__NOTOC__ In

computer graphics Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. ...

, unbiased rendering or photorealistic rendering are rendering techniques that avoid systematic errors, or

statistical bias In the field of statistics, bias is a systematic tendency in which the methods used to gather data and estimate a sample statistic present an inaccurate, skewed or distorted (''biased'') depiction of reality. Statistical bias exists in numerou ...

, in computing an image’s

radiance In radiometry, radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiati ...

. Bias in this context means inaccuracies like dimmer light or missing effects such as soft shadows, caused by approximations. Unbiased methods, such as

path tracing Path tracing is a rendering algorithm in computer graphics that Simulation, simulates how light interacts with Physical object, objects, voxels, and Volumetric_path_tracing, participating media to generate realistic (''physically plausible'') R ...

and its derivatives, simulate real-world

lighting Lighting or illumination is the deliberate use of light to achieve practical or aesthetic effects. Lighting includes the use of both artificial light sources like lamps and light fixtures, as well as natural illumination by capturing daylight. ...

and

shading Shading refers to the depiction of depth perception in 3D models (within the field of 3D computer graphics) or illustrations (in visual art) by varying the level of darkness. Shading tries to approximate local behavior of light on the object's ...

with full physical accuracy. In contrast, biased methods, including traditional ray tracing, sacrifice precision for speed by using approximations that introduce errors—often seen as blur. This blur reduces

variance In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion ...

(random noise) by averaging light samples, enabling faster computation with fewer samples needed for a clean image.

Mathematical definition

In mathematical terms, an unbiased estimator's expected value (E) is the population

mean A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statist ...

, regardless of the number of observations. The errors in an image produced by unbiased rendering are due to random statistical

, which appears as

high-frequency High frequency (HF) is the International Telecommunication Union, ITU designation for the radio band, band of radio waves with frequency between 3 and 30 megahertz (MHz). It is also known as the decameter band or decameter wave as its wavelengt ...

noise. Variance in this context decreases by n (standard deviation decreases by n) for n data points. Consequently, four times as much

data Data ( , ) are a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted for ...

is required to halve the

standard deviation In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...

of the error, making unbiased rendering less suitable for

real-time Real-time, realtime, or real time may refer to: Computing * Real-time computing, hardware and software systems subject to a specified time constraint * Real-time clock, a computer clock that keeps track of the current time * Real-time Control Syst ...

or interactive applications. An image that appears noiseless and smooth from an unbiased renderer is probabilistically correct.

Caustics example

An unbiased technique, like path tracing, cannot consider all possible light paths due to their infinite number. It may not select ideal paths for a given render, as this would introduce bias. For example, path tracing struggles with caustics from a point light source because it is unlikely to randomly generate the exact path needed for accurate reflection. On the other hand, 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 technique, handles caustics effectively. Although biased, PPM is consistent, meaning that as the number of samples increases to infinity, the bias error approaches zero, and the probability that the estimate is correct reaches one.

List of unbiased rendering methods

Path tracing Path tracing is a rendering algorithm in computer graphics that Simulation, simulates how light interacts with Physical object, objects, voxels, and Volumetric_path_tracing, participating media to generate realistic (''physically plausible'') R ...

* Bidirectional path tracing * Metropolis light transport and the related "energy redistribution path tracing" (ESPT)

List of unbiased renderers

Arion Arion (; ) 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 of Corinth. Although notable for his mu ...

* Arnold *

Cycles Cycle, cycles, or cyclic may refer to: Anthropology and social sciences * Cyclic history, a theory of history * Cyclical theory, a theory of American political history associated with Arthur Schlesinger, Sr. * Social cycle, various cycles in ...

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 th ...

LuxRender LuxCoreRender is a free and open-source physically based rendering software. It began as ''LuxRender'' in 2008 before changing its name to LuxCoreRender in 2017 as part of a project reboot. The LuxCoreRender software runs on Linux, Mac OS X, a ...

Mantra A mantra ( ; Pali: ''mantra'') or mantram (Devanagari: मन्त्रम्) is a sacred utterance, a numinous sound, a syllable, word or phonemes, or group of words (most often in an Indo-Iranian language like Sanskrit or Avestan) belie ...

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 Octane Render is an unbiased rendering application with real-time capability developed by graphics software company OTOY Inc. Octane Render was the first commercially available unbiased path-tracer that fully utilized the GPU, allowing users ...

Fstorm Render
(external link)

References

Bibliography