def test_tensor_analysis(self):
tensor = np.array([[1, 0], [0, 1]])
tot_coher, tot_angle, tot_energy = tensor_analysis(tensor)
self.assertArrayAlmostEqual(np.array([0]), tot_coher)
self.assertArrayAlmostEqual(np.array([0]), tot_angle)
self.assertArrayAlmostEqual(np.array([2]), tot_energy)
tensor = np.array([[1, 0], [0, -1]])
tot_coher, tot_angle, tot_energy = tensor_analysis(tensor)
self.assertArrayAlmostEqual(np.array([0]), tot_coher)
self.assertArrayAlmostEqual(np.array([90]), tot_angle)
self.assertArrayAlmostEqual(np.array([2]), tot_energy)
tensor = np.array([[1, 0], [0, 0]])
tot_coher, tot_angle, tot_energy = tensor_analysis(tensor)
self.assertArrayAlmostEqual(np.array([1]), tot_coher)
self.assertArrayAlmostEqual(np.array([90]), tot_angle)
self.assertArrayAlmostEqual(np.array([1]), tot_energy)
tensor = np.array([[0, 0], [0, 1]])
tot_coher, tot_angle, tot_energy = tensor_analysis(tensor)
self.assertArrayAlmostEqual(np.array([1]), tot_coher)
self.assertArrayAlmostEqual(np.array([0]), tot_angle)
self.assertArrayAlmostEqual(np.array([1]), tot_energy)
tensor = np.array([[0, 1], [1, 0]])
tot_coher, tot_angle, tot_energy = tensor_analysis(tensor)
self.assertArrayAlmostEqual(np.array([0]), tot_coher)
self.assertArrayAlmostEqual(np.array([45]), tot_angle)
self.assertArrayAlmostEqual(np.array([0]), tot_energy)
def create_angle_reference(size, min_n=50, max_n=120):
# Make circular test image
size = np.max(np.asarray([min_n, size], dtype=int))
size = np.min(np.asarray([size, max_n], dtype=int))
if np.mod(size, 2) != 0:
size += 1
image_grid = np.mgrid[:size, :size]
for i in range(2):
image_grid[i] -= size * np.array(2 * image_grid[i] / size, dtype=int)
image_grid[i] = np.fft.fftshift(image_grid[i])
image_radius = np.sqrt(np.sum(image_grid**2, axis=0))
image_sine = np.sin(4 * np.pi * image_radius / size)
image_cos = np.cos(4 * np.pi * image_radius / size)
image_rings = image_sine * image_cos
j_tensor = form_structure_tensor(image_rings, sigma=1.0)
pix_j_coher, pix_j_angle, pix_j_energy = tensor_analysis(j_tensor)
pix_j_angle = rotate(pix_j_angle, 90)[:size // 2]
pix_j_coher = pix_j_coher[:size // 2]
pix_j_energy = np.where(image_radius < (size / 2), pix_j_energy,
0)[:size // 2]
return pix_j_angle, pix_j_coher, pix_j_energy
def create_tensor_image(image, min_N=50):
# Form structure tensors for each pixel
j_tensor = form_structure_tensor(image, sigma=1.0)
# Perform coherence and angle analysis on each pixel
pix_j_coher, pix_j_angle, pix_j_energy = tensor_analysis(j_tensor)
hue = (pix_j_angle + 90) / 180
saturation = pix_j_coher / pix_j_coher.max()
brightness = image / image.max()
size = 0.2 * np.sqrt(image.size)
if size >= min_N:
ref_angle, ref_coher, ref_energy = create_angle_reference(size)
size = ref_angle.shape[1]
start = -size // 2
end = image.shape[0]
hue[start:end, :size] = (ref_angle + 90) / 180
saturation[start:end, :size] = ref_coher / ref_coher.max()
brightness[start:end, :size] = ref_energy / ref_energy.max()
# Form structure tensor image
rgb_image = create_hsb_image(image, hue, saturation, brightness)
return rgb_image
def test_1d_tensor(self):
tensor_1d = np.array([[[0, 1], [1, 0]], [[0, 0], [0, 1]]])
tot_coher, tot_angle, tot_energy = tensor_analysis(tensor_1d)
self.assertArrayAlmostEqual(np.array([0, 1]), tot_coher)
self.assertArrayAlmostEqual(np.array([45, 0]), tot_angle)
self.assertArrayAlmostEqual(np.array([0, 1]), tot_energy)
def structure_tensor_metrics(structure_tensor, tag=''):
"""Nematic tensor analysis for a scikit-image region"""
database = pd.Series(dtype=object)
(segment_coher_map, segment_angle_map,
segment_angle_map) = tensor_analysis(structure_tensor)
# Calculate mean structure tensor elements
axis = tuple(range(structure_tensor.ndim - 2))
mean_tensor = np.mean(structure_tensor, axis=axis)
segment_coher, _, _ = tensor_analysis(mean_tensor)
database[f"{tag} Angle SDI"], _ = angle_analysis(segment_angle_map,
segment_coher_map)
database[f"{tag} Coherence"] = segment_coher[0]
database[f"{tag} Local Coherence"] = np.mean(segment_coher_map)
return database