Monte Carlo Sampling


CS 6650: Image Synthesis

Instructor Peter Shirley







XianMing Chen, xchen AT cs DOT utah DOT edu


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Generate images of the following function with Monte Carlo sampling methods.


double f(double x, double y, double kx, double ky, int nx, int ny)
{
return 0.5*(x/nx)*(1+cos( kx* x*x))*(y/ny)*(1+cos(ky*y*y));
}


Analytic Solution

MC Integration, 16 random samples MC Integration, 100 random samples

MC Integration, 16 stratified samples MC Integration, 100 stratified samples

MC Inegration, 16 random samples, bspline filter MC Inegration, 100 random samples, bspline filter

Density Estimation, 16 random samples per pixel on average Density Estimation, 100 random samples per pixel on average

Density Estimation, 16 stratified samples per pixel on average Density Estimation, 100 stratified samples per pixel on average

Metropolis, 100 random samples per pixel on average