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Fix multi-axis shear transform to compose individual shear matrices #8778

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Fix multi-axis shear transform to compose individual shear matrices #8778

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37564b6
Fix multi-axis shear transform to compose individual shear matrices (…
aymuos15 Mar 17, 2026
8db15d5
Merge branch 'dev' into fix/shear-transform
aymuos15 Mar 17, 2026
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46 changes: 30 additions & 16 deletions monai/transforms/utils.py
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Original file line number Diff line number Diff line change
Expand Up @@ -952,14 +952,15 @@ def create_shear(

Args:
spatial_dims: spatial rank
coefs: shearing factors, a tuple of 2 floats for 2D, a tuple of 6 floats for 3D),
take a 3D affine as example::
coefs: shearing factors, a tuple of 2 floats for 2D, a tuple of 6 floats for 3D).
Individual single-axis shear matrices are composed (multiplied) in
coefficient order so that the result is a proper shear with determinant 1.
For 2D with coefs ``(Sx, Sy)`` the composed matrix is::

[
[1.0, coefs[0], coefs[1], 0.0],
[coefs[2], 1.0, coefs[3], 0.0],
[coefs[4], coefs[5], 1.0, 0.0],
[0.0, 0.0, 0.0, 1.0],
[1.0, Sx, 0.0],
[Sy, 1.0 + Sx*Sy, 0.0],
[0.0, 0.0, 1.0],
]

device: device to compute and store the output (when the backend is "torch").
Expand All @@ -982,17 +983,30 @@ def create_shear(
def _create_shear(spatial_dims: int, coefs: Sequence[float] | float, eye_func=np.eye) -> NdarrayOrTensor:
if spatial_dims == 2:
coefs = ensure_tuple_size(coefs, dim=2, pad_val=0.0)
out = eye_func(3)
out[0, 1], out[1, 0] = coefs[0], coefs[1]
return out # type: ignore
if spatial_dims == 3:
rank = 3
shear_indices = [(0, 1, coefs[0]), (1, 0, coefs[1])]
elif spatial_dims == 3:
coefs = ensure_tuple_size(coefs, dim=6, pad_val=0.0)
out = eye_func(4)
out[0, 1], out[0, 2] = coefs[0], coefs[1]
out[1, 0], out[1, 2] = coefs[2], coefs[3]
out[2, 0], out[2, 1] = coefs[4], coefs[5]
return out # type: ignore
raise NotImplementedError("Currently only spatial_dims in [2, 3] are supported.")
rank = 4
shear_indices = [
(0, 1, coefs[0]),
(0, 2, coefs[1]),
(1, 0, coefs[2]),
(1, 2, coefs[3]),
(2, 0, coefs[4]),
(2, 1, coefs[5]),
]
else:
raise NotImplementedError("Currently only spatial_dims in [2, 3] are supported.")
# Compose individual single-axis shear matrices so that the result is a
# proper (area/volume-preserving) shear with determinant 1. Each elementary
# shear is pre-multiplied, so the first coefficient is applied first.
out = eye_func(rank)
for i, j, c in shear_indices:
s = eye_func(rank)
s[i, j] = c
out = s @ out
return out # type: ignore


def create_scale(
Expand Down
20 changes: 19 additions & 1 deletion tests/transforms/test_create_grid_and_affine.py
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Original file line number Diff line number Diff line change
Expand Up @@ -224,13 +224,31 @@ def test_create_rotate(self):

def test_create_shear(self):
test_assert(create_shear, (2, 1.0), np.array([[1.0, 1.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]))
test_assert(create_shear, (2, (2.0, 3.0)), np.array([[1.0, 2.0, 0.0], [3.0, 1.0, 0.0], [0.0, 0.0, 1.0]]))
test_assert(create_shear, (2, (2.0, 3.0)), np.array([[1.0, 2.0, 0.0], [3.0, 7.0, 0.0], [0.0, 0.0, 1.0]]))
test_assert(
create_shear,
(3, 1.0),
np.array([[1.0, 1.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0]]),
)

def test_create_shear_determinant(self):
"""Composed shear must be area/volume-preserving (determinant == 1)."""
for coefs in [(0.3, 0.5), (1.0, 2.0), (-0.5, 0.7)]:
m = create_shear(2, coefs, backend="numpy")
assert_allclose(np.linalg.det(m), 1.0, atol=1e-10)
for coefs in [(0.1, 0.2, 0.3, 0.4, 0.5, 0.6)]:
m = create_shear(3, coefs, backend="numpy")
assert_allclose(np.linalg.det(m), 1.0, atol=1e-10)

