scipy.ndimage.morphology.binary_opening

scipy.ndimage.morphology.binary_opening(input, structure=None, iterations=1, output=None, origin=0)

Multi-dimensional binary opening with the given structuring element.

The opening of an input image by a structuring element is the dilation of the erosion of the image by the structuring element.

Parameters:

input : array_like

Binary array_like to be opened. Non-zero (True) elements form the subset to be opened.

structure : array_like, optional

Structuring element used for the opening. Non-zero elements are considered True. If no structuring element is provided an element is generated with a square connectivity equal to one (i.e., only nearest neighbors are connected to the center, diagonally-connected elements are not considered neighbors).

iterations : {int, float}, optional

The erosion step of the opening, then the dilation step are each repeated iterations times (one, by default). If iterations is less than 1, each operation is repeated until the result does not change anymore.

output : ndarray, optional

Array of the same shape as input, into which the output is placed. By default, a new array is created.

origin : int or tuple of ints, optional

Placement of the filter, by default 0.

Returns:

binary_opening : ndarray of bools

Opening of the input by the structuring element.

See also

grey_opening, binary_closing, binary_erosion, binary_dilation, generate_binary_structure

Notes

Opening [R83] is a mathematical morphology operation [R84] that consists in the succession of an erosion and a dilation of the input with the same structuring element. Opening therefore removes objects smaller than the structuring element.

Together with closing (binary_closing), opening can be used for noise removal.

References

[R83]

(1, 2) http://en.wikipedia.org/wiki/Opening_%28morphology%29

[R84]

(1, 2) http://en.wikipedia.org/wiki/Mathematical_morphology

Examples

>>> a = np.zeros((5,5), dtype=np.int)
>>> a[1:4, 1:4] = 1; a[4, 4] = 1
>>> a
array([[0, 0, 0, 0, 0],
       [0, 1, 1, 1, 0],
       [0, 1, 1, 1, 0],
       [0, 1, 1, 1, 0],
       [0, 0, 0, 0, 1]])
>>> # Opening removes small objects
>>> ndimage.binary_opening(a, structure=np.ones((3,3))).astype(np.int)
array([[0, 0, 0, 0, 0],
       [0, 1, 1, 1, 0],
       [0, 1, 1, 1, 0],
       [0, 1, 1, 1, 0],
       [0, 0, 0, 0, 0]])
>>> # Opening can also smooth corners
>>> ndimage.binary_opening(a).astype(np.int)
array([[0, 0, 0, 0, 0],
       [0, 0, 1, 0, 0],
       [0, 1, 1, 1, 0],
       [0, 0, 1, 0, 0],
       [0, 0, 0, 0, 0]])
>>> # Opening is the dilation of the erosion of the input
>>> ndimage.binary_erosion(a).astype(np.int)
array([[0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0],
       [0, 0, 1, 0, 0],
       [0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0]])
>>> ndimage.binary_dilation(ndimage.binary_erosion(a)).astype(np.int)
array([[0, 0, 0, 0, 0],
       [0, 0, 1, 0, 0],
       [0, 1, 1, 1, 0],
       [0, 0, 1, 0, 0],
       [0, 0, 0, 0, 0]])