EVOLUTION-EQUATIONS FOR CONTINUOUS-SCALE MORPHOLOGICAL FILTERING

Multiscale signal analysis has recently emerged as a useful framework for many computer vision and signal processing tasks. Morphological fi lters can be used to develop nonlinear multiscale operations that have certain advantages over linear multiscale approaches in that they pre serve important signal features such as edges. In this paper, we discu ss several nonlinear partial differential equations that model the sca le evolution associated with continuous-space multiscale morphological erosions, dilations, openings, and closings. These equations relate t he rate of change of the multiscale signal ensemble as scale increases to a nonlinear operator acting on the space of signals. The nonlinear operator is characterized by the shape and dimensionality of the stru cturing element used by the morphological operators, generally taking the form of a nonlinear function of certain partial differential opera tors.