Consequences of stratified sampling in graphics
- 1 August 1996
- proceedings article
- Published by Association for Computing Machinery (ACM)
- p. 277-280
- https://doi.org/10.1145/237170.237265
Abstract
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.Keywords
This publication has 10 references indexed in Scilit:
- Computing the discrepancy with applications to supersampling patternsACM Transactions on Graphics, 1996
- Antialiased ray tracing by adaptive progressive refinementACM SIGGRAPH Computer Graphics, 1989
- Generating antialiased images at low sampling densitiesACM SIGGRAPH Computer Graphics, 1987
- Irregularities of DistributionPublished by Cambridge University Press (CUP) ,1987
- The rendering equationACM SIGGRAPH Computer Graphics, 1986
- Stochastic sampling in computer graphicsACM Transactions on Graphics, 1986
- Antialiasing through stochastic samplingACM SIGGRAPH Computer Graphics, 1985
- Statistically optimized sampling for distributed ray tracingACM SIGGRAPH Computer Graphics, 1985
- A Retrospective and Prospective Survey of the Monte Carlo MethodSIAM Review, 1970
- Monte Carlo MethodsPublished by Springer Nature ,1964