Grid_sample different results in real and complex spaces

vision
1

For a given theta, I want to rotate a 3D tensor (D, H, W) in both real space and Fourier space. The real space application is as usual. The Fourier space application is to do a 3D fft on the volume, and do grid_sample to the real part and imaginary part separately, combine the results with torch.complex(), and inverse fft back to the real space. However, I was getting totally different results for the applications in real and Fourier space. Here’s the example code snippet:

theta = np.array([[0., -1., 0., 0.], [1., 0., 0., 0.], [0., 0., 1., 0.]])
theta = torch.tensor(theta, requires_grad=False).float().unsqueeze(0)

torch.manual_seed(0)
volume = torch.rand((5,5,5))
volume_F = torch.fft.fftshift(torch.fft.fftn(volume))

d, h, w = volume.shape
b = 1
grid = F.affine_grid(theta, (b, 1, d, h, w))

volume = volume.expand((b, d, h, w)) # (B, D, H, W)
volume_F = volume_F.expand((b, d, h, w)) # (B, D, H, W)

rot_vol = F.grid_sample(
        torch.unsqueeze(volume, 1),
        grid,
        mode='bilinear',
        padding_mode="zeros",
        align_corners=True).squeeze(1) # (B, D, H, W)

rot_vol_r = F.grid_sample(
        torch.unsqueeze(volume_F.real.float(), 1),
        grid,
        mode='bilinear',
        padding_mode="zeros",
        align_corners=True).squeeze(1) # (B, D, H, W)/

rot_vol_i = F.grid_sample(
        torch.unsqueeze(volume_F.imag.float(), 1),
        grid,
        mode='bilinear',
        padding_mode="zeros",
        align_corners=True).squeeze(1) # (B, D, H, W)6

rot_vol_F = torch.complex(rot_vol_r, rot_vol_i)
rot_vol2 = torch.fft.ifftn(torch.fft.ifftshift(rot_vol_F[0])).real

print(rot_vol[0,1:4,1:4,1:4])
print(rot_vol2[1:4,1:4,1:4])

I printed the center 3x3x3 for rotated volume in real and Fourier spaces:

tensor([[[0.3287, 0.7239, 0.3600],
         [0.2875, 0.7846, 0.6296],
         [0.6597, 0.4023, 0.3662]],

        [[0.2285, 0.5616, 0.7294],
         [0.1306, 0.2038, 0.5334],
         [0.5179, 0.6016, 0.5511]],

        [[0.2563, 0.5988, 0.7047],
         [0.6328, 0.2577, 0.6991],
         [0.7618, 0.4310, 0.6676]]])
tensor([[[0.3730, 0.6217, 0.2595],
         [0.3322, 0.3079, 0.1674],
         [0.2382, 0.4306, 0.2531]],

        [[0.3308, 0.3927, 0.4002],
         [0.1625, 0.2234, 0.2055],
         [0.0988, 0.1105, 0.1756]],

        [[0.2901, 0.1826, 0.1287],
         [0.1781, 0.1976, 0.2110],
         [0.2818, 0.1371, 0.2022]]])

The results are completely different.

My question is, what could be wrong here? Thanks a lot in advance for any opinions!

2

Based on your code it seems you are using the same grid and I don’t know how you’ve verified that the same results would be expected.
I.e. sampling can be seen as a multiplication with a Dirac comb. The Convolution Theorem explains that “Convolution in time domain equals multiplication in frequency domain” and vice versa. Based on this you would have to respect the Nyquist frequency to avoid aliasing in any domain.
However, as already said I don’t see any frequency calculation, sampling rate etc.