## Consequences of Stratified Sampling in Graphics

Don P. Mitchell

Microsoft CorporationAnti-aliased pixel values are often computed as the mean of N point samples. Using uniformly distributed random samples, the central limit theorem predicts a variance of the mean of

O(N -1). Stratified sampling can further reduce the variance of the mean. This paper investigates how and why stratification effects the convergence to mean value of image pixels, which are observed to converge from N -2 to N -1 , with a rate of about N -3/2 in pixels containing edges. This is consistent with results from the theory of discrepancy. The result is generalized to higher dimensions, as encountered with distributed ray tracing or form-factor computation.

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