Possible bug in equation (9)

[rakhimovv]

Hi! Thank you for your work!

In the equation (9) in the paper:

\tilde{\alpha}(z_0,z_1)=\frac{t(z_1)-t(z_0)}{1-t(z_0)}

the denominator = 1-t(z_0)

While in code:
alpha_value = torch.log(hit_prob / (visibility - hit_prob + eps) + eps)
If we omit log the denominator = visibility - hit_prob = 1 - t(z_0) - (t(z_1) - t(z_0)) = 1-t(z_1)

The denominator in the paper and the code do not match.

Is this intended behaviour? and where is the error in the paper or the code or none?

[liuyuan-pal]

Hi, this is an estimation of the alpha value. In an ideal continuous case, we need to divide the 1-z at z(t). But in discrete cases, we may divide by either the left point or right point here.