Talk:Metropolis light transport

Unbiased?

I believe MLT is a biased algorithm, as it doesn't sample rays randomly. Many papers discuss something called "start-up bias", which results from choosing the paths to be perturbed - those paths are rated as 'more important' by the algorithm.

One would think that as long as completely new paths to mutate are regularly chosen, then the algorithm will eventually converge to the same solution as normal path tracing with no mutating of paths. To take the extreme case, if every possible (within the computational accuracy of the machine) path is sampled an equal number of times, it doesn't matter if you did that using path mutation or not.

Another question, then, is whether or not the mutation process leads the renderer to implicitly favour some paths over others. For example, paths right on the edge of the light may have fewer valid paths near them and will thus be sampled less often. If this is the case, then I think MLT is ultimately biased.

Comments/thoughts/citations? Jnnnnn (talk) 08:33, 8 February 2010 (UTC)

MLT is unbiased. The mutation strategy doesn't really matter (as long as all paths can be generated with a non-zero probability density), what makes it unbiased is that mutated samples are rejected with a probability that depends on the luminance carried along the old and new path, i.e. the more light a ray carries, the more likely it is to be accepted. On the other hand every time a ray is sampled it contributes the same luminance, no matter how much light it actually carries.

Note that start-up bias isn't bias in the sense that the image wouldn't convert to the right solution; it does. Start-up bias refers to the fact that for any finite number of samples, the image generated depends on the initial sample. However, this bias converges to zero as more and more samples are taken, no matter whether completely new paths are chosen regularly or not; if they are not, convergence will just be slower.

--Gidoca (talk) 15:54, 13 March 2012 (UTC)

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