Using Leonard's results and thoughts on TerrainRepsFromSVD, we can come up with some "compressed" representations of terrain by performing an off-line SVD for large data sets. As the diagonal (sigma) matrix tends to encode more important values towards the top left, we could drop off the less important values in the lower right hand corner, thus allowing a bounded error representation of the terrain.

Also, using the SVD to "encode" the terrain allows us to reconstruct certain points or areas without reconstructing the entire terrain, which could be leveraged for queries which only require local data such as the local gradient, etc. This could also be mixed with the "importance ordering" research to create an efficient transport method for large terrain representations which could be constrained by a certain level of accuracy.

All of the above applies very well to performing SVD on height maps, but how does performing an SVD for compression affect other important operations on the reconstructed matrix? This is a key question in topics where it is important to preserve slope data in addition to height data. Is there an arrangement of the data we could use with respect to the SVD such that certain slope calculations are preserved better than others (i.e. forward difference vs. gaussian, etc.)? We know with height maps, the lower right sigmas tend to encode less information, however this certainly does not hold true for the slopes. In light of this, could there be some smart way of selecting certain sigmas or rows or columns from the other two matricies such that slope data is preserved within a certain tolerance while maxmizing the amount of compression?

-- ZachBailey - 18 Feb 2005

Zach, can you do an experiment that shows that "this certainly does not hold true for the slopes? And in general, please expand this to suggest specific experiments. -- JackSnoeyink - 23 Feb 2005
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