A PDE formulation for viscous morphological operators with extensions to intensity-adaptive operators

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.