# Unbiased rendering

This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. (March 2019) (Learn how and when to remove this template message) |

This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (March 2019) (Learn how and when to remove this template message) |

Within the field of computer graphics, **unbiased rendering** refers to any rendering technique that does not introduce systematic error, or bias, into the radiance approximation. The term refers to statistical bias, not the broader meaning of subjective bias. Because of this, an unbiased rendering technique can produce a reference image^{[clarification needed]} to compare against renders that use other techniques. Path tracing and its derivatives can be unbiased, whereas ray tracing was originally biased.

## Mathematical definitionEdit

Mathematically speaking, the expected value (E) of an *unbiased* estimator is the population mean, regardless of the number of observations. The error found in a render produced by an unbiased rendering technique is due to random statistical variance, which manifests as high-frequency noise. Variance is reduced by (standard deviation by ) for data, meaning that *four times* as many data are needed to *halve* the standard deviation of the error; this makes unbiased rendering techniques less attractive for realtime or interactive applications. This means that an image produced by an unbiased renderer that appears noiseless and smooth is *probabilistically correct*.

A *biased* rendering method is not necessarily wrong, and can still produce images close to those given by the rendering equation if the estimator is consistent. These methods, however, introduce a certain bias error (usually in the form of a blur)^{[citation needed]} in efforts to reduce the variance (high-frequency noise). Often biased rendering is optimized to compute faster at the cost of accuracy.

## Caustics exampleEdit

It is important to note that an unbiased technique can not consider all possible paths (because there are infinite), and may not select ideal paths for a given render (because to select certain paths over others introduces bias). Path tracing, an unbiased approach at its core, cannot consistently handle caustics generated from a point light source, as it is highly unlikely to randomly generate the singular path that directly reflects into the point.

Progressive photon mapping (PPM), a *biased* rendering technique, can actually 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 (like an unbiased technique), and the probability that the estimate is correct reaches one.

## List of unbiased rendering methodsEdit

- Path tracing
- Bidirectional path tracing
- Metropolis light transport and the related "energy redistribution path tracing" (ESPT)
^{[1]}

## List of unbiased renderersEdit

- Arion
- Arnold
^{[2]} - Cycles
- Indigo Renderer
- Kerkythea
- LuxRender
- Mantra
- Maxwell Render
- Octane Render
- Fstorm Render (external link)

## See alsoEdit

- Global illumination (GI)
- Physically based rendering (PBR)
- Non-photorealistic rendering (NPR)

## ReferencesEdit

**^**David Cline; Justin Talbot; Parris Egbert. "Energy Redistribution Path Tracing". Brigham Young University. CiteSeerX 10.1.1.63.5938. Cite journal requires`|journal=`

(help)**^**James Arvo; Marcos Fajardo; Pat Hanrahan; Henrik Wann Jensen; Don Mitchell; Matt Pharr; Peter Shirley. "State of the Art in Monte Carlo Ray Tracing for Realistic Image Synthesis". SIGGRAPH 2001 Courses. CiteSeerX 10.1.1.9.6918. Cite journal requires`|journal=`

(help)

## BibliographyEdit

- "fryrender F.A.Q." RandomControl, SLU. Retrieved 2010-05-20.
- Mike Farnsworth. "Biased vs Unbiased Rendering".
*RenderSpud*. Retrieved 2010-05-20. - "How to choose rendering software".

This computer graphics–related article is a stub. You can help Wikipedia by expanding it. |