def wrapped_phase_difference(x, ax):
padding = [[0, 0] for _ in range(2)]
padding[ax][1] = 1
x1 = np.pad(np.diff(x, n=1, axis=ax), padding, "edge")
x2 = np.pad(np.diff(dv.wrap_phase(x + np.pi), n=1, axis=ax), padding, "edge")
out = x1
out[np.absolute(x1) > np.absolute(x2)] = x2[np.absolute(x1) > np.absolute(x2)]
return out
def test_wrap_phase():
# Scalars
assert np.allclose(wrap_phase(0.0), 0.0)
assert np.allclose(wrap_phase(+1.0), +1.0)
assert np.allclose(wrap_phase(-1.0), -1.0)
assert np.allclose(wrap_phase(-6.0), (-6.0 + 2.0 * np.pi))
assert np.allclose(wrap_phase(+6.0), (+6.0 - 2.0 * np.pi))
# ndarray
assert np.allclose(wrap_phase(np.zeros((3, 3))), np.zeros((3, 3)))
assert np.allclose(wrap_phase(np.ones((3, 3))), np.ones((3, 3)))
assert np.allclose(wrap_phase(np.ones((3, 3)) + 2 * np.pi), np.ones(
(3, 3)))
# ND Array
assert np.allclose(wrap_phase(np.array(np.zeros((3, 3)))),
np.array(np.zeros((3, 3))))
def test_tf_phase():
a = np.expand_dims(np.linspace(-np.pi, np.pi, 101, "float32"), -1).transpose()
b = -a
c = dv.wrap_phase(b - a)
a_tf = tf.convert_to_tensor(a, "float32")
b_tf = tf.convert_to_tensor(b, "float32")
c_tf = dvpy.tf.wrapped_phase_difference(a_tf, b_tf)
with tf.Session() as s:
c_tf_eval = s.run(c_tf)
assert np.allclose(c_tf_eval, c)
def test_wrapped_phase_difference():
A = dv.wrap_phase(np.reshape([x for x in range(128)] * 128, (128, 128)))
pos_phase_grad = dv.wrapped_phase_difference(A, 1)
neg_phase_grad = dv.wrapped_phase_difference(-1 * A, 1)
assert np.allclose(pos_phase_grad, np.ones_like(pos_phase_grad))
assert np.allclose(neg_phase_grad, -1 * np.ones_like(neg_phase_grad))
plt.imshow(A, "gray")
plt.show()
plt.imshow(dv.wrapped_phase_difference(A, 1))
plt.show()
plt.imshow(dv.wrapped_phase_difference(-1 * A, 1))
plt.show()
xy_a = (xy_t + xy_p) / 2.0
xy_d = xy_t - xy_p
## Rotation
rt_t = [
np.load(os.path.join(tdir, 'true_rt_mat_batch_%d_hgd_3.npy' % (i)))
for i in range(3)
]
rt_p = [
np.load(os.path.join(tdir, 'prediction_rt_mat_batch_%d_hgd_3.npy' % (i)))
for i in range(3)
]
rt_t = np.concatenate(rt_t) + np.pi
rt_p = np.concatenate(rt_p) + np.pi
rt_t = dv.wrap_phase(rt_t).squeeze()
rt_p = dv.wrap_phase(rt_p).squeeze()
rt_a = dv.wrap_phase(rt_t + rt_p) / 2.0
rt_d = dv.wrap_phase(rt_t - rt_p)
## Zoom
zm_t = [
np.load(os.path.join(tdir, 'true_zm_mat_batch_%d_hgd_3.npy' % (i)))
for i in range(3)
]
zm_p = [
np.load(os.path.join(tdir, 'prediction_zm_mat_batch_%d_hgd_3.npy' % (i)))
for i in range(3)
]
zm_t = np.concatenate(zm_t).squeeze()
import pylab as plt import dvpy as dv d = np.arange(-10, +10, 0.1) w = dv.wrap_phase(d) plt.plot(d) plt.plot(w) plt.show()
g = np.linspace(-np.pi, np.pi, s)
p = np.linspace(-np.pi, np.pi, s)
G, P = np.meshgrid(g, p)
##
##
##
fig1 = plt.figure(figsize=(6, 5))
fig2 = plt.figure(figsize=(6, 5))
ax1 = fig1.add_subplot(1, 1, 1, projection = '3d')
ax2 = fig2.add_subplot(1, 1, 1, projection = '3d')
ax1.plot_surface(G, P, (P - G)**2, cmap=cm.jet, rcount = s, ccount = s)
ax2.plot_surface(G, P, (dv.wrap_phase(P - G))**2, cmap=cm.jet, rcount = s, ccount = s)
for ax in [ax1, ax2]:
ax.set_xlabel(r'$\hat{\theta}$', labelpad = 10)
ax.set_ylabel(r'$\theta$' , labelpad = 10)
ax.invert_yaxis()
ax.view_init(elev = 20.0, azim = -80.0)
ax.set_zlim([0,45])
ax.set_xlim([-np.pi, +np.pi])
ax.set_ylim([-np.pi, +np.pi])
ax.set_xticks([-np.pi, 0.0, np.pi])
ax.set_yticks([-np.pi, 0.0, np.pi])
ax.set_xticklabels(['$-\pi$', '$0$', '$+\pi$'])
ax.set_yticklabels(['$-\pi$', '$0$', '$+\pi$'])
ax1.set_zlabel(r'$\frac{1}{2} (\theta - \hat{\theta})^2$' , labelpad = 10)