A linear heuristic for multiple importance sampling

Multiple importance sampling combines the probability density functions of several sampling techniques into an importance function. The combination weights are the proportion of samples used for the particular techniques. This paper addresses the determination of the optimal combination weights from a few initial samples. Instead of the numerically unstable optimization of the variance, in our solution the quasi-optimal weights are obtained by solving a linear equation, which leads to simpler computations and more robust estimations. The proposed method is validated with 1D numerical examples and with the direct lighting problem of computer graphics.