Understanding Flow SPTransform

[YoussefFathi]

I would appreciate it if you can clarify for me the following points related to specific parts of the "sp_transforms.py" file :

1. In transform_flow() , what is the purpose of the following block of code ?

   `        # inverse transform coords
    x0, y0 = self.inverse_transform_coords(
        width=width, height=height, thetas=theta1)
   
    x1, y1 = self.inverse_transform_coords(
        width=width, height=height, thetas=theta2, offset_x=u, offset_y=v)
   
    # subtract and create new flow
    u = x1 - x0
    v = y1 - y0
    new_flow = torch.stack([u, v], dim=1)`
   

2. Why didn't you use only the following part of the code to transform the optical flow just like the transform_image() function ?

     `  # transform coords
    xq, yq = self.transform_coords(width=width, height=height, thetas=theta1)
   
    # interp2
    transformed = self._flow_interp2(new_flow, xq, yq)`
   

3. What is the difference between the functionality of inverse_transform_coords() and transform_coords() ?

[Liang Liu]

Since spatial transformations will lead in a change to coordinates, we should sample optical flow on the view of transformed coordinates rather than the original one.

In this code, inverse_transform_coords() transform coordinates:

and transform_coords() is its inverse operation.