Closing (morphology)

In mathematical morphology, the closing of a set () A by a structuring element B is the erosion of the dilation of that set, where and denote the dilation and erosion, respectively. In , closing is, together with opening, the basic workhorse of morphological noise removal. Opening removes small objects, while closing removes small holes. It is idempotent, that is, . It is increasing, that is, if , then . It is extensive, i.e., . It is translation invariant. Image Analysis and Mathematical Morphology by Jean Serra, (1982) Image Analysis and Mathematical Morphology, Volume 2: Theoretical Advances by Jean Serra, (1988) An Introduction to Morphological Image Processing by Edward R.