10.1.8.1. Morphomath

This module implements Morphological 1D Operators.

class Musica.Math.Morphomath.BallStructuringElement(radius)

Bases: Musica.Math.Morphomath.StructuringElement

This class implements a ball structuring element.

The domain of the structuring element is [-radius, radius].

class Musica.Math.Morphomath.Domain(inf, sup)

Bases: object

This class implements a functional 1D domain defined by the range [inf, sup].

The size of the domain defined by sup - inf +1 is given by the function len().

To test if x is in the domain, use:

x in domain

__contains__(x)

Test if x is in the domain.

__len__()

Return the size of the domain.

backward_iterator()

Return a backward iterator over the domain.

forward_iterator()

Return a forward iterator over the domain.

range()

Return the list of values in the domain.

class Musica.Math.Morphomath.Function(values)

Bases: object

This class implements a 1D function.

The parameters values is an iterable that define the initial values of the function.

The function domain is set to [0, len(values) -1].

__add__(a, b)

Return sum of a with b.

__eq__(other)

Test if the functions are equal.

__getitem__(i)

Return the function value at i.

__iadd__(obj)

Add a function.

__isub__(obj)

Subtract a function.

__len__()

Return the size of the function domain.

__setitem__(i, value)

Set the function value at i.

__sub__(a, b)

Return the subtraction of a with b.

_pointwise_rank(other, rank_operator)

This method implements a point-wise rank filter.

The function is modified in-place.

_rank_filter(structuring_element, rank_operator)

This method implements a rank filter.

The function is modified in-place.

_rank_filter_vhgw(radius, rank_operator)

This method implements a rank filter using the Van Herk & Gill-Werman algorithm.

This algorithm comes from C. Clienti, M. Bilodeau, and S. Beucher, An Efficient Hardware Architecture without Line Memories for Morphological Image Processing. In Proceedings of ACIVS. 2008, 147-156.

_zeros()

return a Numpy zero array of the same size than the function domain.

add(obj)

Add a function.

clone()

Return a copy of the function.

clone_zeros()

Return a function defined on the same domain with values set to zero.

close(structuring_element)

Perform an closing.

dilate(structuring_element)

Perform a dilation.

dilate_vhgw(radius)

Perform a dilation using the WHGW algorithm.

erode(structuring_element)

Perform an erosion.

erode_vhgw(radius)

Perform an erosion using the WHGW algorithm.

geodesic_reconstruction(marker)

Perform a geodesic reconstruction.

h_dome(level)

Perform an H-dome operation.

max()

Return the sup of the function.

min()

Return the inf of the function.

open(structuring_element)

Perform an opening.

pointwise_max(other)

Perform the point-wise max of the function with another function.

pointwise_min(other)

Perform the point-wise min of the function with another function.

subtract(obj)

Subtract a function.

Negative values are set to zero.

top_hat(structuring_element)

Perform an top-hat.

translate(offset, padd_inf=True)

Translate the function.

If the parameter padd_inf is set to True then the padding value is set to zero else to the sup of the function.

__hash__ = None

unit_ball = <Musica.Math.Morphomath.BallStructuringElement object>

class Musica.Math.Morphomath.StructuringElement(offsets)

Bases: object

This class implements a structuring element.

The parameter offsets is an iterable that contains the offsets of the pixels on of the structuring element.

The neighbor set \(N_G^+\) and \(N_G^-\) is defined in the article: Morphological Grayscale Reconstruction in Image Analysis: Applications and Efficient Algorithms, Luc Vincent, IEEE Transactions on image processing, Vol. 2, No. 2, April 1993.

__iter__()

__len__()

half_length()

iterator_minus()

Iterate over the offset from the reference location.

iterator_plus()

Iterate over the offset up to the reference location.

class Musica.Math.Morphomath.StructuringElementIterator(structuring_element, domain)

Bases: object

This class implements a structuring element iterator.

The parameter structuring_element defines the structuring element and the parameter domain defines the domain of the lattice.

iterate_at(location, sub_domain=None)

Iterate over the structuring element positioned at a location.

The parameter sub_domain is used to restrict the domain of the structuring element, set to ‘+’ to restrict to the positive domain and to ‘-‘ for the negative domain, respectively.

Musica.Math.Morphomath.even(n)

Test if n is even

Musica.Math.Morphomath.odd(n)

Test if n is odd

Musica.Math.Morphomath.unit_ball = <Musica.Math.Morphomath.BallStructuringElement object>

Unit ball structuring element.