Multiple Importance Sampling (MIS) is a technique used by Veach's VCM technique to balance responses of different surfaces to different types of importance sampling for direct illumination. My understanding is that specular surfaces are best lit without sampling the light at all; instead, you pull a direction from the BRDF and hope that it hits the light source. Diffuse surfaces "spread" light more broadly over their domain, so firing rays towards random points on the area covered by the light produces good results without the wastage produced by sampling over the BRDF.
I'm still unsure about a few things, though:
- Veach's demonstration images show flat specular surfaces eventually converging with light sampling; how is this possible? All rays fired towards random points on the light will reach the light (assuming no obstructions), so shouldn't the specular surfaces wash out under all the assumed illumination?
- "Multiple Importance Sampling" implies that tracing gather rays towards the light is an importance-sampled technique (which makes sense, it's very difficult to have invalid rays if all rays approximate the direction of light relative to the surface); does this mean I need to be dividing my direct gathers by a PDF? Given that the "direction" of the light could be anywhere on the unit sphere surrounding the lit point, should the PDF be $4\pi$?