Evolution equations for continuous-scale morphology

Several nonlinear partial differential equations that model the scale evolution associated with continuous-space multiscale morphological erosions, dilations, openings, and closings are discussed. These systems relate the infinitesimal evolution of the multiscale signal ensemble in scale space to a nonlinear operator acting on the space of signals. The type of this nonlinear operator is determined by the shape and dimensionality of the structuring element used by the morphological operators, generally taking the form of nonlinear algebraic functions of certain differential operators.<
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