def test_cubic_spline_derivative():
# Test derivative of the cubic spline, as defined in [Mattes03] eq. (3) by
# comparing the analytical and numerical derivatives
#
# [Mattes03] Mattes, D., Haynor, D. R., Vesselle, H., Lewellen, T. K.,
# & Eubank, W. PET-CT image registration in the chest using
# free-form deformations. IEEE Transactions on Medical Imaging,
# 22(1), 120-8, 2003.
in_list = []
for epsilon in [-1e-9, 0.0, 1e-9]:
for t in [-2.0, -1.0, 0.0, 1.0, 2.0]:
x = t + epsilon
in_list.append(x)
h = 1e-6
in_list = np.array(in_list)
input_h = in_list + h
s = np.array(cubic_spline(in_list))
s_h = np.array(cubic_spline(input_h))
expected = (s_h - s) / h
actual = cubic_spline_derivative(in_list)
assert_array_almost_equal(actual, expected)
def test_cubic_spline_derivative():
# Test derivative of the cubic spline, as defined in [Mattes03] eq. (3) by
# comparing the analytical and numerical derivatives
#
# [Mattes03] Mattes, D., Haynor, D. R., Vesselle, H., Lewellen, T. K.,
# & Eubank, W. PET-CT image registration in the chest using
# free-form deformations. IEEE Transactions on Medical Imaging,
# 22(1), 120-8, 2003.
in_list = []
for epsilon in [-1e-9, 0.0, 1e-9]:
for t in [-2.0, -1.0, 0.0, 1.0, 2.0]:
x = t + epsilon
in_list.append(x)
h = 1e-6
in_list = np.array(in_list)
input_h = in_list + h
s = np.array(cubic_spline(in_list))
s_h = np.array(cubic_spline(input_h))
expected = (s_h - s) / h
actual = cubic_spline_derivative(in_list)
assert_array_almost_equal(actual, expected)