"""
Segmentation with spectral clustering
======================================

This example uses spectral clustering to do segmentation.
"""

import numpy as np
import matplotlib.pyplot as plt

from sklearn.feature_extraction import image
from sklearn.cluster import spectral_clustering

################################################################################
l = 100
x, y = np.indices((l, l))

center1 = (28, 24)
center2 = (40, 50)
center3 = (67, 58)
center4 = (24, 70)

radius1, radius2, radius3, radius4 = 16, 14, 15, 14

circle1 = (x - center1[0])**2 + (y - center1[1])**2 < radius1**2
circle2 = (x - center2[0])**2 + (y - center2[1])**2 < radius2**2
circle3 = (x - center3[0])**2 + (y - center3[1])**2 < radius3**2
circle4 = (x - center4[0])**2 + (y - center4[1])**2 < radius4**2

################################################################################
# 4 circles
img = circle1 + circle2 + circle3 + circle4
mask = img.astype(bool)
img = img.astype(float)

img += 1 + 0.2*np.random.randn(*img.shape)

# Convert the image into a graph with the value of the gradient on the
# edges.
graph = image.img_to_graph(img, mask=mask)

# Take a decreasing function of the gradient: we take it weakly
# dependant from the gradient the segmentation is close to a voronoi
graph.data = np.exp(-graph.data / graph.data.std())

# Force the solver to be arpack, since amg is numerically
# unstable on this example
labels = spectral_clustering(graph, n_clusters=4)
label_im = -np.ones(mask.shape)
label_im[mask] = labels

plt.figure(figsize=(6, 3))
plt.subplot(121)
plt.imshow(img, cmap=plt.cm.spectral, interpolation='nearest')
plt.axis('off')
plt.subplot(122)
plt.imshow(label_im, cmap=plt.cm.spectral, interpolation='nearest')
plt.axis('off')

plt.subplots_adjust(wspace=0, hspace=0., top=0.99, bottom=0.01, left=0.01, right=0.99)
plt.show()