def image_gradient_T(x):
"""
Transpose of the operator that function image_gradient implements.
Computes the transpose of the matrix given by function image_gradient.
Parameters
----------
x : numpy.ndarray or ctorch.ComplexTensor
stack of two identically shaped arrays
Returns
-------
numpy.ndarray or ctorch.ComplexTensor
result of applying to x the transpose of function image_gradient
"""
if isinstance(x, np.ndarray):
x_h = x[0]
x_v = x[1]
# Wrap the first column of x_h around to the end.
x_h_ext = np.hstack((x_h, x_h[:, :1]))
# Wrap the first row of x_v around to the end.
x_v_ext = np.vstack((x_v, x_v[:1]))
# Apply forward differences to the columns of x.
d_x = x_h_ext[:, :-1] - x_h_ext[:, 1:]
# Apply forward differences to the rows of x.
d_y = x_v_ext[:-1] - x_v_ext[1:]
return d_x + d_y
elif isinstance(x, ctorch.ComplexTensor):
x_h = x[0]
x_v = x[1]
# Wrap the first column of x_h around to the end.
x_h_ext = ctorch.cat((x_h, x_h[:, :1]), dim=1)
# Wrap the first row of x_v around to the end.
x_v_ext = ctorch.cat((x_v, x_v[:1]), dim=0)
# Apply forward differences to the columns of x.
d_x = x_h_ext[:, :-1] - x_h_ext[:, 1:]
# Apply forward differences to the rows of x.
d_y = x_v_ext[:-1] - x_v_ext[1:]
return d_x + d_y
else:
raise TypeError('Input must be a numpy.ndarray ' +
'or a ctorch.ComplexTensor.')
def image_gradient(x):
"""
First-order finite-differencing both horizontally and vertically.
Computes a first-order finite-difference approximation to the gradient.
Parameters
----------
x : numpy.ndarray or ctorch.ComplexTensor
image (that is, two-dimensional array)
Returns
-------
numpy.ndarray or ctorch.ComplexTensor
horizontal finite differences of x stacked on top of the vertical
finite differences (separating horizontal from vertical via the
initial dimension)
"""
if isinstance(x, np.ndarray):
# Wrap the last column of x around to the beginning.
x_h = np.hstack((x[:, -1:], x))
# Wrap the last row of x around to the beginning.
x_v = np.vstack((x[-1:], x))
# Apply forward differences to the columns of x.
d_x = (x_h[:, 1:] - x_h[:, :-1])
# Apply forward differences to the rows of x.
d_y = (x_v[1:] - x_v[:-1])
return np.vstack((d_x.ravel(), d_y.ravel()))
elif isinstance(x, ctorch.ComplexTensor):
# Wrap the last column of x around to the beginning.
x_h = ctorch.cat((x[:, -1:], x), dim=1)
# Wrap the last row of x around to the beginning.
x_v = ctorch.cat((x[-1:], x), dim=0)
# Apply forward differences to the columns of x.
d_x = (x_h[:, 1:] - x_h[:, :-1])
# Apply forward differences to the rows of x.
d_y = (x_v[1:] - x_v[:-1])
return ctorch.cat((d_x, d_y)).view(2, -1)
else:
raise TypeError('Input must be a numpy.ndarray ' +
'or a ctorch.ComplexTensor.')