Fix XRayTransform boundary conditions (#561)

* Add failing tests
* Fix boundary handling

scico/linop/xray/_xray.py

@@ -158,20 +158,20 @@ def _project(
         """
         nx = im.shape
         inds, weights = XRayTransform2D._calc_weights(x0, dx, nx, angles, y0)
-        # Handle out of bounds indices. In the .at call, inds >= y0 are
-        # ignored, while inds < 0 wrap around. So we set inds < 0 to ny.
-        inds = jnp.where(inds >= 0, inds, ny)
 
         # avoid incompatible types in the .add (scatter operation)
         weights = weights.astype(im.dtype)
 
+        # Handle out of bounds indices by setting weight to zero
+        weights_valid = jnp.where((inds >= 0) * (inds < ny), weights, 0.0)
         y = (
             jnp.zeros((len(angles), ny), dtype=im.dtype)
             .at[jnp.arange(len(angles)).reshape(-1, 1, 1), inds]
-            .add(im * weights)
+            .add(im * weights_valid)
         )
 
-        y = y.at[jnp.arange(len(angles)).reshape(-1, 1, 1), inds + 1].add(im * (1 - weights))
+        weights_valid = jnp.where((inds + 1 >= 0) * (inds + 1 < ny), 1 - weights, 0.0)
+        y = y.at[jnp.arange(len(angles)).reshape(-1, 1, 1), inds + 1].add(im * weights_valid)
 
         return y
 
@@ -194,14 +194,15 @@ def _back_project(
         """
         ny = y.shape[1]
         inds, weights = XRayTransform2D._calc_weights(x0, dx, nx, angles, y0)
-        # Handle out of bounds indices. In the .at call, inds >= y0 are
-        # ignored, while inds < 0 wrap around. So we set inds < 0 to ny.
-        inds = jnp.where(inds >= 0, inds, ny)
+        # Handle out of bounds indices by setting weight to zero
+        weights_valid = jnp.where((inds >= 0) * (inds < ny), weights, 0.0)
 
         # the idea: [y[0, inds[0]], y[1, inds[1]], ...]
-        HTy = jnp.sum(y[jnp.arange(len(angles)).reshape(-1, 1, 1), inds] * weights, axis=0)
+        HTy = jnp.sum(y[jnp.arange(len(angles)).reshape(-1, 1, 1), inds] * weights_valid, axis=0)
+
+        weights_valid = jnp.where((inds + 1 >= 0) * (inds + 1 < ny), 1 - weights, 0.0)
         HTy = HTy + jnp.sum(
-            y[jnp.arange(len(angles)).reshape(-1, 1, 1), inds + 1] * (1 - weights), axis=0
+            y[jnp.arange(len(angles)).reshape(-1, 1, 1), inds + 1] * weights_valid, axis=0
         )
 
         return HTy
@@ -401,7 +402,7 @@ def _back_project_single(
 
     @staticmethod
     def _calc_weights(
-        input_shape: Shape, matrix: snp.Array, output_shape: Shape, slice_offset: int = 0
+        input_shape: Shape, matrix: snp.Array, det_shape: Shape, slice_offset: int = 0
     ) -> snp.Array:
         # pixel (0, 0, 0) has its center at (0.5, 0.5, 0.5)
         x = jnp.mgrid[: input_shape[0], : input_shape[1], : input_shape[2]] + 0.5  # (3, ...)
@@ -419,13 +420,46 @@ def _calc_weights(
         left_edge = Px - w / 2
         to_next = jnp.minimum(jnp.ceil(left_edge) - left_edge, w)
         ul_ind = jnp.floor(left_edge).astype("int32")
-        ul_ind = jnp.where(ul_ind < 0, max(output_shape), ul_ind)  # otherwise negative values wrap
 
         ul_weight = to_next[0] * to_next[1] * (1 / w**2)
         ur_weight = (w - to_next[0]) * to_next[1] * (1 / w**2)
         ll_weight = to_next[0] * (w - to_next[1]) * (1 / w**2)
         lr_weight = (w - to_next[0]) * (w - to_next[1]) * (1 / w**2)
 
+        # set weights to zero out of bounds
+        ul_weight = jnp.where(
+            (ul_ind[0] >= 0)
+            * (ul_ind[0] < det_shape[0])
+            * (ul_ind[1] >= 0)
+            * (ul_ind[1] < det_shape[1]),
+            ul_weight,
+            0.0,
+        )
+        ur_weight = jnp.where(
+            (ul_ind[0] + 1 >= 0)
+            * (ul_ind[0] + 1 < det_shape[0])
+            * (ul_ind[1] >= 0)
+            * (ul_ind[1] < det_shape[1]),
+            ur_weight,
+            0.0,
+        )
+        ll_weight = jnp.where(
+            (ul_ind[0] >= 0)
+            * (ul_ind[0] < det_shape[0])
+            * (ul_ind[1] + 1 >= 0)
+            * (ul_ind[1] + 1 < det_shape[1]),
+            ll_weight,
+            0.0,
+        )
+        lr_weight = jnp.where(
+            (ul_ind[0] + 1 >= 0)
+            * (ul_ind[0] + 1 < det_shape[0])
+            * (ul_ind[1] + 1 >= 0)
+            * (ul_ind[1] + 1 < det_shape[1]),
+            lr_weight,
+            0.0,
+        )
+
         return ul_ind, ul_weight, ur_weight, ll_weight, lr_weight
 
     @staticmethod

scico/test/linop/xray/test_xray.py → scico/test/linop/xray/test_xray_2d.py

@@ -5,7 +5,8 @@
 import pytest
 
 import scico
-from scico.linop.xray import XRayTransform2D, XRayTransform3D
+import scico.linop
+from scico.linop.xray import XRayTransform2D
 
