Shubodh
commented
2 years ago I relooked again at this and I think there is no issue with your code, even though it doesn't explicitly do inverse, it looks correct. I am explaining below:
In my original comment, I wrote that the Quaternion Angular Error is defined in your paper as
|| 180/pi 2 arccos(dot(q_pred_inv, q_gt)) ||
But actually it is
|| 180/pi 2 arccos(product(q_pred_inv, q_gt)) ||.
"dot" and "product" would mean two different things. For example, if say there are 2 (same) quaternions X and Y which are (a + bi + cj + dk) and (a + bi + cj + dk), then "dot" of these two as 4-vectors [a,b,c,d] & [a,b,c,d] would be (a^2 + b^2 + c^2 + d^2) whereas "product" of the two quaternions would be (a^2 - b^2 - c^2 - d^2 + more terms like abi + aci +...) .
Therefore, even though it is written as quat_inv in the paper, what is implemented in code is correct. Basically,
|| 180/pi 2 arccos(product(q_pred_inv, q_gt)) ||.
is same as
|| 180/pi 2 arccos(dot(q_pred, q_gt)) ||. Note two differences: (product vs dot) and (q_pred_inv vs q_pred).
So if we continue the X and Y example above. X = (a + bi + cj + dk) and Y = (a + bi + cj + dk) (Assuming unit quaternions)
product(X_inv, Y) = (a^2 + b^2 + c^2 + d^2) (This is what paper says)
which is the same as
dot(X, Y) = dot([a,b,c,d],[a,b,c,d]) = (a^2 + b^2 + c^2 + d^2). (This is what is implemented in code)
So what is mentioned is paper seems to be same as that in code mathematically.
In RIO10 paper, for evaluating how close predicted pose is to ground truth pose, the Quaternion Angular Error is defined as
|| 180/pi 2 arccos(dot(q_pred_inv, q_gt)) ||
where q_pred_inv is inverse of q_predicted and q_gt is ground truth, dot means dot product.
However in your code, it is different:
The Quaternion Angular Error is defined here in your code. You didn't do inverse for quaternion here, i.e. it is
|| 180/pi 2 arccos(dot(q_pred, q_gt)) ||
instead of
|| 180/pi 2 arccos(dot(q_pred_inv, q_gt)) ||.
Basically inverse of q_pred is missing.
Am I missing something here? Or is your code incorrect?
(Please excuse the unneccessary title edits)