Environment Light Importance Sampling

The majority of the time spent when raytracing is generally intersecting rays with the scene and the objects in the scene. The two main ways to reduce the time taken to raytrace scenes are to either reduce the cost of each ray intersection (by using acceleration structures), or to send less rays.

Sending less rays obviously has a direct impact on the speed of rendering the scene, but care has to be taken to make sure image quality doesn’t suffer as a result: normally more samples per-pixel are used in order to reduce the noise (or variance) in an image. There are a variety of techniques that can be used to maximise the effectiveness of the rays sent out into the scene from adaptive super-sampling (sending out more rays per-pixel when the samples within the pixel are dissimilar) to efficient sampling (by ensuring that there’s a good distribution of samples across all sampling dimensions) through to importance sampling.

Importance Sampling is a technique whereby samples are selected so that a variable that has the most effect on the variance of the overall end result has the most distribution.

An excellent example of this is with environment lighting - if we use the following environment map for lighting a scene:

there are only two very small areas of illumination coming from the map. Without using importance sampling - by randomly sampling locations from the map - there is a low probability that any of the samples will actually correspond to the two coloured dots on the texture map. This means that either the image will be too dark (and won’t evaluate the two coloured dots correctly), or there will be very high variance where a few samples that sample the light pick up one of the coloured spots, but most don’t. This will result in extreme noise, as can be seen in this render without importance sampling:

With importance sampling, it is possible to build up a two-dimensional map of importance based on the corresponding luminance of the environment map, which allows any light sample for the environment map to map to an actual position on the texture map where there is colour - i.e. one of the two coloured spots. The weighting of the function has to be modified as well, in order to not bias the equation (by assuming that the entire image is yellow and blue with no black) which would give unrealistic results.

The final result with importance sampling can be seen below:

Both images were rendered with 32 samples per-pixel, and the noise-reduction importance sampling gives in this case is striking.