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Incomputer graphics,unbiased rendering refers to techniques that avoid systematic errors, orstatistical bias, in computing an image’sradiance. Bias means inaccuracies like dimmer light or missing effects such as soft shadows, caused by approximations. Unbiased methods, such aspath tracing and its derivatives, simulate real-worldlighting andshading with full physical accuracy. In contrast, biased methods, including traditionalray tracing, sacrifice precision for speed by using approximations that introduce errors—often seen as blur.[1] This blur reducesvariance (random noise) by averaging light samples, enabling faster computation with fewer samples needed for a clean image.[2]
In mathematical terms, an unbiased estimator's expected value (E) is the populationmean, regardless of the number of observations. Theerrors in an image produced by unbiased rendering are due to random statisticalvariance, which appears ashigh-frequency noise. Variance in this context decreases by n (standard deviation decreases by n) for n data points.[3] Consequently, four times as muchdata is required to halve thestandard deviation of the error, making unbiased rendering less suitable forreal-time or interactive applications. An image that appearsnoiseless and smooth from an unbiased renderer is probabilistically correct.
An unbiased technique, like path tracing, cannot consider all possible light paths due to theirinfinite number. It may not select ideal paths for a givenrender, as this would introduce bias. For example, path tracing struggles withcaustics from apoint light source because it is unlikely to randomly generate the exact path needed for accuratereflection.[4]
On the other hand, progressivephoton mapping (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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