# Help with start up bias in Metropolis Light Transport

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)?

• If I remember correctly, MLT usually starts with a frame from general path tracing (one way, or bi-directional). They use this image to find places with high luminance, and explore more in that area. – RichieSams Jun 12 '17 at 13:32
• Oh? I thought it starts randomly, but the probability of moving to a new location favors locations that are brighter. So I do multiple rounds from multiple initial locations to avoid the sampling getting stuck in bright areas. Also, I'm a student in this so I don't know a lot, but I just learned while researching about this that path tracing is not the same as ray tracing. Does that have anything to do with my problem above? Do you know if I can even do MLT using ray tracing? – devil0150 Jun 12 '17 at 20:18
• I'm currently trying to implement the path space MLT on my own, but struggle a bit. Are you willing to share your code with me? – 0xbadf00d Oct 1 '18 at 14:18