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Importance is a necessity for any renderer that traces more than one bounce after tracing a ray from the camera. For example, in a simple path tracer, the "weight" of an eye subpath is accumulated importance divided by the accumulated pdf. At each bounce, the importance is reduced by the B...

Without the We term, W(x,w) would just be zero (since some nonzero portion of light hitting a reflective surface would be absorbed). Importance is basically what portion of reflected or emitted light from a surface contributes to a rendered image. In a path-/ray-tracer We(x,w) should generally only ...