def test_tps_jacobian_manual_sample_b():
tps = ThinPlateSplines(src, tgt_perturbed)
dW_dxy = tps.jacobian_source(square_sample_points)
threesixfouronethree = np.array(
[[0.67244171, -0.0098011],
[-0.77028611, -1.19256858],
[0.8296718, 0.95940495],
[-0.03122042, 1.00073478]])
assert_allclose(dW_dxy[36413], threesixfouronethree, atol=1e-5)
def test_tps_jacobian_manual_sample_a():
tps = ThinPlateSplines(src, tgt_perturbed)
dW_dxy = tps.jacobian_source(square_sample_points)
onetwothreefour = np.array(
[[0.78665966, 0.62374388],
[0.09473867, -0.68910365],
[0.68788235, 0.18713078],
[-0.80552584, 1.11078411]])
assert_allclose(dW_dxy[1234], onetwothreefour, rtol=10 ** -6)
def test_tps_jacobian_manual_corner_value_check():
tps = ThinPlateSplines(src, tgt)
dW_dxy = tps.jacobian_source(square_sample_points)
jacobian_image = dW_dxy.reshape(xx.shape + (4, 2))
dwdx_corner = np.array(
[[1., 0.99619633, 0.99231034, 0.98835616, 0.98434133],
[0.99619633, 0.99240803, 0.98853625, 0.98459474, 0.98059178],
[0.99231034, 0.98853625, 0.98468246, 0.98075813, 0.9767711],
[0.98835616, 0.98459474, 0.98075813, 0.97685217, 0.97288316],
[0.98434133, 0.98059178, 0.9767711, 0.97288316, 0.96893276]])
assert_allclose(jacobian_image[:5, :5, 0, 0], dwdx_corner)
assert_allclose(jacobian_image[:5, :5, 0, 1], dwdx_corner)
def test_tps_jacobian_source():
src = PointCloud(np.array([[-1.0, -1.0], [-1, 1], [1, -1], [1, 1]]))
tgt = PointCloud(np.array([[-2.0, -2.0], [-2, 2], [2, -2], [2, 2]]))
pts = np.array([[-0.1, -1.0], [-0.5, 1.0], [2.1, -2.5]])
tps = ThinPlateSplines(src, tgt)
result = tps.jacobian_source(pts)
expected = np.array([[[1.10799034, 1.10799034], [-0.00799034, -0.00799034],
[0.89200966, 0.89200966], [0.00799034, 0.00799034]],
[[-0.0325033, -0.0325033], [1.5325033, 1.5325033],
[0.0325033, 0.0325033], [0.4674967, 0.4674967]],
[[0.03263195, 0.03263195], [-1.13263195, -1.13263195],
[3.46736805, 3.46736805],
[-0.36736805, -0.36736805]]])
assert_allclose(result, expected, rtol=10 ** -6)
def test_tps_jacobian_unitary_x_y():
tps = ThinPlateSplines(src, tgt)
dW_dxy = tps.jacobian_source(square_sample_points)
jacobian_image = dW_dxy.reshape(xx.shape + (4, 2))
# both the x and y derivatives summed over all values should equal 1
assert_allclose(jacobian_image.sum(axis=2), 1)
