questions about run_8point

[zh7117]

Hello everyone.
I found the implementation of algorithm run_8point is slightly different from wiki-8point
In kornia:

# apply the weights to the linear system
if weights is None:
    X = X.transpose(-2, -1) @ X
else:
    w_diag = torch.diag_embed(weights)
    X = X.transpose(-2, -1) @ w_diag @ X

_, _, V = _torch_svd_cast(X)
F_mat = V[..., -1].view(-1, 3, 3)

# reconstruct and force the matrix to have rank2
U, S, V = _torch_svd_cast(F_mat)
rank_mask = torch.tensor([1.0, 1.0, 0.0], device=F_mat.device, dtype=F_mat.dtype)

F_projected = U @ (torch.diag_embed(S * rank_mask) @ V.transpose(-2, -1))

But according wiki, there is no need to multiply X by its own transpose.

[edgarriba]

i believe this is a trick to normalize the matrix before the singular values decomposition so that is squared /cc @ducha-aiki

[zh7117]

Thanks for your response.
I found wherther or not multiply the X^T does not affect the value of V[...,-1].
So this would be a trick to reduce computations or something else.

[edgarriba]

yes, it's a performance trick