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, k=4, mode='arpack')
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')
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()) labels = spectral_clustering(graph, k=4) label_im = -np.ones(mask.shape) label_im[mask] = labels pl.figure(1, figsize=(8, 8)) pl.clf() pl.subplot(2, 2, 1) pl.imshow(img) pl.subplot(2, 2, 3) pl.imshow(label_im)
import numpy as np import scipy as sp import pylab as pl from scikits.learn.feature_extraction import image from scikits.learn.cluster import spectral_clustering lena = sp.lena() # Downsample the image by a factor of 4 lena = lena[::2, ::2] + lena[1::2, ::2] + lena[::2, 1::2] + lena[1::2, 1::2] lena = lena[::2, ::2] + lena[1::2, ::2] + lena[::2, 1::2] + lena[1::2, 1::2] # Convert the image into a graph with the value of the gradient on the # edges. graph = image.img_to_graph(lena) # Take a decreasing function of the gradient: an exponential # The smaller beta is, the more independant the segmentation is of the # actual image. For beta=1, the segmentation is close to a voronoi beta = 5 eps = 1e-6 graph.data = np.exp(-beta*graph.data/lena.std()) + eps # Apply spectral clustering (this step goes much faster if you have pyamg # installed) N_REGIONS = 11 labels = spectral_clustering(graph, k=N_REGIONS) labels = labels.reshape(lena.shape) ################################################################################