How to implement basic morphological filtering in Python

There are four most basic morphological operations, namely corrosion, expansion, open calculation and closed calculation. `scipy.ndimage implements these four operations for binary arrays and grayscale arrays respectively

##binary_erosiongrey_erosionCorrosionbinary_dilationgrey_dilationInflationbinary_closinggrey_closingClose (expand first and then corrode)binary_openinggrey_openingOpen (corrode first and then expand)

Binary	Grayscale

Binary Morphology

The so-called corrosion is expressed in mathematical symbols as

where B

ij _{represents the set of all values ​​​​that are 1 in B when the origin of B BB is at (i, j).}

This formula means that when structure B is used to corrode A, when the origin of B is translated to the pixel (i,j) of image A, if B is completely surrounded by the overlapping area of ​​the two, then Assigned a value of 1, otherwise assigned a value of 0. When a certain element in B is 1, if the corresponding position in A is also 1, then the value at (i, j) is 1. This is a more intuitive example.

Inflation is the opposite, and can be expressed as

#In other words, as long as the overlapping area of ​​B and A is not an empty set, then (i,j) point Just set it to 1.

An example is as follows

import numpy as np
import matplotlib.pyplot as plt
import scipy.ndimage as sn

x = np.zeros([20,20])
x[5:15, 5:15] = 1
x_ero = sn.binary_erosion(x)
x_dil = sn.binary_dilation(x)

fig = plt.figure()
ax = fig.add_subplot(1,3,1)
ax.imshow(x)
plt.title("original")
ax = fig.add_subplot(1,3,2)
ax.imshow(x_ero)
plt.title("erosion")
ax = fig.add_subplot(1,3,3)
ax.imshow(x_dil)
plt.title("dilation")
plt.show()

The effect is as follows

The opening operation is to corrode first and then expand; the closing operation is to expand first and then corrode. The example is as follows

x = np.zeros([20,20])
x[5:15, 5:15] = 1
x[10:12,10:12] = 0
x[2:4, 2:4] = 1

x_open = sn.binary_opening(x)
x_close = sn.binary_closing(x)

fig = plt.figure()
ax = fig.add_subplot(1,3,1)
ax.imshow(x)
plt.title("original")
ax = fig.add_subplot(1,3,2)
ax.imshow(x_open)
plt.title("opening")
ax = fig.add_subplot(1,3,3)
ax.imshow(x_close)
plt.title("closing")
plt.show()

The effect is as follows. It can be seen that the opening operation will remove the isolated 1, and the closing operation will remove the isolated 0.

Grayscale morphology

The corrosion, expansion and opening and closing operations of grayscale images are an extension of its binary situation, using similar For the logic of convolution, the staircase image is directly retrieved from

scipy, and the erosion, expansion, and opening and closing operations are performed in sequence.

from scipy.misc import ascent
img = ascent()

funcs = {
    "original": lambda x, tmp:x,
    "erosion" : sn.grey_erosion,
    "dilation" : sn.grey_dilation,
    "opening" : sn.grey_opening,
    "closing" : sn.grey_closing
}

fig = plt.figure()
for i, key in enumerate(funcs):
    ax = fig.add_subplot(2,3,i+1)
    plt.imshow(funcs[key](img, (10,10)), cmap=plt.cm.gray)
    plt.title(key)

plt.show()

Parameter list

The parameters of the binary function and the grayscale function are not the same. The following takes the closing operation as an example. All parameters of the binary and grayscale functions , in addition to the input input, the parameters shared by both are

• structure is an array type, indicating the construction element, which can be understood as a convolution template

• output is an array with the same dimensions as the input, and can save the result

• orgin filter setting, the default is 0

Binary form Other parameters for learning filtering are as follows

binary_closing(input, iterations=1, mask=None, border_value=0, brute_force=False)

• iterations is the number of executions

• mask mask array, which is bool type Array, the position corresponding to False will not change

• border_value The value at the edge

• brute_force If it is False, only the last iteration Only the changed values ​​in will be updated

grey_closing(input, size=None, footprint=None, mode='reflect', cval=0.0)

• size is the filter template

• mode optional reflect,constant, nearest, mirror, wrap, edge filling method

• cval edge filling value

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