Consequences of Stratified Sampling in Graphics

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Consequences of Stratified Sampling in Graphics
Antialiased 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. CR Categories and Descriptors: I.3.3 [Computer Graphics]: Picture/Image generation. Additional Key Words: Sampling, Stratification, Discrepancy, Antialiasing, Variance Reduction.
Don P. Mitchell
Added 08 Aug 2010
Updated 08 Aug 2010
Type Conference
Year 1996
Authors Don P. Mitchell
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