 
 @pytest.mark.filterwarnings("error")
@@ -71,45 +72,12 @@ def test_apply_adjoint():
     assert y.shape[1] == det_count
 
 
-def test_3d_scaling():
-    x = jnp.zeros((4, 4, 1))
-    x = x.at[1:3, 1:3, 0].set(1.0)
-
-    input_shape = x.shape
-    output_shape = x.shape[:2]
-
-    # default spacing
-    M = XRayTransform3D.matrices_from_euler_angles(input_shape, output_shape, "X", [0.0])
-    H = XRayTransform3D(input_shape, matrices=M, det_shape=output_shape)
-
-    # fmt: off
-    truth = jnp.array(
-        [[[0.0, 0.0, 0.0, 0.0],
-          [0.0, 1.0, 1.0, 0.0],
-          [0.0, 1.0, 1.0, 0.0],
-          [0.0, 0.0, 0.0, 0.0]]]
-    )  # fmt: on
-    np.testing.assert_allclose(H @ x, truth)
-
-    # bigger voxels in the x (first index) direction
-    M = XRayTransform3D.matrices_from_euler_angles(
-        input_shape, output_shape, "X", [0.0], voxel_spacing=[2.0, 1.0, 1.0]
-    )
-    H = XRayTransform3D(input_shape, matrices=M, det_shape=output_shape)
-    # fmt: off
-    truth = jnp.array(
-        [[[0. , 0.5, 0.5, 0. ],
-          [0. , 0.5, 0.5, 0. ],
-          [0. , 0.5, 0.5, 0. ],
-          [0. , 0.5, 0.5, 0. ]]]
-    )  # fmt: on
-    np.testing.assert_allclose(H @ x, truth)
-
-    # bigger detector pixels in the x (first index) direction
-    M = XRayTransform3D.matrices_from_euler_angles(
-        input_shape, output_shape, "X", [0.0], det_spacing=[2.0, 1.0]
-    )
-    H = XRayTransform3D(input_shape, matrices=M, det_shape=output_shape)
-    # fmt: off
-    truth = None  # fmt: on  # TODO: Check this case more closely.
-    # np.testing.assert_allclose(H @ x, truth)
+def test_matched_adjoint():
+    """See https://github.com/lanl/scico/issues/560."""
+    N = 16
+    det_count = int(N * 1.05 / np.sqrt(2.0))
+    dx = 1.0 / np.sqrt(2)
+    n_projection = 3
+    angles = np.linspace(0, np.pi, n_projection, endpoint=False)
+    A = XRayTransform2D((N, N), angles, det_count=det_count, dx=dx)
+    assert scico.linop.valid_adjoint(A, A.T, eps=1e-5)

scico/test/linop/xray/test_xray_3d.py

@@ -0,0 +1,66 @@
+import numpy as np
+
+import jax.numpy as jnp
+
+import scico.linop
+from scico.linop.xray import XRayTransform3D
+
+
+def test_matched_adjoint():
+    """See https://github.com/lanl/scico/issues/560."""
+    N = 16
+    det_count = int(N * 1.05 / np.sqrt(2.0))
+    n_projection = 3
+
+    input_shape = (N, N, N)
+    det_shape = (det_count, det_count)
+
+    M = XRayTransform3D.matrices_from_euler_angles(
+        input_shape, det_shape, "X", np.linspace(0, np.pi, n_projection, endpoint=False)
+    )
+    H = XRayTransform3D(input_shape, matrices=M, det_shape=det_shape)
+
+    assert scico.linop.valid_adjoint(H, H.T, eps=1e-5)
+
+
+def test_scaling():
+    x = jnp.zeros((4, 4, 1))
+    x = x.at[1:3, 1:3, 0].set(1.0)
+
+    input_shape = x.shape
+    det_shape = x.shape[:2]
+
+    # default spacing
+    M = XRayTransform3D.matrices_from_euler_angles(input_shape, det_shape, "X", [0.0])
+    H = XRayTransform3D(input_shape, matrices=M, det_shape=det_shape)
+    # fmt: off
+    truth = jnp.array(
+        [[[0.0, 0.0, 0.0, 0.0],
+          [0.0, 1.0, 1.0, 0.0],
+          [0.0, 1.0, 1.0, 0.0],
+          [0.0, 0.0, 0.0, 0.0]]]
+    )  # fmt: on
+    np.testing.assert_allclose(H @ x, truth)
+
+    # bigger voxels in the x (first index) direction
+    M = XRayTransform3D.matrices_from_euler_angles(
+        input_shape, det_shape, "X", [0.0], voxel_spacing=[2.0, 1.0, 1.0]
+    )
+    H = XRayTransform3D(input_shape, matrices=M, det_shape=det_shape)
+    # fmt: off
+    truth = jnp.array(
+        [[[0. , 0.5, 0.5, 0. ],
+          [0. , 0.5, 0.5, 0. ],
+          [0. , 0.5, 0.5, 0. ],
+          [0. , 0.5, 0.5, 0. ]]]
+    )  # fmt: on
+    np.testing.assert_allclose(H @ x, truth)
+
+    # bigger detector pixels in the x (first index) direction
+    M = XRayTransform3D.matrices_from_euler_angles(
+        input_shape, det_shape, "X", [0.0], det_spacing=[2.0, 1.0]
+    )
+    H = XRayTransform3D(input_shape, matrices=M, det_shape=det_shape)
+    # fmt: off
+    truth = None  # fmt: on  # TODO: Check this case more closely.
+    # np.testing.assert_allclose(H @ x, truth)