Convergence criteria for iterative nonlinear filters

The authors present a general theory for the convergence of iterative nonlinear filters. An introduction to lattice theory is provided, and the theory of mathematical morphology is presented in the context of lattice theory. An important form of a nonlinear filter is provided by the iteration of the original nonlinear filter. The result of repeated iteration of a convergent nonlinear filter is called a root of the filter. In many cases, the root of a nonlinear filter is a particularly desired outcome (e.g., median filter). Conditions for the convergence of the iteration of a nonlinear filter are proposed