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The paper deals with a generalization of the complex diffusion in order to introduce pseudo-morphological complex filters which mimic dilation/erosion operators. The non- linearization paradigm is based on the counter-harmonic mean. The physical model underlying complex diffusion is the free Schrodinger equation and consequently the proposed operators can be interpreted as the asymptotic "pseudo-morphological" solution of this fundamental equation. Theoretical results are illustrated with some image filtering examples.