Classical Computer Vision: Image Segmentation with Mumford & Shah

     The Mumford & Shah is another segmentation algorithm that is much more efficient than K-Means, that uses the following math equation to decide which pixels of an image should belong to which segment

    The idea here is not to go deep under the hood for this equation, because we're not trying to implement it, but to use it. 

    

    So, lets get the example extracted from professor Aldo von Wangenheim  (@UFSC/Brazil) for Mumford & Shah image segmentation:

from ipywidgets import interact, interactive, interact_manual

import cv2, scipy

from skimage import data

from matplotlib import pyplot as plt

# Import the M&S-equivalent Ambrosio Tortorelli Minimizer (we'll call it A&Tmin)

# You have to download it before from

https://github.com/jacobgil/Ambrosio-Tortorelli-Minimizer

# or from my mirror (is NOT updated):

https://github.com/awangenh/Ambrosio-Tortorelli-Minimizer

from AmbrosioTortorelliMinimizer import *

image = cv2.imread("../data/ct-02.jpg", cv2.IMREAD_GRAYSCALE)

def my_ATmin(iterations, solver_maxiterations, tol, alpha, beta, epsilon, colormap):

global image

colormap = eval('plt.cm.' + colormap)

solver = AmbrosioTortorelliMinimizer(

image, iterations, solver_maxiterations, tol, alpha, beta, epsilon)

seg, edges = solver.minimize()

fig, axes = plt.subplots(ncols=3, figsize=(20, 7),

sharex=True, sharey=True)

ax = axes.ravel()

ax[0].imshow(image, cmap=plt.cm.gray)

ax[0].set_title('Original image')

ax[1].imshow(edges, cmap=plt.cm.gray)

ax[1].set_title('Edges')

ax[2].imshow(seg, cmap=colormap)

ax[2].set_title('Result')

for a in ax:

a.axis('off')

fig.tight_layout()

plt.show()

interact_manual(my_ATmin, iterations=(1, 100, 1), \

    solver_maxiterations=(1, 100), tol=(0.01, 1.0), alpha=(100, 10000, 100), \

beta=(0.001, 0.1, 0.001), epsilon=(0.001, 0.1, 0.001), \

    colormap=['nipy_spectral', 'hot', 'magma', 'seismic'])

# Default values: iterations = 1, solver_maxiterations = 10, tol = 0.1, alpha = 1000, beta = 0.01, epsilon = 0.01

Aldo von Wangenheim