def compose_tps_after_translation_test():
a = PointCloud(np.random.random([10, 2]))
b = PointCloud(np.random.random([10, 2]))
t = Translation([3, 4])
tps = TPS(a, b)
chain = tps.compose_after(t)
assert(isinstance(chain, TransformChain))
def chain_tps_after_pwa_test():
a_tm = TriMesh(np.random.random([10, 2]))
b = PointCloud(np.random.random([10, 2]))
pwa = PiecewiseAffineTransform(a_tm, b)
tps = TPS(b, a_tm)
chain = tps.compose_after(pwa)
assert(isinstance(chain, TransformChain))
def test_tps_apply():
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 = PointCloud(np.array([[-0.1, -1.0], [-0.5, 1.0], [2.1, -2.5]]))
tps = TPS(src, tgt)
result = tps.apply(pts)
expected = np.array([[-0.2, -2.], [-1., 2.], [4.2, -5.]])
assert_allclose(result.points, expected)
def test_tps_jacobian_manual_sample_b():
tps = TPS(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 = TPS(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_points():
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]]))
tps = TPS(src, tgt)
result = tps.jacobian_points(src.points)
assert_allclose(result, np.array([[[2, 0], [0., 2]],
[[2, 0], [0, 2]],
[[2, 0], [0, 2]],
[[2, 0], [0, 2]]]), atol=10 ** -14)
def chain_tps_after_tps_test():
a = PointCloud(np.random.random([10, 2]))
b = PointCloud(np.random.random([10, 2]))
tps_one = TPS(a, b)
tps_two = TPS(b, a)
chain = tps_one.compose_after(tps_two)
assert(isinstance(chain, TransformChain))
points = PointCloud(np.random.random([10, 2]))
chain_res = chain.apply(points)
manual_res = tps_one.apply(tps_two.apply(points))
assert (np.all(chain_res.points == manual_res.points))
def test_tps_jacobian_manual_corner_value_check():
tps = TPS(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_weight_points():
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 = TPS(src, tgt)
result = tps.weight_points(pts)
expected = np.array([[[0.55399517, 0.55399517], [-0.00399517, -0.00399517],
[0.44600483, 0.44600483], [0.00399517, 0.00399517]],
[[-0.01625165, -0.01625165], [0.76625165, 0.76625165],
[0.01625165, 0.01625165], [0.23374835, 0.23374835]],
[[0.01631597, 0.01631597], [-0.56631597, -0.56631597],
[1.73368403, 1.73368403],
[-0.18368403, -0.18368403]]])
assert_allclose(result, expected, rtol=10 ** -6)
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 = TPS(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 chain_compose_before_tps_test():
a = PointCloud(np.random.random([10, 2]))
b = PointCloud(np.random.random([10, 2]))
tps = TPS(a, b)
t = Translation([3, 4])
s = Scale([4, 2])
chain = TransformChain([t, s])
chain_mod = chain.compose_before(tps)
points = PointCloud(np.random.random([10, 2]))
manual_res = tps.apply(s.apply(t.apply(points)))
chain_res = chain_mod.apply(points)
assert(np.all(manual_res.points == chain_res.points))
def test_tps_jacobian_unitary_x_y():
tps = TPS(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)
def test_tps_maps_src_to_tgt():
tps = TPS(src, tgt_perturbed)
assert_allclose(tps.apply(square_src_landmarks), perturbed_tgt_landmarks)