def test_structure_tensor_eigenvalues_3d():
image = np.pad(cube(9), 5, mode='constant') * 1000
boundary = (np.pad(cube(9), 5, mode='constant') -
np.pad(cube(7), 6, mode='constant')).astype(bool)
A_elems = structure_tensor(image, sigma=0.1)
e0, e1, e2 = structure_tensor_eigenvalues(A_elems)
# e0 should detect facets
assert np.all(e0[boundary] != 0)
def test_structure_tensor_eigenvalues():
square = np.zeros((5, 5))
square[2, 2] = 1
A_elems = structure_tensor(square, sigma=0.1, order='rc')
l1, l2 = structure_tensor_eigenvalues(A_elems)
assert_array_equal(
l1,
np.array([[0, 0, 0, 0, 0], [0, 2, 4, 2, 0], [0, 4, 0, 4, 0],
[0, 2, 4, 2, 0], [0, 0, 0, 0, 0]]))
assert_array_equal(
l2,
np.array([[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0],
[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]))
def test_structure_tensor_eigenvalues(dtype):
square = np.zeros((5, 5), dtype=dtype)
square[2, 2] = 1
A_elems = structure_tensor(square, sigma=0.1, order='rc')
l1, l2 = structure_tensor_eigenvalues(A_elems)
out_dtype = _supported_float_type(dtype)
assert all(a.dtype == out_dtype for a in (l1, l2))
assert_array_equal(
l1,
np.array([[0, 0, 0, 0, 0], [0, 2, 4, 2, 0], [0, 4, 0, 4, 0],
[0, 2, 4, 2, 0], [0, 0, 0, 0, 0]]))
assert_array_equal(
l2,
np.array([[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0],
[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]))
# About the brightest region (i.e., at row ~ 22 and column ~ 17), we can see # variations (and, hence, strong gradients) over 2 or 3 (resp. 1 or 2) pixels # across columns (resp. rows). We may thus choose, say, ``sigma = 1.5`` for # the window # function. Alternatively, we can pass sigma on a per-axis basis, e.g., # ``sigma = (1, 2, 3)``. Note that size 1 sounds reasonable along the first # (Z, plane) axis, since the latter is of size 8 (13 - 5). Viewing slices in # the X-Z or Y-Z planes confirms it is reasonable. sigma = (1, 1.5, 2.5) A_elems = feature.structure_tensor(sample, sigma=sigma) ##################################################################### # We can then compute the eigenvalues of the structure tensor. eigen = feature.structure_tensor_eigenvalues(A_elems) eigen.shape ##################################################################### # Where is the largest eigenvalue? coords = np.unravel_index(eigen.argmax(), eigen.shape) assert coords[0] == 0 # by definition coords ##################################################################### # .. note:: # The reader may check how robust this result (coordinates # ``(plane, row, column) = coords[1:]``) is to varying ``sigma``. # # Let us view the spatial distribution of the eigenvalues in the X-Y plane