry this process as far as it will go without introducing noticeable shape distortion, and switch to the triangle method for further removal of vertices that are to be treated as noise. In the second step the authors remove the vertices that form the smallest area triangles. The authors submit experimental results of the tests that demonstrate that this two-step process successfully removes vertices that should be dismissed as noise while preserving dominant vertices that can be accepted as relevant features and give a faithful description of the shape of the polygon. In experimental tests of this procedure the authors demonstrate successful removal of noise and excellent preservation of shape, thanks to appropriate emphasis of dominant vertices.