Nonlinear scale-space representation with morphological levelings

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, det ails vanish, but the contours of the remaining objects are preserved sharp and perfectly localized. Both the lattice algebraic and the scale-space pro perties of levelings are analyzed and illustrated. We also develop a nonlin ear partial differential equation that models the generation of levelings a s the limit of a controlled growth starting from an initial seed signal. Fi nally, we outline the use of levelings in improving the Gaussian scale-spac e by using the latter as an initial seed to generate multiscale levelings t hat have a superior preservation of image edges. (C) 2000 Academic Press.