def example_multinomial():
# generate dataset with three stripes
np.random.seed(15)
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.argmin(x, axis=2)
unaries = (unaries * 10).astype(np.int32)
x_thresh = np.argmin(unaries, axis=2)
# potts potential
#pairwise_potts = -2 * np.eye(3, dtype=np.int32)
# potential that penalizes 0-1 and 1-2 less thann 0-2
pairwise_1d = -15 * np.eye(3, dtype=np.int32) - 8
pairwise_1d[-1, 0] = 5
pairwise_1d[0, -1] = 5
print(pairwise_1d)
result_1d = alpha_expansion_grid(unaries, pairwise_1d)
result_gco = cut_simple(unaries, pairwise_1d)
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_gco, interpolation="nearest")
plt.subplot(144, title="1d topology potentials")
plt.imshow(result_1d, interpolation="nearest")
plt.show()
def example_multinomial():
# generate dataset with three stripes
np.random.seed(15)
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.argmin(x, axis=2)
unaries = (unaries * 10).astype(np.int32)
x_thresh = np.argmin(unaries, axis=2)
# potts potential
#pairwise_potts = -2 * np.eye(3, dtype=np.int32)
# potential that penalizes 0-1 and 1-2 less thann 0-2
pairwise_1d = -15 * np.eye(3, dtype=np.int32) - 8
pairwise_1d[-1, 0] = 5
pairwise_1d[0, -1] = 5
print(pairwise_1d)
result_1d = alpha_expansion_grid(unaries, pairwise_1d)
result_gco = cut_simple(unaries, pairwise_1d)
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_gco, interpolation="nearest")
plt.subplot(144, title="1d topology potentials")
plt.imshow(result_1d, interpolation="nearest")
plt.show()
def latent(self, x, y, w):
# augment unary potentials for latent states
x_wide = np.repeat(x, self.n_states_per_label, axis=-1)
# do usual inference
unary_params = w[:self.n_states]
pairwise_flat = np.asarray(w[self.n_states:])
pairwise_params = np.zeros((self.n_states, self.n_states))
pairwise_params[np.tri(self.n_states, dtype=np.bool)] = pairwise_flat
pairwise_params = (pairwise_params + pairwise_params.T
- np.diag(np.diag(pairwise_params)))
unaries = (- 10 * unary_params * x_wide).astype(np.int32)
# forbid h that is incompoatible with y
# by modifying unary params
other_states = (np.arange(self.n_states) / self.n_states_per_label !=
y[:, :, np.newaxis])
unaries[other_states] = +1000000
pairwise = (-10 * pairwise_params).astype(np.int32)
h = alpha_expansion_grid(unaries, pairwise)
if (h / self.n_states_per_label != y).any():
if np.any(w):
print("inconsistent h and y")
tracer()
h = y * self.n_states_per_label
else:
h = y * self.n_states_per_label
return h
def inference(self, x, w):
if w.shape != (self.size_psi,):
raise ValueError("Got w of wrong shape. Expected %s, got %s" %
(self.size_psi, w.shape))
unary_params = w[:self.n_states]
pairwise_flat = np.asarray(w[self.n_states:])
pairwise_params = np.zeros((self.n_states, self.n_states))
pairwise_params[np.tri(self.n_states, dtype=np.bool)] = pairwise_flat
pairwise_params = pairwise_params + pairwise_params.T\
- np.diag(np.diag(pairwise_params))
unaries = (-1000 * unary_params * x).astype(np.int32)
pairwise = (-1000 * pairwise_params).astype(np.int32)
y = alpha_expansion_grid(unaries, pairwise)
return y
def potts_example():
img1 = np.asarray(Image.open("scene1.row3.col1.ppm")) / 255.
img2 = np.asarray(Image.open("scene1.row3.col2.ppm")) / 255.
unaries = (stereo_unaries(img1, img2) * 100).astype(np.int32)
n_disps = unaries.shape[2]
#newshape = unaries.shape[:2]
potts_cut = alpha_expansion_grid(unaries, -5 * np.eye(n_disps,
dtype=np.int32), n_iter=5)
x, y = np.ogrid[:n_disps, :n_disps]
one_d_topology = np.abs(x - y).astype(np.int32).copy("C")
one_d_cut = alpha_expansion_grid(unaries, 5 * one_d_topology, n_iter=5)
plt.subplot(231, xticks=(), yticks=())
plt.imshow(img1)
plt.subplot(232, xticks=(), yticks=())
plt.imshow(img1)
plt.subplot(233, xticks=(), yticks=())
plt.imshow(np.argmax(unaries, axis=2), interpolation='nearest')
plt.subplot(223, xticks=(), yticks=())
plt.imshow(potts_cut, interpolation='nearest')
plt.subplot(224, xticks=(), yticks=())
plt.imshow(one_d_cut, interpolation='nearest')
plt.show()
def potts_example():
img1 = np.asarray(Image.open("scene1.row3.col1.ppm")) / 255.
img2 = np.asarray(Image.open("scene1.row3.col2.ppm")) / 255.
