def test_hessian_matrix():
square = cp.zeros((5, 5))
square[2, 2] = 4
Hrr, Hrc, Hcc = hessian_matrix(square, sigma=0.1, order="rc")
# fmt: off
assert_array_almost_equal(
Hrr,
cp.asarray([
[0, 0, 0, 0, 0], # noqa
[0, 0, 0, 0, 0], # noqa
[2, 0, -2, 0, 2], # noqa
[0, 0, 0, 0, 0], # noqa
[0, 0, 0, 0, 0], # noqa
]))
assert_array_almost_equal(
Hrc,
cp.asarray([
[0, 0, 0, 0, 0], # noqa
[0, 1, 0, -1, 0], # noqa
[0, 0, 0, 0, 0], # noqa
[0, -1, 0, 1, 0], # noqa
[0, 0, 0, 0, 0], # noqa
]))
assert_array_almost_equal(
Hcc,
cp.asarray([
[0, 0, 2, 0, 0], # noqa
[0, 0, 0, 0, 0], # noqa
[0, 0, -2, 0, 0], # noqa
[0, 0, 0, 0, 0], # noqa
[0, 0, 2, 0, 0], # noqa
]))
def test_hessian_matrix_3d():
cube = cp.zeros((5, 5, 5))
cube[2, 2, 2] = 4
Hs = hessian_matrix(cube, sigma=0.1, order="rc")
assert len(
Hs) == 6, "incorrect number of Hessian images (%i) for 3D" % len(Hs)
# fmt: off
assert_array_almost_equal(
Hs[2][:, 2, :],
cp.asarray([
[0, 0, 0, 0, 0], # noqa
[0, 1, 0, -1, 0], # noqa
[0, 0, 0, 0, 0], # noqa
[0, -1, 0, 1, 0], # noqa
[0, 0, 0, 0, 0], # noqa
]))
def test_hessian_matrix_eigvals_3d(im3d):
H = hessian_matrix(im3d)
E = hessian_matrix_eigvals(H)
E = cp.asnumpy(E)
# test descending order:
e0, e1, e2 = E
assert np.all(e0 >= e1) and np.all(e1 >= e2)
E0, E1, E2 = E[:, E.shape[1] // 2] # cross section
row_center, col_center = np.asarray(E0.shape) // 2
circles = [
draw.circle_perimeter(row_center, col_center, radius, shape=E0.shape)
for radius in range(1, E0.shape[1] // 2 - 1)
]
response0 = np.array([np.mean(E0[c]) for c in circles])
response2 = np.array([np.mean(E2[c]) for c in circles])
# eigenvalues are negative just inside the sphere, positive just outside
assert np.argmin(response2) < np.argmax(response0)
assert np.min(response2) < 0
assert np.max(response0) > 0
def test_hessian_matrix_eigvals():
square = cp.zeros((5, 5))
square[2, 2] = 4
H = hessian_matrix(square, sigma=0.1, order="rc")
l1, l2 = hessian_matrix_eigvals(H)
# fmt: off
assert_array_almost_equal(
l1,
cp.asarray([
[0, 0, 2, 0, 0], # noqa
[0, 1, 0, 1, 0], # noqa
[2, 0, -2, 0, 2], # noqa
[0, 1, 0, 1, 0], # noqa
[0, 0, 2, 0, 0], # noqa
]))
assert_array_almost_equal(
l2,
cp.asarray([
[0, 0, 0, 0, 0], # noqa
[0, -1, 0, -1, 0], # noqa
[0, 0, -2, 0, 0], # noqa
[0, -1, 0, -1, 0], # noqa
[0, 0, 0, 0, 0], # noqa
]))