Closing (morphology)

In mathematical morphology, the closing of a set (binary image) A by a structuring element B is the erosion of the dilation of that set, where

In image processing, closing is, together with opening, the basic workhorse of morphological noise removal.

Opening removes small objects, while closing removes small holes.

): Suppose A is the following 11 x 11 matrix and B is the following 3 x 3 matrix: For each pixel in A that has a value of 1, superimpose B, with the center of B aligned with the corresponding pixel in A.

Each pixel of every superimposed B is included in the dilation of A by B.

is given by : Now, Perform Erosion on the result: (

superimpose the origin of B, if B is completely contained by A the pixel is retained, else deleted.

is given by: Therefore Closing Operation fills small holes and smoothes the object by filling narrow gaps.

The closing of the dark-blue shape (union of two squares) by a disk, resulting in the union of the dark-blue shape and the light-blue areas.