Opening and Closing

The erosion of an image not only removes all structures that cannot contain the structuring element but it also shrinks all the other ones. The search for an operator recovering most structures lost by the erosion leads to the definition of the morphological opening operator. The principle consists in dilating the image previously eroded using the same structuring element. In general, not all structures are recovered. For example, objects completely destroyed by the erosion are not recovered at all. This behaviour is at the very basis of the filtering properties of the opening operator: image structures are selectively filtered out, the selection depending on the shape and size of the SE. The dual operator of the morphological opening is the morphological closing. Both operators are at the basis of the morphological approach to image filtering developed in Chap. 8.