Quadratic Structuring Functions in Mathematical Morphology

In this contribution we look at the quadratic structuring functions as alternatives to the often used “flat” structuring functions. The quadratic structuring functions (henceforth abbreviated as QSF’s) are the morphological counterpart of the Gaussian function in linear image processing in the sense that: the class of QSF’s is closed under dilation (i.e. dilating two QSF’s results in a third QSF), the QSF’s are easily dimensionally decomposed, (i.e. any n-dimensional QSF can be obtained through dilation of n one-dimensional QSF’s in n independent directions) and the class of QSF’s contains the unique rotational symmetric structuring function that can be dimensionally decomposed with respect to dilation.