Unbiased rendering

<h2 id="mathematical-definition">Mathematical definition</h2>
<p>In mathematical terms, an unbiased estimator's expected value (E) is the population <a href="/facts/Mean/swcEd4Pg">mean</a>, regardless of the number of observations. The <a href="/facts/Error/20QgR4EI">errors</a> in an image produced by unbiased rendering are due to random statistical <a href="/facts/Variance/ULBJKXD1">variance</a>, which appears as <a href="/facts/High_frequency/JmDJLR5I">high-frequency</a> noise. Variance in this context decreases by n (standard deviation decreases by n) for n data points.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> Consequently, four times as much <a href="/facts/Data/AUBFN97o">data</a> is required to halve the <a href="/facts/Standard_deviation/qSug9BRl">standard deviation</a> of the error, making unbiased rendering less suitable for <a href="/facts/Real-time_computing/p9HxgL4L">real-time</a> or interactive applications. An image that appears <a href="/facts/Noiseless/krNeCwev">noiseless</a> and smooth from an unbiased renderer is probabilistically correct.
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<h2 id="caustics-example">Caustics example</h2>
<p>An unbiased technique, like path tracing, cannot consider all possible light paths due to their <a href="/facts/Infinity/cF506uD7">infinite</a> number. It may not select ideal paths for a given <a href="/facts/Rendering_(computer_graphics)/YYxfnmAq">render</a>, as this would introduce bias. For example, path tracing struggles with <a href="/facts/Caustic_(optics)/og01czyx">caustics</a> from a <a href="/facts/Point_source/AHmNlt03">point light source</a> because it is unlikely to randomly generate the exact path needed for accurate <a href="/facts/Reflection_(physics)/BhcjDs79">reflection</a>.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a>
</p><p>On the other hand, progressive <a href="/facts/Photon_mapping/t58p6V7w">photon mapping</a> (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.
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<h2 id="list-of-unbiased-rendering-methods">List of unbiased rendering methods</h2>
<ul><li><a href="/facts/Path_tracing/fxhaM84b">Path tracing</a></li>
<li><a href="/facts/Path_tracing/fxhaM84b">Bidirectional path tracing</a></li>
<li><a href="/facts/Metropolis_light_transport/wRoPqI2f">Metropolis light transport</a> and the related "energy redistribution path tracing" (ESPT)<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a></li></ul>
<h2 id="list-of-unbiased-renderers">List of unbiased renderers</h2>
<ul><li><a href="/facts/Arion_(software)/XbP6y7me">Arion</a></li>
<li><a href="/facts/Arnold_(software)/huRftsKR">Arnold</a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a></li>
<li><a href="/facts/Blender_(software)/yzuvB0fL">Cycles</a></li>
<li><a href="/facts/Kerkythea/nVBG2VjJ">Kerkythea</a></li>
<li><a href="/facts/LuxRender/pYQNxN0B">LuxRender</a></li>
<li><a href="/facts/Houdini_(software)/h7PwskFC">Mantra</a></li>
<li><a href="/facts/Maxwell_Render/KUlJEfRk">Maxwell Render</a></li>
<li><a href="/facts/Octane_Render/Jlf5xvN6">Octane Render</a></li>
<li><a href="https://fstormrender.ru/">Fstorm Render</a> (external link)</li></ul>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Global_illumination/CbQX6CWM">Global illumination</a> (GI)</li>
<li><a href="/facts/Physically_based_rendering/bRK5alKl">Physically based rendering</a> (PBR)</li>
<li><a href="/facts/Non-photorealistic_rendering/r8qIQogo">Non-photorealistic rendering</a> (NPR)</li></ul>

<h2 id="bibliography">Bibliography</h2>

<ul><li><a href="https://web.archive.org/web/20160303194610/http://randomcontrol.com/component/rcfaq/?faqid=1&id=3">"fryrender F.A.Q."</a> RandomControl, SLU. Archived from <a href="http://randomcontrol.com/component/rcfaq/?faqid=1&id=3">the original</a> on 2016-03-03. Retrieved 2010-05-20.</li>
<li>Mike Farnsworth. <a href="http://renderspud.blogspot.com/2006/10/biased-vs-unbiased-rendering.html">"Biased vs Unbiased Rendering"</a>. <i>RenderSpud</i>. Retrieved 2010-05-20.</li>
<li><a href="http://www.3dworldmag.com/2010/01/15/how_to_choose_rendering_software_part_2/">"How to choose rendering software"</a>.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>David Cline; Justin Talbot; Parris Egbert. "Energy Redistribution Path Tracing". CiteSeerX 10.1.1.63.5938. <a href="/wiki/CiteSeerX_(identifier)" target="_blank">/wiki/CiteSeerX_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>"Bias In Rendering" (PDF). <a href="https://www.cs.cmu.edu/~kmcrane/Projects/Other/BiasInRendering.pdf" target="_blank">https://www.cs.cmu.edu/~kmcrane/Projects/Other/BiasInRendering.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>James Arvo; Marcos Fajardo; Pat Hanrahan; Henrik Wann Jensen; Don Mitchell; Matt Pharr; Peter Shirley (2001). "State of the Art in Monte Carlo Ray Tracing for Realistic Image Synthesis". CiteSeerX 10.1.1.9.6918. <a href="/wiki/Pat_Hanrahan" target="_blank">/wiki/Pat_Hanrahan</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Opulent, Ken. "Mastering Path Tracing and 3D Rendering". <a href="https://3drenderingpro.com/path-tracing-and-3d-rendering/" target="_blank">https://3drenderingpro.com/path-tracing-and-3d-rendering/</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>David Cline; Justin Talbot; Parris Egbert. "Energy Redistribution Path Tracing". CiteSeerX 10.1.1.63.5938. <a href="/wiki/CiteSeerX_(identifier)" target="_blank">/wiki/CiteSeerX_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>James Arvo; Marcos Fajardo; Pat Hanrahan; Henrik Wann Jensen; Don Mitchell; Matt Pharr; Peter Shirley (2001). "State of the Art in Monte Carlo Ray Tracing for Realistic Image Synthesis". CiteSeerX 10.1.1.9.6918. <a href="/wiki/Pat_Hanrahan" target="_blank">/wiki/Pat_Hanrahan</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
</ol>

Unbiased rendering open-in-new

Unbiased rendering