def test_create_shear_sequential_equivalence(self):
"""Composing single-axis shears must equal a single multi-axis shear."""
sx, sy = 0.3, 0.5
shear_x = create_shear(2, (sx, 0.0), backend="numpy")
shear_y = create_shear(2, (0.0, sy), backend="numpy")
combined = create_shear(2, (sx, sy), backend="numpy")
# shear_y applied after shear_x
assert_allclose(shear_y @ shear_x, combined, atol=1e-10)

def test_create_scale(self):
test_assert(create_scale, (2, 2), np.array([[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]))
test_assert(create_scale, (2, [2, 2, 2]), np.array([[2.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 1.0]]))
Expand Down
4 changes: 2 additions & 2 deletions tests/transforms/test_rand_affine.py
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Original file line number Diff line number Diff line change
Expand Up @@ -102,7 +102,7 @@
{"img": p(torch.arange(64).reshape((1, 8, 8))), "spatial_size": (3, 3)},
p(
torch.tensor(
[[[18.7362, 15.5820, 12.4278], [27.3988, 24.2446, 21.0904], [36.0614, 32.9072, 29.7530]]]
[[[18.7575, 15.5552, 12.3528], [27.4202, 24.2178, 21.0154], [36.0828, 32.8805, 29.6781]]]
)
),
]
Expand All @@ -122,7 +122,7 @@
{"img": p(torch.arange(64).reshape((1, 8, 8)))},
p(
torch.tensor(
[[[18.7362, 15.5820, 12.4278], [27.3988, 24.2446, 21.0904], [36.0614, 32.9072, 29.7530]]]
[[[18.7575, 15.5552, 12.3528], [27.4202, 24.2178, 21.0154], [36.0828, 32.8805, 29.6781]]]
)
),
]
Expand Down
26 changes: 13 additions & 13 deletions tests/transforms/test_rand_affined.py
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Original file line number Diff line number Diff line change
Expand Up @@ -93,7 +93,7 @@
"img": MetaTensor(torch.arange(64).reshape((1, 8, 8))),
"seg": MetaTensor(torch.arange(64).reshape((1, 8, 8))),
},
torch.tensor([[[18.7362, 15.5820, 12.4278], [27.3988, 24.2446, 21.0904], [36.0614, 32.9072, 29.7530]]]),
torch.tensor([[[18.7575, 15.5552, 12.3528], [27.4202, 24.2178, 21.0154], [36.0828, 32.8805, 29.6781]]]),
]
)
TESTS.append(
Expand All @@ -118,14 +118,14 @@
torch.tensor(
[
[
[18.736153, 15.581954, 12.4277525],
[27.398798, 24.244598, 21.090399],
[36.061443, 32.90724, 29.753046],
[18.757534, 15.55517, 12.352802],
[27.420181, 24.217815, 21.01545],
[36.08283, 32.880463, 29.678097],
]
]
)
),
"seg": MetaTensor(torch.tensor([[[19.0, 20.0, 12.0], [27.0, 28.0, 20.0], [35.0, 36.0, 29.0]]])),
"seg": MetaTensor(torch.tensor([[[19.0, 12.0, 12.0], [27.0, 28.0, 20.0], [35.0, 36.0, 29.0]]])),
},
]
)
Expand Down Expand Up @@ -168,14 +168,14 @@
np.array(
[
[
[18.736153, 15.581954, 12.4277525],
[27.398798, 24.244598, 21.090399],
[36.061443, 32.90724, 29.753046],
[18.757534, 15.55517, 12.352802],
[27.420181, 24.217815, 21.01545],
[36.08283, 32.880463, 29.678097],
]
]
)
),
"seg": MetaTensor(np.array([[[19.0, 20.0, 12.0], [27.0, 28.0, 20.0], [35.0, 36.0, 29.0]]])),
"seg": MetaTensor(np.array([[[19.0, 12.0, 12.0], [27.0, 28.0, 20.0], [35.0, 36.0, 29.0]]])),
},
]
)
Expand All @@ -202,14 +202,14 @@
torch.tensor(
[
[
[18.736153, 15.581954, 12.4277525],
[27.398798, 24.244598, 21.090399],
[36.061443, 32.90724, 29.753046],
[18.757534, 15.55517, 12.352802],
[27.420181, 24.217815, 21.01545],
[36.08283, 32.880463, 29.678097],
]
]
)
),
"seg": MetaTensor(torch.tensor([[[19.0, 20.0, 12.0], [27.0, 28.0, 20.0], [35.0, 36.0, 29.0]]])),
"seg": MetaTensor(torch.tensor([[[19.0, 12.0, 12.0], [27.0, 28.0, 20.0], [35.0, 36.0, 29.0]]])),
},
]
)
Expand Down
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