According to Wikipedia “Mathematical morphology (MM) is a theory and technique for the analysis and processing of geometrical structures, based on set theory, lattice theory, topology, and random functions”. It is mainly applied to digital images for image processing. There are many operations of mathematical morphology but mainly used operations are dilation for increasing the image regions, erosion for shrinking the image regions and thinning for structured erosion using image pattern matching.

Basic Operations of Mathematical Morphology are:

Dilation – increasing the image regions

 

Erosion – Shrinking the image regions

 

Opening – Structured removal of image region boundary pixels

Closing – structured filling in of image region boundary pixels

Hit and Miss Transform – image pattern matching and marking

Thinning – structured erosion using image pattern matching

Thickening – structured dilation using image pattern matching

Skeletonization/Medial Axis Transform – finding skeletons of binary regions

REFERENCE:

https://homepages.inf.ed.ac.uk/rbf/HIPR2/morops.htm