Markov chain Monte Carlo

Monte Carlo integration

Hybrid Monte Carlo

Algorithm

Statistics

Applied mathematics

Variance reduction

Computer graphics (images)

Importance sampling

Computer science

Mathematical optimization

Rendering (computer graphics)

Control variates

Mathematics

Monte Carlo method

ACM SIGGRAPH Computer Graphics

We present an integral equation which generalizes a variety of known rendering algorithms. In the course of discussing a monte carlo solution we also present a new form of variance reduction, called Hierarchical sampling and give a number of elaborations shows that it may be an efficient new technique for a wide variety of monte carlo procedures. The resulting rendering algorithm extends the range of optical phenomena which can be effectively simulated.

The rendering equation