View-Dependent Reconstruction

For view dependent reconstruction we need to evaluate L(x) where x is the point on the surface that is hit by a ray (or is derived from some other rendering approach). This is in some ways very similar to view independent reconstruction, but has few significant twists. In both cases we are reconstructing L(x) at a point, but in view dependent reconstruction we often include more elaborate texturing and non-diffuse surfaces. Perhaps the biggest issue is that we (tend to) sample at a much higher rate than we do for view independent reconstruction. This means that any rapidly changing error in the reconstruction will be much more noticeable.

Gathering from the Radiosity Solution

This approach was first introduced in a Master's thesis by Mark Reichert[29] and discussed in CW[10]. The initial version was done using progressive radiosity and was quite slow. Complete form factor and visibility information was computed for every surface (shooting patch) in the environment to every point needed for reconstruction. Using HR we can do this much more efficiently at the risk of a few complications.

Gather at each point using the collection of surfaces (sources) defined by the links. This is still expensive.

Try to gather only over some links, not all. With piecewise constant basis functions this causes problems because your gathering strategy changes on each leaf node (different set of links, different set of sources, different set explicitly gathered over.)

Break up the error by randomly choosing some set to gather from, using either intensity or error estimates to weight the choice. This can work if done right. We want to use as much of the computed information as we can, either using the value off the link, or recomputing it with some probability. To do this right, we need to use Russian Roulette, otherwise we get the following

$$E(L) = p L(x) + (1-p) \widehat{L}(x)$$

In order to fix this problem we replace $\widehat{L}(x)$ with $\frac{L(x) - (1-p)\widehat{L}(x)}{p}$. Now the expected value is

$$p \frac{L(x) - (1-p)\widehat{L}(x)}{p} + (1-p) \widehat{L}(x)$$ E(L) = (17)

= L(x). (18)

This works (Details in [32]). One interesting problem is that the amount of noise on each leaf can vary, creating annoying artifacts. Also, if the probability p is very small, reducing noise can be a problem. Another problem is that far too much work is done in uninteresting areas in order to get the interesting areas right. A problem which I've never seen, and is potentially insignificant is that when moving between surfaces, the representations of the environment may be different, resulting in a different solution. This is probably well taken care of by the global refinement.

The inefficiencies of this method are caused by dealing with the discontinuous change of strategies that occurs between leaves. A piecewise linear mesh should solve this problem, and allow many of the energy transfers to be computed once and interpolated.

For environments with arbitrary BRDF's, the BRDF can be evaluated at each point. Uneven use of the incoming links may require more of the links to be recomputed for each pixel. Also, the spread of the near specular lobe can cause problems if it is narrower than the projection of a patch. Highly specular BRDF's can be treated by sending out rays to sample them.

Monte Carlo

Brute force

Use none of the information available to you, except for the radiosity solution. Use that when you have reached your maximum path length. Given the amount of information available, this seems like a bad idea.

Use the links

For this we pick a link at random, and trace a ray to a point on it's surface. This links define an importance sampling function over the receiver. Each link doesn't hold roughly equal radiance transfer, but each holds roughly equal error, so each should be roughly equally hard to estimate.