Adjunctions in Pyramids, Curve Evolution and Scale-Spaces

摘要

We have been witnessing lately a convergence among mathematical morphology and other nonlinear fields, such as curve evolution, PDE-based geometrical image processing, and scale-spaces. An obvious benefit of such a convergence is a cross-fertilization of concepts and techniques among these fields. The concept of adjunction however, so fundamental in mathematical morphology, is not yet shared by other disciplines. The aim of this paper is to show that other areas in image processing can possibly benefit from the use of adjunctions. In particular, a strong relationship between pyramids and adjunctions is presented. We show how this relationship may help in analyzing existing pyramids, and construct new pyramids. Moreover, it will be explained that adjunctions based on a curve evolution scheme can provide idempotent shape filters. This idea is illustrated in this paper by means of a simple affine-invariant polygonal flow. Finally, the use of adjunctions in scale-space theory is also addressed.