A PDE formulation for viscous morphological operators with extensions to intensity-adaptive operators
Petros Maragos, Corinne Vachier · 2008
Viscous morphological operators have shown very good performance in regularizing various image analysis tasks such as detection of intensity-varying boundaries and segmentation. This paper presents a novel formulation of viscous morphological operators as solutions of nonlinear partial differential equations (PDEs) of the hyperbolic type with level-varying speed. Efficient numerical algorithms are also developed to solve these PDEs and generate the viscous operations. It also generalizes the viscous operators by studying the class of intensity level-varying operators, of which special cases are intensity adaptive connected operators such as volume openings and viscous reconstruction filters. We present both theoretical aspects and applications of the above ideas. Index Terms — Morphological operations, Adaptive filters, Partial differential equations. 1.