# Unbiased rendering

An example of an unbiased render using Indigo Renderer

In computer graphics, unbiased rendering refers to a rendering technique that does not introduce any systematic error, or bias, into the radiance approximation. Because of this, it is often used to generate the reference image to which other rendering techniques are compared. Mathematically speaking, the expected value of the unbiased estimator will always be the population mean, for any number of observations. Error found in an unbiased rendering will be due to variance, which manifests itself as high-frequency noise in the resultant image. Variance is reduced by ${\displaystyle n}$ and standard deviation by ${\displaystyle {\sqrt {n}}}$ for ${\displaystyle n}$ data points, meaning that four times as many data points are needed to halve the standard deviation of the error. This makes unbiased rendering techniques less attractive for realtime or interactive rate applications. Conversely, an image produced by an unbiased renderer that appears smooth and noiseless is probabilistically correct.

A biased rendering method is not necessarily wrong, and it can still converge to the correct answer if the estimator is consistent. It does, however, introduce a certain bias error, usually in the form of a blur, in efforts to reduce the variance (high-frequency noise). It is important to note that an unbiased technique may not consider all possible paths. Path tracing can not consistently handle caustics generated from a point light source, as it is highly unlikely to randomly generate the path that directly reflects into the point. Progressive photon mapping (PPM), a biased rendering technique, can handle caustics quite well. Although biased, PPM is provably consistent, meaning that as the number of samples goes to infinity, the bias error goes to zero, and the probability that the estimate is correct reaches one.

Unbiased rendering methods include: