Monte Carlo integration is typically interpreted as an estimator of the expected value using stochastic samples. There exists alternative interpretation in calculus where can be seen estimating a constant function---from evaluations integrand---that integrates to original integral. The integral mean theorem states that this function should (or expectation) integrand. Since both interpretations ...

Quasi-Monte Carlo integration is said to be better than Monte-Carlo integration since its error bound can be in the order of O(N (1 )) instead of the O(N 0:5) probabilistic bound of classical Monte-Carlo integration if the integrand has finite variation. However, since in computer graphics the integrand of the rendering equation is usually discontinuous and thus has infinite variation, the supe...

Monte Carlo integration is a widely used method to approximate high dimensional integrals. However, the randomness of this method causes the convergence to be very slow. Quasi-Monte Carlo integration uses low discrepancy sequences instead of pseudorandom sequences. The points from these sequences are more uniformly distributed. This causes the convergence to be much faster. Most research in qua...