Segmenting the picture of greek coins in regions

This example uses Spectral clustering on a graph created from voxel-to-voxel difference on an image to break this image into multiple partly-homogeneous regions.

This procedure (spectral clustering on an image) is an efficient approximate solution for finding normalized graph cuts.

There are two options to assign labels:

  • with ‘kmeans’ spectral clustering will cluster samples in the embedding space using a kmeans algorithm

  • whereas ‘discrete’ will iteratively search for the closest partition space to the embedding space.

# Author: Gael Varoquaux <gael.varoquaux@normalesup.org>, Brian Cheung
# License: BSD 3 clause

import time

import numpy as np
from scipy.ndimage.filters import gaussian_filter
import matplotlib.pyplot as plt
import skimage
from skimage.data import coins
from skimage.transform import rescale

from sklearn.feature_extraction import image
from sklearn.cluster import spectral_clustering
from sklearn.utils.fixes import parse_version

# these were introduced in skimage-0.14
if parse_version(skimage.__version__) >= parse_version("0.14"):
    rescale_params = {"anti_aliasing": False, "multichannel": False}
else:
    rescale_params = {}

# load the coins as a numpy array
orig_coins = coins()

# Resize it to 20% of the original size to speed up the processing
# Applying a Gaussian filter for smoothing prior to down-scaling
# reduces aliasing artifacts.
smoothened_coins = gaussian_filter(orig_coins, sigma=2)
rescaled_coins = rescale(smoothened_coins, 0.2, mode="reflect", **rescale_params)

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

# Take a decreasing function of the gradient: an exponential
# The smaller beta is, the more independent the segmentation is of the
# actual image. For beta=1, the segmentation is close to a voronoi
beta = 10
eps = 1e-6
graph.data = np.exp(-beta * graph.data / graph.data.std()) + eps

# Apply spectral clustering (this step goes much faster if you have pyamg
# installed)
N_REGIONS = 25

Visualize the resulting regions

for assign_labels in ("kmeans", "discretize"):
    t0 = time.time()
    labels = spectral_clustering(
        graph, n_clusters=N_REGIONS, assign_labels=assign_labels, random_state=42
    )
    t1 = time.time()
    labels = labels.reshape(rescaled_coins.shape)

    plt.figure(figsize=(5, 5))
    plt.imshow(rescaled_coins, cmap=plt.cm.gray)
    for l in range(N_REGIONS):
        plt.contour(labels == l, colors=[plt.cm.nipy_spectral(l / float(N_REGIONS))])
    plt.xticks(())
    plt.yticks(())
    title = "Spectral clustering: %s, %.2fs" % (assign_labels, (t1 - t0))
    print(title)
    plt.title(title)
plt.show()
  • Spectral clustering: kmeans, 4.12s
  • Spectral clustering: discretize, 3.65s

Out:

Spectral clustering: kmeans, 4.12s
Spectral clustering: discretize, 3.65s

Total running time of the script: ( 0 minutes 8.619 seconds)

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