def generate_scene(num_views: int, num_points: int) -> Dict[str, torch.Tensor]:
# Generate the 3d points
points3d = torch.rand(1, num_points, 3) # NxMx3
# Create random camera matrix
K = epipolar.random_intrinsics(0.0, 100.0) # 1x3x3
# Create random rotation per view
ang = torch.rand(num_views, 1) * kornia.pi * 2.0
rvec = torch.rand(num_views, 3)
rvec = ang * rvec / torch.norm(rvec, dim=1, keepdim=True) # Nx3
rot_mat = kornia.angle_axis_to_rotation_matrix(rvec) # Nx3x3
# matches with cv2.Rodrigues -> yay !
# Create random translation per view
tx = torch.empty(num_views).uniform_(-0.5, 0.5)
ty = torch.empty(num_views).uniform_(-0.5, 0.5)
tz = torch.empty(num_views).uniform_(-1.0, 2.0)
tvec = torch.stack([tx, ty, tz], dim=1)[..., None]
# Make sure the shape is in front of the camera
points3d_trans = (rot_mat @ points3d.transpose(-2, -1)) + tvec
min_dist = torch.min(points3d_trans[:, 2], dim=1)[0]
tvec[:, 2, 0] = torch.where(min_dist < 0, tz - min_dist + 1.0, tz)
# compute projection matrices
P = epipolar.projection_from_KRt(K, rot_mat, tvec)
# project points3d and backproject to image plane
points2d = kornia.transform_points(P, points3d.expand(num_views, -1, -1))
return dict(K=K, R=rot_mat, t=tvec, P=P, points3d=points3d, points2d=points2d)
def test_shape(self, batch_size, device, dtype):
B: int = batch_size
K = torch.rand(B, 3, 3, device=device, dtype=dtype)
R = torch.rand(B, 3, 3, device=device, dtype=dtype)
t = torch.rand(B, 3, 1, device=device, dtype=dtype)
P = epi.projection_from_KRt(K, R, t)
assert P.shape == (B, 3, 4)
def test_projection_from_krt(self, device, dtype):
K = torch.tensor(
[[[17.006138, 122.441254, 390.211426],
[0.0, 228.743622, 577.167480], [0.0, 0.0, 712.675232]]],
device=device,
dtype=dtype,
)
R = torch.tensor(
[[[0.396559, 0.511023, -0.762625], [
0.743249, -0.666318, -0.060006
], [0.538815, 0.543024, 0.644052]]],
device=device,
dtype=dtype,
)
t = torch.tensor([[[-6.477699], [1.129624], [0.143123]]],
device=device,
dtype=dtype)
P_expected = torch.tensor(
[[[308.0, 139.0, 231.0, 84.0], [481.0, 161.0, 358.0, 341.0],
[384.0, 387.0, 459.0, 102.0]]],
device=device,
dtype=dtype,
)
P_estimated = epi.projection_from_KRt(K, R, t)
assert_allclose(P_estimated, P_expected, atol=1e-4, rtol=1e-4)
def test_simple(self, device, dtype):
K = torch.tensor([[
[10., 0., 30.],
[0., 20., 40.],
[0., 0., 1.],
]],
device=device,
dtype=dtype)
R = torch.tensor([[
[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.],
]],
device=device,
dtype=dtype)
t = torch.tensor([
[[1.], [2.], [3.]],
], device=device, dtype=dtype)
P_expected = torch.tensor([[
[10., 0., 30., 100.],
[0., 20., 40., 160.],
[0., 0., 1., 3.],
]],
device=device,
dtype=dtype)
P_estimated = epi.projection_from_KRt(K, R, t)
assert_allclose(P_estimated, P_expected)
def test_simple(self, device, dtype):
K = torch.tensor(
[[[10.0, 0.0, 30.0], [0.0, 20.0, 40.0], [0.0, 0.0, 1.0]]],
device=device,
dtype=dtype)
R = torch.tensor([[[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]],
device=device,
dtype=dtype)
t = torch.tensor([[[1.0], [2.0], [3.0]]], device=device, dtype=dtype)
P_expected = torch.tensor(
[[[10.0, 0.0, 30.0, 100.0], [0.0, 20.0, 40.0, 160.0],
[0.0, 0.0, 1.0, 3.0]]],
device=device,
dtype=dtype)
P_estimated = epi.projection_from_KRt(K, R, t)
assert_allclose(P_estimated, P_expected, atol=1e-4, rtol=1e-4)
def test_smoke(self, device, dtype):
K = torch.rand(1, 3, 3, device=device, dtype=dtype)
R = torch.rand(1, 3, 3, device=device, dtype=dtype)
t = torch.rand(1, 3, 1, device=device, dtype=dtype)
P = epi.projection_from_KRt(K, R, t)
assert P.shape == (1, 3, 4)
