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__NOTOC__ Within the field of
computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great dea ...
, unbiased rendering refers to any rendering technique that does not introduce systematic error, or
bias Bias is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group ...
, into the radiance approximation. The term refers to
statistical bias Statistical bias is a systematic tendency which causes differences between results and facts. The bias exists in numbers of the process of data analysis, including the source of the data, the estimator chosen, and the ways the data was analyzed. ...
, not the broader meaning of subjective bias. Because of this, an unbiased rendering technique can produce a reference image to compare against renders that use other techniques. In simple terms, unbiased rendering tries to mimic the real world as closely as possible without taking short cuts.
Path tracing Path tracing is a computer graphics Monte Carlo method of rendering images of three-dimensional scenes such that the global illumination is faithful to reality. Fundamentally, the algorithm is integrating over all the illuminance arriving to ...
and its derivatives can be unbiased, whereas ray tracing was originally biased.


Mathematical definition

Mathematically speaking, the
expected value In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a ...
(E) of an ''unbiased''
estimator In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the ...
is the
population mean In statistics, a population is a set of similar items or events which is of interest for some question or experiment. A statistical population can be a group of existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hyp ...
, regardless of the number of observations. The error found in a render produced by an unbiased rendering technique is due to
random In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual rand ...
statistical variance, which manifests as
high-frequency High frequency (HF) is the ITU designation for the range of radio frequency electromagnetic waves (radio waves) between 3 and 30 megahertz (MHz). It is also known as the decameter band or decameter wave as its wavelengths range from one to ten ...
noise Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference aris ...
. Variance is reduced by n (
standard deviation In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, whil ...
by \sqrt) for n 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) in efforts to reduce the variance (high-frequency noise). Often biased rendering is optimized to compute faster at the cost of accuracy.


Caustics example

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 Path tracing is a computer graphics Monte Carlo method of rendering images of three-dimensional scenes such that the global illumination is faithful to reality. Fundamentally, the algorithm is integrating over all the illuminance arriving to ...
, 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 In computer graphics, photon mapping is a two-pass global illumination rendering algorithm developed by Henrik Wann Jensen between 1995 and 2001Jensen, H. (1996). ''Global Illumination using Photon Maps''. nlineAvailable at: http://graphics.sta ...
(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 Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions a ...
, the bias error goes to zero (like an unbiased technique), and the probability that the estimate is correct reaches one.


List of unbiased rendering methods

*
Path tracing Path tracing is a computer graphics Monte Carlo method of rendering images of three-dimensional scenes such that the global illumination is faithful to reality. Fundamentally, the algorithm is integrating over all the illuminance arriving to ...
* Bidirectional path tracing *
Metropolis light transport Metropolis light transport (MLT) is a global illumination application of a variant of the Monte Carlo method called the Metropolis–Hastings algorithm to the rendering equation for generating images from detailed physical descriptions of three ...
and the related "energy redistribution path tracing" (ESPT)


List of unbiased renderers

*
Arion Arion (; grc-gre, Ἀρίων; fl. c. 700 BC) was a kitharode in ancient Greece, a Dionysiac poet credited with inventing the dithyramb. The islanders of Lesbos claimed him as their native son, but Arion found a patron in Periander, tyrant o ...
* Arnold * Cycles *
Indigo Renderer Indigo Renderer is a 3D rendering software that uses unbiased rendering technologies to create photo-realistic images. In doing so, it uses equations that simulate the behaviour of light. By simulating the interactions of light, it can prod ...
*
Kerkythea Kerkythea is a standalone rendering system that supports raytracing and Metropolis light transport, uses physically accurate materials and lighting, and is distributed as freeware. Currently, the program can be integrated with any software tha ...
* LuxRender *
Mantra A mantra (Pali: ''manta'') or mantram (मन्त्रम्) is a sacred utterance, a numinous sound, a syllable, word or phonemes, or group of words in Sanskrit, Pali and other languages believed by practitioners to have religious, ma ...
*
Maxwell Render Maxwell Render is an unbiased 3D render engine, developed by Next Limit Technologies in Madrid, Spain. This stand-alone software is used in the film, animation, and VFX industry, as well as in architectural and product design visualization. It o ...
* Octane Render
Fstorm Render
(external link)


See also

*
Global illumination Global illumination (GI), or indirect illumination, is a group of algorithms used in 3D computer graphics that are meant to add more realistic lighting to 3D scenes. Such algorithms take into account not only the light that comes directly from ...
(GI) *
Physically based rendering Physically based rendering (PBR) is a computer graphics approach that seeks to render images in a way that models the flow of light in the real world. Many PBR pipelines aim to achieve photorealism. Feasible and quick approximations of the b ...
(PBR) *
Non-photorealistic rendering Non-photorealistic rendering (NPR) is an area of computer graphics that focuses on enabling a wide variety of expressive styles for digital art, in contrast to traditional computer graphics, which focuses on photorealism. NPR is inspired by other ...
(NPR)


References


Bibliography

* * * 3D rendering {{compu-graphics-stub