Structural Mathematical Morphology

Structuring element

pylena.morpho.make_structuring_element_2d(kind, *args)

Compute a predifined structuring element. The morphological operations for these structuring elements have been optimized for their use.

Three kinds of structuring element can be computed using this method:

• 2-D rectangle

• Disc

• 2-D periodic line

For these structuring elements, argument taken by the function are different.

• 2-D rectangle

The supplementary arguments are the width and the height

>>> se = make_structuring_element_2d("rect", width, height)

• Disc

The supplementary argument is the radius of the disc

>>> se = make_structuring_element_2d("disc", radius)

• 2-D periodic line

The supplementary argument are the period (represented by a tuple of int of size 2 corresponding to a point) and the half number of pixel in the line

>>> se = make_structuring_element_2d("periodic_line", (2, 5), 10)

Parameters:

• kind – The structuring element to be computed.

• args – The parameters for the computation of a structuring element

Returns:

A structuring element

Return type:

structuring_element_2d

Raises:

ValueError – If the kind argument is incorrect or if the argument for the structuring element computation is incorrect.

Example

The following code sample show how to compute a rectangle structuring element

>>> se = make_structuring_element_2d("rect", 10, 5)  # width=10 and height=5

pylena.morpho.erosion(img: ndarray, se: ndarray | structuring_element_2d, padding_value: int = None)

Performs an erosion by a structuring element.

Given a structuring element \(B\), the erosion \(\varepsilon(f)\) of the input image \(f\) is defined as

\[\varepsilon(f)(x) = \bigwedge \{f(y), y \in B_x\}\]

Parameters:

• img (2-D array (dtype=uint8)) – The image to be processed

• se (structuring_element_2d or 2-D array) – The structuring element

Returns:

The resulting image

Return type:

2-D array

Example

>>> img = ...  # Get an image
>>> from pylena.morpho import make_structuring_element_2d, erosion
>>> se = make_structring_element_2d("rect", 10, 10)
>>> out = erosion(img, se)

pylena.morpho.dilation(img: ndarray, se: ndarray | structuring_element_2d, padding_value: int = None)

Performs an dilation by a structuring element.

Given a structuring element \(B\), the dilation \(\delta(f)\) of the input image \(f\) is defined as

\[\delta(f)(x) = \bigvee \{f(y), y \in B_x\}\]

Parameters:

• img (2-D array (dtype=uint8)) – The image to be processed

• se (structuring_element_2d or 2-D array) – The structuring element

Returns:

The resulting image

Return type:

2-D array

Example

>>> img = ...  # Get an image
>>> from pylena.morpho import make_structuring_element_2d, dilation
>>> se = make_structring_element_2d("rect", 10, 10)
>>> out = dilation(img, se)

pylena.morpho.opening(img: ndarray, se: ndarray | structuring_element_2d, padding_value: int = None)

Performs an opening by a structuring element.

Given a structuring element \(B\), the dilation \(\gamma(f)\) of the input image \(f\) is defined as

\[\gamma(f) = \delta_{B}(\varepsilon_{B}(f))\]

Parameters:

• img (2-D array (dtype=uint8)) – The image to be processed

• se (structuring_element_2d or 2-D array) – The structuring element

Returns:

The resulting image

Return type:

2-D array

Example

>>> img = ...  # Get an image
>>> from pylena.morpho import make_structuring_element_2d, opening
>>> se = make_structring_element_2d("rect", 10, 10)
>>> out = opening(img, se)

pylena.morpho.closing(img: ndarray, se: ndarray | structuring_element_2d, padding_value: int = None)

Performs an closing by a structuring element.

Given a structuring element \(B\), the dilation \(\gamma(f)\) of the input image \(f\) is defined as

\[\gamma(f) = \varepsilon_{B}(\delta_{B}(f))\]

Parameters:

• img (2-D array (dtype=uint8)) – The image to be processed

• se (structuring_element_2d or 2-D array) – The structuring element

Returns:

The resulting image

Return type:

2-D array

Example

>>> img = ...  # Get an image
>>> from pylena.morpho import make_structuring_element_2d, closing
>>> se = make_structring_element_2d("rect", 10, 10)
>>> out = closing(img, se)

pylena.morpho.gradient(img: ndarray, se: ndarray | structuring_element_2d, padding_value: int = None)

Performs a morphological gradient, also called Beucher gradient.

Given a structuring element \(B\) and an image \(f\), the morphological gradient is defined as

\[\rho_B = \delta_B - \varepsilon_B\]

Parameters:

• img (2-D array (dtype=uint8)) – The image to be processed

• se (structuring_element_2d or 2-D array) – The structuring element

Returns:

The resulting image

Return type:

2-D array

Example

>>> img = ...  # Get an image
>>> from pylena.morpho import make_structuring_element_2d, gradient
>>> se = make_structring_element_2d("rect", 10, 10)
>>> out = gradient(img, se)