  We present an application of Mathematical Morphology (MM) for the
classification of astronomical objects, both for star/galaxy differentiation
and galaxy morphology classification. We demonstrate that, for CCD images, 99.3
+/- 3.8 % of galaxies can be separated from stars using MM, with 19.4 +/- 7.9 %
of the stars being misclassified. We demonstrate that, for photographic plate
images, the number of galaxies correctly separated from the stars can be
increased using our MM diffraction spike tool, which allows 51.0 +/- 6.0 % of
the high-brightness galaxies that are inseparable in current techniques to be
correctly classified, with only 1.4 +/- 0.5 % of the high-brightness stars
contaminating the population. We demonstrate that elliptical (E) and late-type
spiral (Sc-Sd) galaxies can be classified using MM at an accuracy of 91.4 +/-
7.8 %. It is a method involving less `free parameters' than current techniques,
especially automated machine learning algorithms. The limitation of MM galaxy
morphology based on seeing and distance is also presented. We examine various
star/galaxy differentiation and galaxy morhpology classification techniques
commonly used today, and show that the above MM techniques compare very
favourably.
