Rw. Brockett et P. Maragos, EVOLUTION-EQUATIONS FOR CONTINUOUS-SCALE MORPHOLOGICAL FILTERING, IEEE transactions on signal processing, 42(12), 1994, pp. 3377-3386
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.