A simple grid MRF with Potts potentials in AD3



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import itertools
import ad3

Set parameters of the model



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grid_size = 20
num_states = 5

Create a factor graph



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factor_graph = ad3.PFactorGraph()

Create variables lying on a grid with random potentials.



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multi_variables = []
random_grid = np.random.uniform(size=(grid_size, grid_size, num_states))
for i in xrange(grid_size):
    multi_variables.append([])
    for j in xrange(grid_size):
        new_variable = factor_graph.create_multi_variable(num_states)
        for state in xrange(num_states):
            new_variable.set_log_potential(state, random_grid[i, j, state])
        multi_variables[i].append(new_variable)

Create potts potentials for edges.



In [5]:

    
alpha = .5
potts_matrix = alpha * np.eye(num_states)
potts_potentials = potts_matrix.ravel().tolist()

Create factors for edges from potts potentials



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for i, j in itertools.product(xrange(grid_size), repeat=2):
    if (j > 0):
        #horizontal edge
        edge_variables = [multi_variables[i][j - 1], multi_variables[i][j]]
        factor_graph.create_factor_dense(edge_variables, potts_potentials)
    
    if (i > 0):
        #horizontal edge
        edge_variables = [multi_variables[i - 1][j], multi_variables[i][j]]
        factor_graph.create_factor_dense(edge_variables, potts_potentials)

Set model parameters and compute the map using AD3



In [7]:

    
factor_graph.set_eta_ad3(.1)
factor_graph.adapt_eta_ad3(True)
factor_graph.set_max_iterations_ad3(1000)
value, marginals, edge_marginals = factor_graph.solve_lp_map_ad3()

Visualize resulting MAP



In [13]:

    
res = np.array(marginals).reshape(20, 20, 5)
plt.matshow(np.argmax(random_grid, axis=-1), vmin=0, vmax=4)
plt.matshow(np.argmax(res, axis=-1), vmin=0, vmax=4)









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<matplotlib.image.AxesImage at 0xb159d2c>



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