Affine transformation order in AffineGrid wrong?

[Spenhouet]

Describe the bug
I thought that the transformation order when applying affine transformations matters since the transformations can effect each other.

I thought the correct order is:

• Scale
• Rotate
• Translate

The order in AffineGrid is:

• Scale
• Translate
• Shear
• Rotate

affine = torch.eye(spatial_dims + 1, device=_device)
if self.rotate_params:
    affine = affine @ create_rotate(spatial_dims, self.rotate_params, device=_device, backend=_b)
if self.shear_params:
    affine = affine @ create_shear(spatial_dims, self.shear_params, device=_device, backend=_b)
if self.translate_params:
    affine = affine @ create_translate(spatial_dims, self.translate_params, device=_device, backend=_b)
if self.scale_params:
    affine = affine @ create_scale(spatial_dims, self.scale_params, device=_device, backend=_b)

Scaling affects the size of the object, which in turn affects the position and orientation of the object. Therefore, scaling should be applied first.
Rotation affects the orientation of the object, but not its position. Therefore, it should be applied after scaling.
Translation affects the position of the object, but not its size or orientation. Therefore, it should be applied last.
(not quite sure what to do with the order of shear and rotate)

Shouldn't this then be:

affine = torch.eye(spatial_dims + 1, device=_device)
if self.translate_params:
    affine = affine @ create_translate(spatial_dims, self.translate_params, device=_device, backend=_b)
if self.rotate_params:
    affine = affine @ create_rotate(spatial_dims, self.rotate_params, device=_device, backend=_b)
if self.shear_params:
    affine = affine @ create_shear(spatial_dims, self.shear_params, device=_device, backend=_b)
if self.scale_params:
    affine = affine @ create_scale(spatial_dims, self.scale_params, device=_device, backend=_b)

To Reproduce
N/A

Expected behavior
Correct order of affine transformations.

Screenshots
N/A

Environment
N/A

Additional context
N/A

[wyli]

these parameters are mainly for data augmentations, so I think they are just different conventions (no preference for one over another). if the rotation is applied first, then the translation will be along the rotated direction...

[Spenhouet]

translation will be along the rotated direction

Sure, one can define everything. Just wondering who would expect it that way?
Seems rather unexpected to me.

[wyli]

translation will be along the rotated direction

Sure, one can define everything. Just wondering who would expect it that way? Seems rather unexpected to me.

that's what this ticket proposes... translation applied last

[Spenhouet]

Sorry if my statement was confusing. Was referring to this "I think they are just different conventions".
And yes, I'm proposing to follow a different convention than what is currently implemented.

[wyli]

I don't have a preference here, if there are more upvotes for this I can help make a pull request to change it.

maybe rotating first would somehow reduce the artefacts as mentioned in #6023