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google / mipnerf

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IPE explained #22

Closed theFilipko closed 2 years ago

theFilipko commented 2 years ago

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? image

How did you get the formula for the y_var? image

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

jonbarron commented 2 years ago

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 commented 2 years ago

Thank you for the explanation :)

theFilipko commented 2 years ago

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 commented 2 years ago

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.