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This numerical tour explores mathematical morphology of binary images.
from __future__ import division
import nt_toolbox as nt
from nt_solutions import denoisingadv_5_mathmorph as solutions
%matplotlib inline
%load_ext autoreload
%autoreload 2
Here we process binary images using local operator defined using a structuring element, which is here chosen to be a discrete disk of varying radius.
Load an image
n = 256
M = rescale(load_image('cortex', n))
Display.
imageplot(M)
Make it binary.
M = double(M >.45)
Display.
imageplot(M)
Round structuring element.
wmax = 7
[Y, X] = meshgrid(-wmax: wmax, -wmax: wmax)
normalize = lambda x: x/ sum(x(: ))
strel = lambda w: normalize(double(X.^2 + Y.^2 <= w^2))
Exercise 1
Display structuring elements of increasing sizes.
solutions.exo1()
## Insert your code here.
A dilation corresponds to take the maximum value of the image aroung each pixel, in a region equal to the structuring element.
It can be implemented using a convolution with the structuring element followed by a thresholding.
dillation = lambda x, w: double(perform_convolution(x, strel(w)) >0)
Md = dillation(M, 2)
Display.
imageplot(Md)
Exercise 2
Test with structing elements of increasing size.
solutions.exo2()
## Insert your code here.
An errosion corresponds to take the maximum value of the image aroung each pixel, in a region equal to the structuring element.
It can be implemented using a convolution with the structuring element followed by a thresholding.
errosion = lambda x, w: double(perform_convolution(x, strel(w)) >= .999)
Me = errosion(M, 2)
Display.
imageplot(Me)
Exercise 3
Test with structing elements of increasing size.
solutions.exo3()
## Insert your code here.
An opening smooth the boundary of object (and remove small object) by performing an errosion and then a dillation.
Define a shortcut.
opening = lambda x, w: dillation(errosion(x, w), w)
Perform the opening, here using a very small disk.
w = 1
Mo = opening(M, w)
Display.
imageplot(Mo)
Exercise 4
Test with structing elements of increasing size.
solutions.exo4()
## Insert your code here.