In this paper we present a nonlinear scale-space representation based on a general class of
morphological strong filters, the levelings, which include the openings and closings by
reconstruction. These filters are very useful for image simplification and segmentation. From
one scale to the next, details vanish, but the contours of the remaining objects are preserved
sharp and perfectly localized. Both the lattice algebraic and the scale-space properties of
levelings are analyzed and illustrated. We also develop a nonlinear partial differential …