Unbiased rendering in computer graphics refers to techniques that avoid systematic errors, or biases, in the radiance approximation of an image. This term specifically relates to statistical bias, not subjective bias. Unbiased rendering aims to replicate real-world lighting and shading as accurately as possible without shortcuts. Path tracing and its derivatives are examples of unbiased techniques, whereas traditional ray tracing methods are typically biased.[1]

## Mathematical definition

In mathematical terms, an unbiased estimator's expected value (E) is the population mean, regardless of the number of observations. The errors in an image produced by unbiased rendering are due to random statistical variance, which appears as high-frequency noise. Variance in this context decreases by n (standard deviation decreases by n) for n data points.[2] Consequently, four times as much data is required to halve the standard deviation of the error, making unbiased rendering less suitable for real-time or interactive applications. An image that appears noiseless and smooth from an unbiased renderer is probabilistically correct.

## Biased vs. unbiased rendering

A biased rendering method can still produce images close to the desired result but introduces a certain amount of error (often seen as a blur) to reduce variance (noise). These methods are typically optimized for faster computation at the expense of some accuracy.[3]

## 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.[4]

On the other hand, progressive photon 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.