content: import matplotlib.pyplot as plt
  import numpy as np
  from ad3 import simple_grid, general_graph
  
  
  def example_binary():
      # generate trivial data
      x = np.ones((10, 10))
      x[:, 5:] = -1
      x_noisy = x + np.random.normal(0, 0.8, size=x.shape)
      x_thresh = x_noisy > .0
  
      # create unaries
      unaries = x_noisy
      # as we convert to int, we need to multipy to get sensible values
      unaries = np.dstack([-unaries, unaries])
      # create potts pairwise
      pairwise = np.eye(2)
  
      # do simple cut
      result = np.argmax(simple_grid(unaries, pairwise)[0], axis=-1)
  
      # use the gerneral graph algorithm
      # first, we construct the grid graph
      inds = np.arange(x.size).reshape(x.shape)
      horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
      vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
      edges = np.vstack([horz, vert])
  
      # we flatten the unaries
      pairwise_per_edge = np.repeat(pairwise[np.newaxis, :, :], edges.shape[0],
                                    axis=0)
      result_graph = np.argmax(general_graph(unaries.reshape(-1, 2), edges,
                                             pairwise_per_edge)[0], axis=-1)
  
      # plot results
      plt.subplot(231, title="original")
      plt.imshow(x, interpolation='nearest')
      plt.subplot(232, title="noisy version")
      plt.imshow(x_noisy, interpolation='nearest')
      plt.subplot(234, title="thresholding result")
      plt.imshow(x_thresh, interpolation='nearest')
      plt.subplot(235, title="cut_simple")
      plt.imshow(result, interpolation='nearest')
      plt.subplot(236, title="cut_from_graph")
      plt.imshow(result_graph.reshape(x.shape), interpolation='nearest')
  
      plt.show()
  
  
  def example_multinomial():
      # generate dataset with three stripes
      np.random.seed(4)
      x = np.zeros((10, 12, 3))
      x[:, :4, 0] = 1
      x[:, 4:8, 1] = 1
      x[:, 8:, 2] = 1
      unaries = x + 1.5 * np.random.normal(size=x.shape)
      x = np.argmax(x, axis=2)
      unaries = unaries
      x_thresh = np.argmax(unaries, axis=2)
  
      # potts potential
      pairwise_potts = 2 * np.eye(3)
      result = np.argmax(simple_grid(unaries, pairwise_potts)[0], axis=-1)
      # potential that penalizes 0-1 and 1-2 less than 0-2
      pairwise_1d = 2 * np.eye(3) + 2
      pairwise_1d[-1, 0] = 0
      pairwise_1d[0, -1] = 0
      print(pairwise_1d)
      result_1d = np.argmax(simple_grid(unaries, pairwise_1d)[0], axis=-1)
      plt.subplot(141, title="original")
      plt.imshow(x, interpolation="nearest")
      plt.subplot(142, title="thresholded unaries")
      plt.imshow(x_thresh, interpolation="nearest")
      plt.subplot(143, title="potts potentials")
      plt.imshow(result, interpolation="nearest")
      plt.subplot(144, title="1d topology potentials")
      plt.imshow(result_1d, interpolation="nearest")
      plt.show()
  
  
  #example_binary()
  example_multinomial()
  