Image convergence under two dimensional separable median filtering

The two dimensional median filter has recently become popular as a technique to smooth images without rounding edges. The root structures (image segments invariant to filtering) of these nonlinear operations are important to the understanding of this filter´s properties. The root structures of the two dimensional separable median filter have been developed and will be presented here. In addition, it has been proven that with some rare exceptions any two dimensional image will converge to such a root structure under repetitive passes of the separable median filter.