Chapter Fourteen Monte Carlo Integration II: Improving Efficiency

Variance in Monte Carlo ray tracing manifests itself as noise in the image—an unpleasant artifact (Figure 14.1). The battle against variance is the basis of most of the work in optimizing Monte Carlo. Recall that Monte Carlo’s convergence rate means that it is necessary to quadruple the number of samples in order to reduce the variance by half. Because the run time of the estimation procedure is proportional to the number of samples, the cost of reducing variance can be high. This chapter will develop the theory and practice of techniques for improving the efficiency of Monte Carlo integration without necessarily increasing the number of samples.

The efficiency of an estimator ...

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