def find_tfrom_between_shapes(from_shape: np.matrix,
to_shape: np.matrix
) -> Tuple[np.matrix]:
"""
Find transform between shapes
Parameters:
----------
:param from_shape: type(numpy.matrix
Input shape
:param to_shape: type(numpy.matrix
Output shape
:return: tran_m - transformation matrix, tran_b - transformation matrix
"""
assert from_shape.shape[0] == to_shape.shape[0] and from_shape.shape[0] % 2 == 0
sigma_from = 0.0
sigma_to = 0.0
cov = np.matrix([[0.0, 0.0], [0.0, 0.0]])
# compute the mean and cov
from_shape_points = from_shape.reshape(from_shape.shape[0] // 2, 2)
to_shape_points = to_shape.reshape(to_shape.shape[0] // 2, 2)
mean_from = from_shape_points.mean(axis=0)
mean_to = to_shape_points.mean(axis=0)
for i in range(from_shape_points.shape[0]):
temp_dis = np.linalg.norm(from_shape_points[i] - mean_from)
sigma_from += temp_dis * temp_dis
temp_dis = np.linalg.norm(to_shape_points[i] - mean_to)
sigma_to += temp_dis * temp_dis
cov += (to_shape_points[i].transpose() - mean_to.transpose()) * (
from_shape_points[i] - mean_from
)
sigma_from = sigma_from / to_shape_points.shape[0]
sigma_to = sigma_to / to_shape_points.shape[0]
cov = cov / to_shape_points.shape[0]
# compute the affine matrix
s = np.matrix([[1.0, 0.0], [0.0, 1.0]])
u, d, vt = np.linalg.svd(cov)
if np.linalg.det(cov) < 0:
if d[1] < d[0]:
s[1, 1] = -1
else:
s[0, 0] = -1
r = u * s * vt
c = 1.0
if sigma_from != 0:
c = 1.0 / sigma_from * np.trace(np.diag(d) * s)
tran_b = mean_to.transpose() - c * r * mean_from.transpose()
tran_m = c * r
return tran_m, tran_b
def superhill_enc(mat: np.matrix, pt: np.matrix, vector: np.array):
shape = pt.shape
pt = pt.flatten()
vector = np.array(vector)
pmat = pt.reshape((-1, 2))
for i in range(pmat.shape[0]):
pmat[i] = hill_encode(mat, pmat[i])
# pmat[i] = (pmat[i] * mat) % 256
if i % 2 == 0:
# print(mat[0, 0], mat[0, 0] * vector[0], vector[0])
mat[0, 0] = mat[0, 0] * vector[0, 0] % 256
mat[0, 1] = mat[0, 1] * vector[0, 1] % 256
else:
mat[1, 0] = mat[1, 0] * vector[0, 0] % 256
mat[1, 1] = mat[1, 1] * vector[0, 1] % 256
return pmat.reshape(shape)