def on_cone_rotation(theta_image, normal_image, s):
theta = theta_image.as_vector()
nprime = normal_image.as_vector(keep_channels=True)
# cross product and break in to row vectors
C = np.cross(nprime, s)
C = normalise_vector(C)
u = C[:, 0]
v = C[:, 1]
w = C[:, 2]
# expects |nprime| = |sec| = 1
# represents intensity and can never be < 0
d = np.squeeze(np.inner(nprime, s) / (row_norm(nprime) * row_norm(s)))
d = np.nan_to_num(d)
d[d < 0.0] = 0.0
beta = np.arccos(d)
# flip beta and theta so that it rotates along the correct axis
alpha = beta - theta
c = np.cos(alpha)
cprime = 1.0 - c
s = np.sin(alpha)
# setup structures
N = nprime.shape[0]
phi = np.zeros([N, 3, 3])
phi[:, 0, 0] = c + u ** 2 * cprime
phi[:, 0, 1] = -w * s + u * v * cprime
phi[:, 0, 2] = v * s + u * w * cprime
phi[:, 1, 0] = w * s + u * v * cprime
phi[:, 1, 1] = c + v ** 2 * cprime
phi[:, 1, 2] = -u * s + v * w * cprime
phi[:, 2, 0] = -v * s + u * w * cprime
phi[:, 2, 1] = u * s + v * w * cprime
phi[:, 2, 2] = c + w ** 2 * cprime
n = np.einsum('kjl, klm -> kj', phi, nprime[..., None])
# Normalize the result ??
n = normalise_vector(n)
return normal_image.from_vector(n)
def on_cone_rotation(theta_image, normal_image, s):
theta = theta_image.as_vector()
nprime = normal_image.as_vector(keep_channels=True)
# cross product and break in to row vectors
C = np.cross(nprime, s)
C = normalise_vector(C)
u = C[:, 0]
v = C[:, 1]
w = C[:, 2]
# expects |nprime| = |sec| = 1
# represents intensity and can never be < 0
d = np.squeeze(np.inner(nprime, s) / (row_norm(nprime) * row_norm(s)))
d = np.nan_to_num(d)
d[d < 0.0] = 0.0
beta = np.arccos(d)
# flip beta and theta so that it rotates along the correct axis
alpha = beta - theta
c = np.cos(alpha)
cprime = 1.0 - c
s = np.sin(alpha)
# setup structures
N = nprime.shape[0]
phi = np.zeros([N, 3, 3])
phi[:, 0, 0] = c + u ** 2 * cprime
phi[:, 0, 1] = -w * s + u * v * cprime
phi[:, 0, 2] = v * s + u * w * cprime
phi[:, 1, 0] = w * s + u * v * cprime
phi[:, 1, 1] = c + v ** 2 * cprime
phi[:, 1, 2] = -u * s + v * w * cprime
phi[:, 2, 0] = -v * s + u * w * cprime
phi[:, 2, 1] = u * s + v * w * cprime
phi[:, 2, 2] = c + w ** 2 * cprime
n = np.einsum('kjl, klm -> kj', phi, nprime[..., None])
# Normalize the result ??
n = normalise_vector(n)
return normal_image.from_vector(n)
def expmap(self, tangent_vectors):
# If we've been passed a single vector to map, then add the extra axis
# Number of sample first
if len(tangent_vectors.shape) < 3:
tangent_vectors = tangent_vectors[None, ...]
# Expmap
v1 = tangent_vectors[..., 0]
v2 = tangent_vectors[..., 1]
normv = row_norm(tangent_vectors)
exp = np.concatenate([(v1 * np.sin(normv) / normv)[..., None],
(v2 * np.sin(normv) / normv)[..., None],
np.cos(normv)[..., None]], axis=2)
near_zero_ind = normv < np.spacing(1)
exp[near_zero_ind, :] = [0.0, 0.0, 1.0]
# Rotate back to geodesic mean from north pole
# Apply inverse rotation matrix due to data ordering
ns = np.einsum('fvi, ijv -> fvj', exp, self.rotation_matrices)
return ns
def expmap(self, tangent_vectors):
# If we've been passed a single vector to map, then add the extra axis
# Number of sample first
if len(tangent_vectors.shape) < 3:
tangent_vectors = tangent_vectors[None, ...]
# Expmap
v1 = tangent_vectors[..., 0]
v2 = tangent_vectors[..., 1]
normv = row_norm(tangent_vectors)
exp = np.concatenate([(v1 * np.sin(normv) / normv)[..., None],
(v2 * np.sin(normv) / normv)[..., None],
np.cos(normv)[..., None]],
axis=2)
near_zero_ind = normv < np.spacing(1)
exp[near_zero_ind, :] = [0.0, 0.0, 1.0]
# Rotate back to geodesic mean from north pole
# Apply inverse rotation matrix due to data ordering
ns = np.einsum('fvi, ijv -> fvj', exp, self.rotation_matrices)
return ns