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A two step procedure for removing noise from polygonal shapes is presented here. The first step is the removal of vertices by linear and different nonlinear inverse diffusion filters. In the second step we apply the triangle method which identifies least dominant vertices from the polygon obtained from the first stage. Those vertices whose adjacent sides form triangles of the smallest area are defined as least dominant and most likely to be noise. A thorough testing of this method on the shapes typical in video images demonstrates that it successfully removes noise vertices while it preserves dominant ones.