I'm trying to implement metropolis light transport based on this paper, and I have the basic thing working. I run the algorithm multiple times with different starting points, add the results for each starting point together and multiply them by a scaling factor to approximate the real image.
The scaling factor is the one described in the paper:
$average\_brightess / average\_samples\_per\_pixel$.
In the resulting image, the starting points are noticeably brighter (they are aligned in a grid below).
The paper I was reading doesn't have any advice on avoiding this start up bias. I found this other paper that has advice on this, but I find the paper a little hard to understand.
It says each initial path should be assigned a weight $f(x_0) / p_0(x_0)$.
$f(x_0)$ should be the luminance of the sample at the starting point $x_0$, but is it raw luminance or normalized? $p_0$ is supposed to be a path distribution (possibly sampled by path tracing). How do I get the value of a path distribution at a specified point? Is it the ratio of the point's luminance over the average luminance of the distribution (i.e. average brightness of the image)?