2010-06-01

A personal annotations of Veach's thesis (8)

Page 11: Light implementation

In page 11, there is a paragraph about light implementation.
Ideally, the performance of the light transport algorithm should depend only on what the scene represents, rather than the details of how it is represented. For example, consider a scene illuminated by a square area light source. If this light source is replaced with a 10 by 10 grid of point sources, then the visual results will be nearly identical. However, the performance of many light transport algorithms will be much worse in the second case.
Why 10x10 points is more expensive? As an amateur, I think if the area light is sampled by 20x20, then it seems 10x10 points is cheaper. But this is just an example. It seems the author want to say if you tell the renderer more straight forward way, the rendere can usually optimize the process. It is better to say that an area light is an area light, not an area light is many points. (Thanks to D.S.)

Page 14: unbias and consistent

This page mentions about Unbias and Consistent. If we see the equation, they are

  Consistent: error -> 0
  Unbias:     E(error) -> 0.

Consistent is that the error becomes zero at the end. This means the solution converges with no error, we could get always the correct error if we have enough computation power. Please note: this doesn't talk about intermediate solution. It is possible some intermediate solution has a large error.

On the other hand, unbias is expectation of error (average of error) is zero. In this case, if intermediate solutions have a lot of error, then average of error isn't zero.

Consistent is a larger concept since there is a case it is consistent (= converges) but biased. (I think here there is an assumption that the function is integrable. I think this is not a bad assumption for light transport problem anyway.) If the function is integrable and the integrated value exists, I think unbias is always consistent.

By the way, I don't know what is the error's variance. Does it matter in this context? Since error itself and its first moment matter. Then second moment could matter also? I should ask this to someone.

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