IPE explained

[theFilipko]

Hello.
First of all, thank you for sharing this great work.

I would like to kindly ask you to elaborate more on how did you derive the formulas for IPE.

Why do you concatenate it this way?

How did you get the formula for the y_var?

I cannot quiet get it from the article.
Thank you :)

[jonbarron]

expected_sin() is just the expectation of sin() with respect to a normal distribution, you can re-derive it using Mathematica or something by integrating the product of a normal distribution and sin(x). That concatenation of sin(x) and sin(x + pi/2) is just a way of computing sin(x) and cos(x) quickly, as cos(x) = sin(x+pi/2).

[theFilipko]

Thank you for the explanation :)

[theFilipko]

Why do you omit y_var returned by the expected_sin in IPE?
https://github.com/google/mipnerf/blob/main/internal/mip.py#L182-L184

[jonbarron]

We don't use y_var anywhere in the algorithm. It's only computed in the code because I thought someone might find it useful some day.