View-based Rendering: Slide 7 of 17.

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But even if we knew the exact surface geometry, all rays seeing the same point may not be equal.

First, the reflectance of many materials is different to different directions.

Second, if we only have approximate geometrical information, like when we estimate the surface from range data, similar directions should be preferred to reduce the likelihood and magnitude of errors.

In the left image we have the query ray and two other rays pointing to the same spot. However, only one of the rays really sees the same point as the query ray does. In general, the likelihood of self-occlusions increases the farther the rays are apart.

In the right image we think that the surface is at the solid line, but it's really a bit farther. Now this ray [the ray that is almost parallel to the query ray] still intersects the real surface close to where the query ray does, while with the other ray we get a larger error.