def advanced_solve_ellipse(img, center, lengths, angle, phase_width, radius, num_points=500):
""" This is a method in development. Better at optimizing angular correlations
This method is in development. Due to the fact that an ellipse will have maximum 2-fold symmetry when the center
is correctly determined and maximum 2*n-fold symmetry when the major/ minor axes as well as the angle of rotation
is correct. This algorithm optimizes for these quantities.
Parameters:
-----------
img: Array-like
2-d Array of some image
range: list
The lower and upper limits to look at. Usually should just look at the first ring.
num_points: int
The number of points to look at to determine the characteristic ellipse.
Return:
-------------
center: list
The x and y coordinates of the center
lengths: list
The major and minor axes
angle: float
The angle of rotation for the ellipse
"""
# Brute force testing method...
x = np.linspace(-5,5,20)
y = np.linspace(-5, 5, 20)
pol =[[convert(img, angle=None, lengths=None, center=np.add(center[x1,y1]), phase_width=phase_width, radius=radius)
for x1 in x]for y1 in y]
def test_simulation_correction(self):
center = [263, 274]
angle = np.pi/3
lengths =[11,10]
i = simulate_pattern(4,
k=100,
num_clusters=300,
probe_size=20,
center=center,
angle=angle,
lengths=lengths)
i = np.random.poisson(i)
c, l, a = solve_ellipse(i)
# asserting the ellipse is correctly identified
self.assertAlmostEqual(center[0], c[0], places=-1)
self.assertAlmostEqual(center[1], c[1], places=-1)
self.assertAlmostEqual(l[0]/l[1], max(lengths)/min(lengths), places=-1)
self.assertAlmostEqual(angle, a, places=1)
# converting to polar coordinates
conversion = convert(img=i, center=c, lengths=l, angle=a)
ac = angular_correlation(conversion, normalize=True)
ps = power_spectrum(ac)
#plt.imshow(i)
#plt.show()
plt.imshow(conversion[:, 0:359])
plt.figure()
plt.imshow(conversion[:, 360:719])
plt.show()
#plt.imshow(ac)
plt.imshow(ps[:, 0:12])
plt.show()
def test_polar_unwrapping(self):
i = np.ones((512, 512)) * .01
for j in range(0, 10):
s = np.random.choice([2, 4, 6, 8, 10])
print(s)
v, ro = sample_spherical_cap()
i = i + simulate_pattern(
symmetry=s, k=12, radius=6, rotation_vector=v, rotation=ro)
i = i + np.random.random((512, 512)) * np.max(i) / 4
plt.imshow(i)
plt.show()
pol = convert(i,
center=(256, 256),
angle=None,
lengths=None,
radius=[0, 200],
phase_width=720)
plt.imshow(pol)
plt.show()
ang = angular_correlation(pol)
ps = power_spectrum(ang)
plt.imshow(ang)
plt.show()
plt.imshow(ps[50:, 0:12], aspect=.05)
plt.show()
def test_2d_convert(self):
start = timeit()
conversion = convert(self.d,
center=self.center,
angle=self.angle,
lengths=self.lengths,
phase_width=720)
stop = timeit()
print((stop - start))
s = np.sum(conversion, axis=1)
even = np.sum(conversion, axis=0)
self.assertLess((s > max(s) / 2).sum(), 4)
def test_polar_unwrapping(self):
i = simulate_pattern(symmetry=6,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=0.6)
i = i + simulate_pattern(symmetry=4,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=0.2)
i = i + simulate_pattern(symmetry=4,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=0.7)
i = i + simulate_pattern(symmetry=8,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=0.9)
i = i + simulate_pattern(symmetry=10,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=0.8)
i = i + simulate_pattern(symmetry=4,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=1.5)
i = i + simulate_pattern(symmetry=4,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=6.4)
i = i + simulate_pattern(symmetry=8,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=4.9)
i = i + simulate_pattern(symmetry=10,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=2.3)
i = i + simulate_pattern(symmetry=10,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=2.8)
i = i + simulate_pattern(symmetry=4,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=13.5)
i = i + simulate_pattern(symmetry=4,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=6.4)
i = i + simulate_pattern(symmetry=8,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=5.9)
i = i + simulate_pattern(symmetry=10,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=5.3)
i = i + simulate_pattern(symmetry=10,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=3.8)
i = i + simulate_pattern(symmetry=4,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=12.5)
i = i + simulate_pattern(symmetry=4,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=3.4)
i = i + simulate_pattern(symmetry=8,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=4.9)
i = i + simulate_pattern(symmetry=10,
k=12,
radius=6,
rotation_vector=(0, 0, 1),
rotation=3.8)
i = i + np.random.random((512, 512)) * 3
plt.imshow(i)
plt.show()
pol = convert(i,
center=(256, 256),
angle=None,
lengths=None,
radius=[0, 200],
phase_width=720)
plt.imshow(pol)
plt.show()
ang = angular_correlation(pol)
ps = power_spectrum(ang)
plt.imshow(ang)
plt.show()
plt.imshow(ps[50:, 0:12], aspect=.05)
plt.show()