Non-linearization of free Schrödinger equation and pseudo-morphological complex diffusion operators

Jesus Angulo (1)

1 CMM - Centre de Morphologie Mathématique

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 Schrödinger 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.

Mots clés: Complex filters; Diffusion operators; Dilation/erosion; Dinger equation; Fundamental equations; Image filtering; Laplacians; Physical model; Theoretical result; Diffusion; Image processing; Linearization; Mathematical operators; Nonlinear equations; Mathematical morphology

Domaines: Informatique [cs]; Traitement des images [eess.IV]; Mathématiques [math]; Traitement d'image

Jesus Angulo. Non-linearization of free Schrödinger equation and pseudo-morphological complex diffusion operators. 18th IEEE International Conference on Image Processing (ICIP), Sep 2011, Bruxelles, Belgium. pp.73-76, ⟨10.1109/ICIP.2011.6116660⟩. ⟨hal-00834436⟩