Allow for defining reference grid on non-integer coordinates (#7032)

This is a non-breaking change that is disabled by default. It allows for
defining the reference identity grid on non-integer values. This can be
beneficial for registration applications as shown in: B. Likar and F.
Pernus. A heirarchical approach to elastic registration based on mutual
information. Image and Vision Computing, 19:33-44, 2001.

cc: @nvahmadi

---------

Signed-off-by: Mikael Brudfors <mbrudfors@nvidia.com>

monai/networks/blocks/warp.py

@@ -32,7 +32,7 @@ class Warp(nn.Module):
     Warp an image with given dense displacement field (DDF).
     """
 
-    def __init__(self, mode=GridSampleMode.BILINEAR.value, padding_mode=GridSamplePadMode.BORDER.value):
+    def __init__(self, mode=GridSampleMode.BILINEAR.value, padding_mode=GridSamplePadMode.BORDER.value, jitter=False):
         """
         For pytorch native APIs, the possible values are:
 
@@ -47,6 +47,11 @@ def __init__(self, mode=GridSampleMode.BILINEAR.value, padding_mode=GridSamplePa
             - padding_mode: ``"zeros"``, ``"border"``, ``"reflection"``, 0, 1, ...
 
         See also: :py:class:`monai.networks.layers.grid_pull`
+
+        - jitter: bool, default=False
+            Define reference grid on non-integer values
+            Reference: B. Likar and F. Pernus. A heirarchical approach to elastic registration
+            based on mutual information. Image and Vision Computing, 19:33-44, 2001.
         """
         super().__init__()
         # resolves _interp_mode for different methods
@@ -84,8 +89,9 @@ def __init__(self, mode=GridSampleMode.BILINEAR.value, padding_mode=GridSamplePa
             self._padding_mode = GridSamplePadMode(padding_mode).value
 
         self.ref_grid = None
+        self.jitter = jitter
 
-    def get_reference_grid(self, ddf: torch.Tensor) -> torch.Tensor:
+    def get_reference_grid(self, ddf: torch.Tensor, jitter: bool = False, seed: int = 0) -> torch.Tensor:
         if (
             self.ref_grid is not None
             and self.ref_grid.shape[0] == ddf.shape[0]
@@ -96,6 +102,11 @@ def get_reference_grid(self, ddf: torch.Tensor) -> torch.Tensor:
         grid = torch.stack(meshgrid_ij(*mesh_points), dim=0)  # (spatial_dims, ...)
         grid = torch.stack([grid] * ddf.shape[0], dim=0)  # (batch, spatial_dims, ...)
         self.ref_grid = grid.to(ddf)
+        if jitter:
+            # Define reference grid on non-integer values
+            with torch.random.fork_rng(enabled=seed):
+                torch.random.manual_seed(seed)
+                grid += torch.rand_like(grid)
         self.ref_grid.requires_grad = False
         return self.ref_grid
 
@@ -117,7 +128,7 @@ def forward(self, image: torch.Tensor, ddf: torch.Tensor):
                 f"Given input {spatial_dims}-d image shape {image.shape}, the input DDF shape must be {ddf_shape}, "
                 f"Got {ddf.shape} instead."
             )
-        grid = self.get_reference_grid(ddf) + ddf
+        grid = self.get_reference_grid(ddf, jitter=self.jitter) + ddf
         grid = grid.permute([0] + list(range(2, 2 + spatial_dims)) + [1])  # (batch, ..., spatial_dims)
 
         if not USE_COMPILED:  # pytorch native grid_sample