Estimating product integrals using a composition of warps

Abstract

Sampling a function is used for many applications, such as rendering images. The challenge is how to select the best samples to minimize computations and produce accurate results. An alternative is to use a larger number of samples that may not be carefully selected in an attempt to increase accuracy. For a function that is an integral, such as functions used to render images, a sample distribution may be computed by inverting the integral. Unfortunately, for many integrals, it is neither easy nor practical to compute the inverted integral. Instead, warp functions may be combined to provide a sample distribution that accurately approximates the factors of the product being integrated. Each warp function approximates an inverted term of the product while accounting for the effects of warp functions approximating other factors in the product. The selected warp functions are customized or 'fitted' to implement importance sampling for the approximated product.