def example_binary():
x = np.ones((10, 10))
x[:, 5:] = -1
x_noisy = x + np.random.normal(0, .8, size=x.shape)
x_thresh = x_noisy > .0
fig, axes = plt.subplots(1, 5)
axes[0].set_title("Original")
axes[0].matshow(x)
axes[1].set_title("binary")
axes[1].matshow(x_noisy)
axes[2].set_title("thresholded")
axes[2].matshow(x_thresh)
inds = np.arange(x.size).reshape(x.shape).astype(np.int64)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert])
#unaries = 2 * x_thresh.astype(np.float).ravel() - 1
unaries = x_noisy.ravel()
unaries = np.c_[np.exp(-unaries), np.exp(unaries)]
axes[3].set_title("Potts MRF")
result = potts_mrf(unaries, edges, 1.1, verbose=1)
axes[3].matshow(result.reshape(x.shape))
# repeat pairwise for each edge
pairwise = np.exp(np.eye(2) * 1.1)
pairwise = np.repeat(pairwise[np.newaxis, :, :], len(edges), axis=0)
result_mrf = mrf(unaries, edges, pairwise, verbose=1, alg="trw")
axes[4].set_title("MRF")
axes[4].matshow(result_mrf.reshape(x.shape))
for ax in axes:
ax.set_xticks(())
ax.set_yticks(())
plt.show()
def example_binary():
x = np.ones((10, 10))
x[:, 5:] = -1
x_noisy = x + np.random.normal(0, .8, size=x.shape)
x_thresh = x_noisy > .0
fig, axes = plt.subplots(1, 5)
axes[0].set_title("Original")
axes[0].matshow(x)
axes[1].set_title("binary")
axes[1].matshow(x_noisy)
axes[2].set_title("thresholded")
axes[2].matshow(x_thresh)
inds = np.arange(x.size).reshape(x.shape).astype(np.int64)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert])
#unaries = 2 * x_thresh.astype(np.float).ravel() - 1
unaries = x_noisy.ravel()
unaries = np.c_[np.exp(-unaries), np.exp(unaries)]
axes[3].set_title("Potts MRF")
result = potts_mrf(unaries, edges, 1.1, verbose=1)
axes[3].matshow(result.reshape(x.shape))
# repeat pairwise for each edge
pairwise = np.exp(np.eye(2) * 1.1)
pairwise = np.repeat(pairwise[np.newaxis, :, :], len(edges), axis=0)
result_mrf = mrf(unaries, edges, pairwise, verbose=1, alg="trw")
axes[4].set_title("MRF")
axes[4].matshow(result_mrf.reshape(x.shape))
for ax in axes:
ax.set_xticks(())
ax.set_yticks(())
plt.show()
def example_multinomial():
np.random.seed(45)
unaries = np.zeros((10, 12, 3))
unaries[:, :4, 0] = 1
unaries[:, 4:8, 1] = 1
unaries[:, 8:, 2] = 1
x = np.argmax(unaries, axis=2)
unaries_noisy = unaries + np.random.normal(size=unaries.shape)
x_thresh = np.argmax(unaries_noisy, axis=2)
unaries_noisy = np.exp(unaries_noisy).reshape(-1, 3)
inds = np.arange(x.size).reshape(x.shape).astype(np.int64)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert])
result = potts_mrf(unaries_noisy, edges, 1.1)
pairwise = np.eye(3) + np.ones((1, 1))
pairwise[-1, 0] = 0
pairwise[0, -1] = 0
print(pairwise)
# repeat pairwise for each edge
pairwise = np.repeat(pairwise[np.newaxis, :, :], len(edges), axis=0)
result_mrf = mrf(unaries_noisy, edges, np.exp(pairwise), alg="jt")
plot, axes = plt.subplots(1, 4)
axes[0].set_title("original")
axes[0].matshow(x)
axes[1].set_title("thresholded")
axes[1].matshow(x_thresh)
axes[1].set_title("Potts MRF")
axes[2].matshow(result.reshape(x.shape))
axes[1].set_title("MRF")
axes[3].matshow(result_mrf.reshape(x.shape))
for ax in axes:
ax.set_xticks(())
ax.set_yticks(())
plt.show()
def example_multinomial():
np.random.seed(45)
unaries = np.zeros((10, 12, 3))
unaries[:, :4, 0] = 1
unaries[:, 4:8, 1] = 1
unaries[:, 8:, 2] = 1
x = np.argmax(unaries, axis=2)
unaries_noisy = unaries + np.random.normal(size=unaries.shape)
x_thresh = np.argmax(unaries_noisy, axis=2)
unaries_noisy = np.exp(unaries_noisy).reshape(-1, 3)
inds = np.arange(x.size).reshape(x.shape).astype(np.int64)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert])
result = potts_mrf(unaries_noisy, edges, 1.1)
pairwise = np.eye(3) + np.ones((1, 1))
pairwise[-1, 0] = 0
pairwise[0, -1] = 0
print(pairwise)
# repeat pairwise for each edge
pairwise = np.repeat(pairwise[np.newaxis, :, :], len(edges), axis=0)
result_mrf = mrf(unaries_noisy, edges, np.exp(pairwise), alg="jt")
plot, axes = plt.subplots(1, 4)
axes[0].set_title("original")
axes[0].matshow(x)
axes[1].set_title("thresholded")
axes[1].matshow(x_thresh)
axes[1].set_title("Potts MRF")
axes[2].matshow(result.reshape(x.shape))
axes[1].set_title("MRF")
axes[3].matshow(result_mrf.reshape(x.shape))
for ax in axes:
ax.set_xticks(())
ax.set_yticks(())
plt.show()
