Next step?

Besides completing my Lightcuts implementation during the last week, I have searched for possible next steps in my thesis.
One possible extention to the Lighcuts algorithm, as already identified in the paper, is the addition of bounds on the visibility term. I have read a number of papers on this subject:

• Shaft Culling For Efficient Ray-Cast Radiosity - Haines E. & Wallace J. (1991)
  
• ShieldTester: Cell-to-Cell Visibility Test for Surface Occluders - Navazo I., Rossignac J., Jou J. & Shariff R. (2003)
• Conservative Volumetric Visibility with Occluder Fusion - Schaufler G., Julie D., Decoret X. & Sillion F. (2000)

and found one other paper that might be interesting:

• Ray Space Factorization for From-Region Visibility - Leyvand T., Sorkine O. & Cohen-Or D. (2003)

All these techniques have fairly large disadvantages in the context of the calculation of bounds on the visibility. For example the first paper can only guarantee total occlusion if it is cause by a single object (i.e. 1 triangle). In practice this will only work well if there are a number of large polygons in the scene. There do exist a number of extensions that can detect the aggregate occlusion of a number of objects by for example reconstruction larger planes from a number of smaller triangles. The second paper is only applicable to triangles and needs structural information about the meshes (ex. neighbors of a triangle). In the last paper, the scene is discretized which inevitably leads to missing small features (ex. small holes).
Further more all these techniques are quite expensive. This means they can only be used in very selective cases during lightcut calculation or only during a pre-processing phase.

The shaft-culling technique is able to efficiently detect clusters that are totally visible. This could be used to calculate lower bounds on the cluster contribution which results in better error estimates and lower cut sizes.

A totally different approach is to drop the deterministic nature of the lightcuts algorithm and use inexact estimates of the visibility. One possibility would be to first calculate a cut using the bounds and then construct a pdf over the resulting clusters using their estimated contribution. The total contribution of all lights can the be estimated by generating a number of samples from this pdf.
Ideally the user should be able to control the amount of determinism (i.e. the solution goes from the lightcuts solution to totally stochastic according to a parameter).