# Talk:Unbiased rendering

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To-do list for Unbiased rendering: edit·history·watch·refresh· Updated 2019-02-28

 Here are some tasks awaiting attention: Expand : Describe some common methods for photorealistic rendering

## Biased vs. Unbiased vs. Consistent

"Given enough time, unbiased renderers can produce extremely photo-realistic images that surpass the quality of those produced by a biased renderer."

I believe this statement is wholly inaccurate.

In an unbiased rendering technique (and we're going to assume ray tracing for now), the expected value is the correct answer. In the example of a pixel, as you fire many rays in path tracing, your rays are your "random variables" and the results of each of them will average into the correct answer. The expected value of an estimator ${\displaystyle \Psi _{\text{unbiased}}}$  is

${\displaystyle E\{\Psi _{\text{unbiased}}\}=I,}$

where ${\displaystyle I}$  is the solution to the integral we're trying to solve. The only error that occurs here is in the variance. In a biased estimator,

${\displaystyle E\{\Psi _{\text{biased}}\}=I+\epsilon ,}$

where ${\displaystyle \epsilon }$  is the bias error term. This is sometimes a "blur" to help smooth out variance. A biased algorithm is consistent if

${\displaystyle \lim _{N\to \infty }\epsilon =0,}$

meaning that the bias error goes to zero as more samples are used. A consistent, biased technique and an unbiased (and therefore consistent) technique will both converge to the correct answer. Using just the terms biased and unbiased is not enough to compare how fast these will converge. Therefore, an unbiased renderer cannot state that it surpasses the quality of a biased, but consistent, renderer, since both converge to the expected value as ${\displaystyle \lim _{N\to \infty }}$ . 128.213.17.35 (talk) 13:08, 1 September 2010 (UTC)

Also, nothing about the definition of an unbiased renderer states that it considers all possible light paths. In fact, for point light sources, the probability of hitting ${\displaystyle LS(DS)^{+}E}$  paths are zero in path tracing, an unbiased technique. Progressive photon mapping can handle caustics and caustics viewed through a specular surface, and it is an biased technique.
128.213.17.35 (talk) 13:17, 1 September 2010 (UTC)

## Usefulness of list of renderers

I would question the usefulness of the list of renderers. Most of them support several estimators/integrators, some of them possibly not unbiased. A list of unbiased rendering algorithms would add a lot more value. — Preceding unsigned comment added by 141.3.42.183 (talk) 08:49, 25 June 2015 (UTC)

I'm curious to know of a renderer that could occupy such a list. All of the listed renderers are biased.CalebPM (talk) 19:24, 18 October 2018 (UTC)

## Unbiased is biased

The page should reflect that these unbiased renderers use approximations. They're good approximations, but approximations, nonetheless. In ten years' time, when rendering algorithms are likely to be even more accurate than today's, they will call the renderers of 2018 biased and theirs unbiased. A truly unbiased renderer is purely hypothetical.

I'm not going to suggest we change the terms because it's too late for that. Rather, it should at the very least be conveyed that there are improvements to be made. Unbiased renderers of 2018 do have bias.CalebPM (talk) 19:07, 18 October 2018 (UTC)

## Light tracing

It looks like light tracing is a feature of 3ds max. And not a physically accurate one. 2601:647:CB03:5930:7D9F:E023:7DD8:2D53 (talk) 16:46, 2 December 2019 (UTC)

## Path Selection

In the section Caustics Example the article states that "...an unbiased technique... may not select ideal paths for a given render (because to select certain paths over others introduces bias)." The parenthetical here needs clarification as it could be describing Importance sampling#Application_to_simulation which does not necessarily introduce bias. Wuzelwazel (talk) 23:41, 31 May 2020 (UTC)