add coarse alignment example in a separate file

.gitignore

@@ -103,6 +103,7 @@ ENV/
 
 # IDE settings
 .vscode/
+.idea/
 
 libtilt/_version.py
 src/libtilt/_version.py

examples/coarse_alignment.py

@@ -0,0 +1,112 @@
+import mrcfile
+import numpy as np
+import torch
+import torch.nn.functional as F
+import einops
+
+from libtilt.backprojection import backproject_fourier
+from libtilt.fft_utils import dft_center
+from libtilt.patch_extraction import extract_squares
+from libtilt.rescaling.rescale_fourier import rescale_2d
+from libtilt.shapes import circle
+from libtilt.shift.shift_image import shift_2d
+from libtilt.transformations import Ry, Rz, T
+from libtilt.correlation import correlate_2d
+
+IMAGE_FILE = 'data/tomo200528_100.st'
+IMAGE_PIXEL_SIZE = 1.724
+STAGE_TILT_ANGLE_PRIORS = torch.arange(-51, 51, 3)
+TILT_AXIS_ANGLE_PRIOR = -88.7
+ALIGNMENT_PIXEL_SIZE = 13.79 * 2
+# set 0 degree tilt as reference
+REFERENCE_TILT = STAGE_TILT_ANGLE_PRIORS.abs().argmin()
+
+tilt_series = torch.as_tensor(mrcfile.read(IMAGE_FILE))
+
+tilt_series, _ = rescale_2d(
+    image=tilt_series,
+    source_spacing=IMAGE_PIXEL_SIZE,
+    target_spacing=ALIGNMENT_PIXEL_SIZE,
+    maintain_center=True,
+)
+
+tilt_series -= einops.reduce(tilt_series, 'tilt h w -> tilt 1 1', reduction='mean')
+tilt_series /= torch.std(tilt_series, dim=(-2, -1), keepdim=True)
+n_tilts, h, w = tilt_series.shape
+center = dft_center((h, w), rfft=False, fftshifted=True)
+center = einops.repeat(center, 'yx -> b yx', b=len(tilt_series))
+tilt_series = extract_squares(
+    image=tilt_series,
+    positions=center,
+    sidelength=min(h, w),
+)
+
+# set tomogram and tilt-series shape
+size = min(h, w)
+tomogram_dimensions = (size, ) * 3
+tilt_dimensions = (size, ) * 2
+
+# mask for coarse alignment
+coarse_alignment_mask = circle(
+    radius=size // 3,
+    smoothing_radius=size // 6,
+    image_shape=tilt_dimensions,
+)
+
+# do an IMOD style coarse tilt-series alignment
+reference_shift = torch.tensor([.0, .0])
+center = dft_center(tilt_dimensions, rfft=False, fftshifted=True)
+coarse_shifts = torch.zeros((len(tilt_series), 2), dtype=torch.float32)
+
+# find coarse alignment for negative tilts
+current_shift = reference_shift.clone()
+for i in range(REFERENCE_TILT, 0, -1):
+    correlation = correlate_2d(
+        tilt_series[i] * coarse_alignment_mask,
+        tilt_series[i - 1] * coarse_alignment_mask,
+        normalize=True
+    )
+    shift = center - torch.tensor(
+        np.unravel_index(correlation.argmax(), shape=tilt_dimensions)
+    )
+    current_shift += shift
+    coarse_shifts[i - 1] = current_shift
+
+# find coarse alignment positive tilts
+current_shift = reference_shift.clone()
+for i in range(REFERENCE_TILT, tilt_series.shape[0] - 1, 1):
+    correlation = correlate_2d(
+        tilt_series[i] * coarse_alignment_mask,
+        tilt_series[i + 1] * coarse_alignment_mask,
+        normalize=True
+    )
+    shift = center - torch.tensor(
+        np.unravel_index(correlation.argmax(), shape=tilt_dimensions)
+    )
+    current_shift += shift
+    coarse_shifts[i + 1] = current_shift
+
+tomogram_center = dft_center(tomogram_dimensions, rfft=False, fftshifted=True)
+tilt_image_center = dft_center(tilt_dimensions, rfft=False, fftshifted=True)
+
+s0 = T(-tomogram_center)
+r0 = Ry(STAGE_TILT_ANGLE_PRIORS, zyx=True)
+r1 = Rz(TILT_AXIS_ANGLE_PRIOR, zyx=True)
+s2 = T(F.pad(tilt_image_center, pad=(1, 0), value=0))
+M = s2 @ r1 @ r0 @ s0
+
+# coarse reconstruction
+coarse_aligned_tilt_series = shift_2d(tilt_series, shifts=-coarse_shifts)
+coarse_aligned_reconstruction = backproject_fourier(
+    images=coarse_aligned_tilt_series,
+    rotation_matrices=torch.linalg.inv(M[:, :3, :3]),
+    rotation_matrix_zyx=True,
+)
+
+import napari
+
+viewer = napari.Viewer()
+viewer.add_image(tilt_series.detach().numpy(), name='experimental')
+viewer.add_image(coarse_aligned_tilt_series.detach().numpy(), name='coarse aligned')
+viewer.add_image(coarse_aligned_reconstruction.detach().numpy(), name='coarse reconstruction')
+napari.run()