Wrong calculation of EPE

[sueskind]

Usually the (average) end-point error (EPE) is defined as such:

$$EPE = \frac{1}{n} \sum_{i,j}\lVert v(i,j) - g(i,j) \rVert$$

where

• $v(i,j)$ is the predicted optical flow at image pixel $(i,j)$,
• $g(i,j)$ the target (ground truth) optical flow and
• $n$ the total number of pixels.

Notice that the flows are 2-dimensional as they have an entry $v_x,g_x$ for $x$ and $v_y,g_y$ for $y$ disposition. Therefore, the norm here is the square root of the sum of two squares:

$$EPE = \frac{1}{n} \sum_{i,j} \sqrt{ \left( v_x(i,j) - g_x(i,j) \right)^2 + \left( v_y(i,j) - g_y(i,j) \right)^2 }$$

In losses.py however, the EPE is calculated wrongly as the MSE:

$$MSE = \frac{1}{n} \sum_{i,j,k} \left( v_k(i,j) -gk(i,j) \right)^2 = \frac{1}{n} \sum{i,j} \left( v_x(i,j) -g_x(i,j) \right)^2 + \left( v_y(i,j) -g_y(i,j) \right)^2$$

Although they look very similar, the actual EPE involves a square root which is missing in the MSE.

[sueskind]

Well I got a bit confused there... Depending on the shapes of the tensors it looks like the error is implemented correctly after all.

However, the L2Loss is usually implemented as the MSE, which is not the case in this code. At least the EPE and L2 having the same implementation is a contradiction.