Stochastic sampling in computer graphics
ACM Transactions on Graphics (TOG)
Generating antialiased images at low sampling densities
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Spectrally optimal sampling for distribution ray tracing
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Consequences of stratified sampling in graphics
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Antialiasing through stochastic sampling
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
A multidimensional Monte Carlo quadrature with adaptive stratified sampling
Communications of the ACM
Reconstruction filters in computer-graphics
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
Proceedings of the 12th Eurographics Workshop on Rendering Techniques
A signal-processing framework for reflection
ACM Transactions on Graphics (TOG)
A frequency analysis of light transport
ACM SIGGRAPH 2005 Papers
ACM SIGGRAPH 2007 papers
Statistical Hypothesis Testing for Assessing Monte Carlo Estimators: Applications to Image Synthesis
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
Multidimensional adaptive sampling and reconstruction for ray tracing
ACM SIGGRAPH 2008 papers
ACM Transactions on Graphics (TOG)
Frequency analysis and sheared reconstruction for rendering motion blur
ACM SIGGRAPH 2009 papers
Monte Carlo and Quasi-Monte Carlo Methods 2006
Monte Carlo and Quasi-Monte Carlo Methods 2006
Accurate multidimensional Poisson-disk sampling
ACM Transactions on Graphics (TOG)
Physically Based Rendering, Second Edition: From Theory To Implementation
Physically Based Rendering, Second Edition: From Theory To Implementation
Parallel Poisson disk sampling with spectrum analysis on surfaces
ACM SIGGRAPH Asia 2010 papers
Differential domain analysis for non-uniform sampling
ACM SIGGRAPH 2011 papers
Reconstructing the indirect light field for global illumination
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Point sampling with general noise spectrum
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
A theory of monte carlo visibility sampling
ACM Transactions on Graphics (TOG)
Analysis and synthesis of point distributions based on pair correlation
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Real-time shading with filtered importance sampling
EGSR'08 Proceedings of the Nineteenth Eurographics conference on Rendering
Linear efficient antialiased displacement and reflectance mapping
ACM Transactions on Graphics (TOG)
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Each pixel in a photorealistic, computer generated picture is calculated by approximately integrating all the light arriving at the pixel, from the virtual scene. A common strategy to calculate these high-dimensional integrals is to average the estimates at stochastically sampled locations. The strategy with which the sampled locations are chosen is of utmost importance in deciding the quality of the approximation, and hence rendered image. We derive connections between the spectral properties of stochastic sampling patterns and the first and second order statistics of estimates of integration using the samples. Our equations provide insight into the assessment of stochastic sampling strategies for integration. We show that the amplitude of the expected Fourier spectrum of sampling patterns is a useful indicator of the bias when used in numerical integration. We deduce that estimator variance is directly dependent on the variance of the sampling spectrum over multiple realizations of the sampling pattern. We then analyse Gaussian jittered sampling, a simple variant of jittered sampling, that allows a smooth trade-off of bias for variance in uniform (regular grid) sampling. We verify our predictions using spectral measurement, quantitative integration experiments and qualitative comparisons of rendered images.