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Importance Sampling

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Importance sampling is a powerful variance reduction technique that exploits the fact that the Monte Carlo estimator converges more quickly if the samples are taken from a distribution that is similar to the function in the integrand. The basic idea is that by concentrating work where the value of the integrand is relatively high, an accurate estimate is computed more efficiently (Figure 13.19). For example, suppose we are evaluating the scattering equation, Equation (5.9). Consider what happens when this integral is estimated; if a direction is randomly sampled that is nearly perpendicular to the surface normal, the cosine term will be close to 0. All the expense of evaluating the BSDF and tracing a ray to find the incoming radiance at that sample location will be essentially wasted, as the contribution to the final result will be minuscule. In general, we would be better served if we sampled directions in a way that reduced the likelihood of choosing directions near the horizon. Mo

Importance Sampling 13.10 Importance Sampling Importance sampling is a powerful variance reduction technique that exploits the fact that the Monte Carlo estimator converges more quickly if the samples are taken from a distribution that is similar to the function in the integrand. The basic idea is that by concentrating work where the value of the integrand is relatively high, an accurate estimate is computed more efficiently (Figure 13.19 ). Figure 13.19: (1) Using a stratified uniform distribution of rays over the hemisphere gives an image with much more variance than (2) applying importance

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