unaries = (stereo_unaries(img1, img2) * 100).astype(np.int32)
n_disps = unaries.shape[2]
#newshape = unaries.shape[:2]
potts_cut = alpha_expansion_grid(unaries,
-5 * np.eye(n_disps, dtype=np.int32),
n_iter=5)
x, y = np.ogrid[:n_disps, :n_disps]
one_d_topology = np.abs(x - y).astype(np.int32).copy("C")
one_d_cut = alpha_expansion_grid(unaries, 5 * one_d_topology, n_iter=5)
plt.subplot(231, xticks=(), yticks=())
plt.imshow(img1)
plt.subplot(232, xticks=(), yticks=())
plt.imshow(img1)
plt.subplot(233, xticks=(), yticks=())
plt.imshow(np.argmax(unaries, axis=2), interpolation='nearest')
plt.subplot(223, xticks=(), yticks=())
plt.imshow(potts_cut, interpolation='nearest')
plt.subplot(224, xticks=(), yticks=())
plt.imshow(one_d_cut, interpolation='nearest')
plt.show()
def test_multinomial_grid_unaries():
# test handling on unaries for multinomial grid CRFs
# on multinomial datasets
for ds in toy_datasets.multinomial:
X, Y = ds(n_samples=1)
x, y = X[0], Y[0]
n_labels = len(np.unique(Y))
crf = MultinomialGridCRF(n_states=n_labels)
w_unaries_only = np.zeros(crf.size_psi)
w_unaries_only[:n_labels] = 1.
# test that inference with unaries only is the
# same as argmax
inf_unaries = crf.inference(x, w_unaries_only)
pw_z = np.zeros((n_labels, n_labels), dtype=np.int32)
un = np.ascontiguousarray(-1000 * x).astype(np.int32)
unaries = alpha_expansion_grid(un, pw_z)
assert_array_equal(inf_unaries, unaries)
assert_array_equal(inf_unaries, np.argmax(x, axis=2))
def example_multinomial_checkerboard():
# generate a checkerboard
np.random.seed(1)
x = np.zeros((12, 10, 3))
x[::2, ::2, 0] = -2
x[1::2, 1::2, 1] = -2
x[:, :, 2] = -1
x_noisy = x + np.random.normal(0, 1.0, size=x.shape)
x_org = np.argmin(x, axis=2)
# create unaries
unaries = (10 * x_noisy).astype(np.int32)
x_thresh = np.argmin(unaries, axis=2)
# as we convert to int, we need to multipy to get sensible values
# create potts pairwise
pairwise = 100 * np.eye(3, dtype=np.int32)
# do alpha expansion
result_qpbo = alpha_expansion_grid(unaries, pairwise, n_iter=4)
# use the gerneral graph algorithm
# first, we construct the grid graph
inds = np.arange(x_org.size).reshape(x_org.shape)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert]).astype(np.int32)
result_qpbo_graph = alpha_expansion_graph(edges,
unaries.reshape(-1, 3),
pairwise,
n_iter=4)
# plot results
plt.subplot(221, title="original")
plt.imshow(x_org, interpolation='nearest')
plt.subplot(222, title="thresholding result")
plt.imshow(x_thresh, interpolation='nearest')
plt.subplot(223, title="qpbo")
plt.imshow(result_qpbo, interpolation='nearest')
plt.subplot(224, title="qpbo graph")
plt.imshow(result_qpbo_graph.reshape(x_org.shape), interpolation='nearest')
plt.show()
def test_multinomial_grid_unaries():
# test handling on unaries for multinomial grid CRFs
# on multinomial datasets
for ds in toy_datasets.multinomial:
X, Y = ds(n_samples=1)
x, y = X[0], Y[0]
n_labels = len(np.unique(Y))
crf = MultinomialGridCRF(n_states=n_labels)
w_unaries_only = np.zeros(crf.size_psi)
w_unaries_only[:n_labels] = 1.
# test that inference with unaries only is the
# same as argmax
inf_unaries = crf.inference(x, w_unaries_only)
pw_z = np.zeros((n_labels, n_labels), dtype=np.int32)
un = np.ascontiguousarray(
-1000 * x).astype(np.int32)
unaries = alpha_expansion_grid(un, pw_z)
assert_array_equal(inf_unaries, unaries)
assert_array_equal(inf_unaries, np.argmax(x, axis=2))
def example_multinomial_checkerboard():
# generate a checkerboard
np.random.seed(1)
x = np.zeros((12, 10, 3))
x[::2, ::2, 0] = -2
x[1::2, 1::2, 1] = -2
x[:, :, 2] = -1
x_noisy = x + np.random.normal(0, 1.0, size=x.shape)
x_org = np.argmin(x, axis=2)
# create unaries
unaries = (10 * x_noisy).astype(np.int32)
x_thresh = np.argmin(unaries, axis=2)
# as we convert to int, we need to multipy to get sensible values
# create potts pairwise
pairwise = 100 * np.eye(3, dtype=np.int32)
# do alpha expansion
result_qpbo = alpha_expansion_grid(unaries, pairwise, n_iter=4)
# use the gerneral graph algorithm
# first, we construct the grid graph
inds = np.arange(x_org.size).reshape(x_org.shape)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert]).astype(np.int32)
result_qpbo_graph = alpha_expansion_graph(edges, unaries.reshape(-1, 3),
pairwise, n_iter=4)
# plot results
plt.subplot(221, title="original")
plt.imshow(x_org, interpolation='nearest')
plt.subplot(222, title="thresholding result")
plt.imshow(x_thresh, interpolation='nearest')
plt.subplot(223, title="qpbo")
plt.imshow(result_qpbo, interpolation='nearest')
plt.subplot(224, title="qpbo graph")
plt.imshow(result_qpbo_graph.reshape(x_org.shape), interpolation='nearest')
plt.show()
