In computer graphics

Computer graphics

Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....

, unbiased rendering refers to a rendering

Rendering (computer graphics)

Rendering is the process of generating an image from a model , by means of computer programs. A scene file contains objects in a strictly defined language or data structure; it would contain geometry, viewpoint, texture, lighting, and shading information as a description of the virtual scene...

 technique that does not introduce any systematic error, or bias

Bias of an estimator

In statistics, bias of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. Otherwise the estimator is said to be biased.In ordinary English, the term bias is...

, into the radiance approximation

Rendering equation

In computer graphics, the rendering equation is an integral equation in which the equilibrium radiance leaving a point is given as the sum of emitted plus reflected radiance under a geometric optics approximation. It was simultaneously introduced into computer graphics by David Immel et al. and...

. Because of this, they are often used to generate the reference image to which other rendering techniques are compared. Mathematically speaking, the expected value

Expected value

In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...

 of the unbiased estimator

Estimator

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule and its result are distinguished....

 will always be the correct value, for any number of samples. Error found in an unbiased rendering will be due to variance

Variance

In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...

, which manifests itself as high-frequency noise in the resultant image. Variance is reduced by for samples, meaning that four times as many samples are needed to halve 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

Consistent estimator

In statistics, a sequence of estimators for parameter θ0 is said to be consistent if this sequence converges in probability to θ0...

. It does, however, introduce a certain bias error

Bias of an estimator

In statistics, bias of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. Otherwise the estimator is said to be biased.In ordinary English, the term bias is...

, usually in the form of a blur, in efforts to reduce variance and noise. It is important to note that an unbiased technique may not consider all possible paths. Path tracing

Path Tracing

Path tracing is a computer graphics rendering technique that attempts to simulate the physical behaviour of light as closely as possible. It is a generalisation of conventional ray tracing, tracing rays from the virtual camera through several bounces on or through objects...

 can not handle caustics

Caustic (optics)

In optics, a caustic or caustic network is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface. The caustic is a curve or surface to which each of the light rays is tangent, defining a boundary of an...

 generated from a point light source, as it is impossible to randomly generate the path that directly reflects into the point. Progressive photon mapping (PPM), a biased rendering technique, can handle caustics quite well. PPM is also provably consistent, meaning that as the number of samples goes to infinity

Infinity

Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...

, the bias error goes to zero, and the probability that the estimate is correct reaches one.

Unbiased rendering methods include:

• Path Tracing
  Path Tracing
  Path tracing is a computer graphics rendering technique that attempts to simulate the physical behaviour of light as closely as possible. It is a generalisation of conventional ray tracing, tracing rays from the virtual camera through several bounces on or through objects...
  
  
• Metropolis light transport
  Metropolis light transport
  The Metropolis light transport is a SIGGRAPH 1997 paper by Eric Veach and Leonidas J. Guibas, describing an 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...
  
  
• Energy Redistribution Path Tracing

Some of the programs that support unbiased rendering are:

• Arion
• Blender 3D Cycles Note: In development, but working
• Fryrender
• Houdini's Mantra (PBR)
• Indigo Renderer
  Indigo Renderer
  Indigo Renderer is a 3D rendering software that uses unbiased rendering technologies to create photo-realistic images. In doing so, Indigo uses equations that simulate the behaviour of light, with no approximations or guesses taken...
  
  
• LuxRender
  LuxRender
  LuxRender is an open source software rendering system for physically correct image synthesis. The program runs on Microsoft Windows, Mac OS X and Linux and exporters are available for Blender, SketchUp, Cinema 4D, XSI, DAZ Studio, and Maya.-Overview:...
  
  
• Maxwell Render
  Maxwell Render
  Maxwell Render is a software package that aids in the production of photorealistic images from computer 3D model data; a 3D renderer. It was introduced as an early alpha on December 2004 and it utilized a global illumination algorithm based on a metropolis light transport variation.- Overview...
  
  
• Mental Images iRay
• Octane Render
  Octane Render
  -Integration with other software:Octane Render comes with free plugins for the following software:* Autodesk 3ds Max* Autodesk Maya* Autodesk Softimage* MAXON Cinema 4D* Google Sketchup* Blender * Luxology Modo...
  
  

• Thea Render