A performance drawback of our feature-based warping technique is that each point in the warped volume is influenced by all elements, since the influence fields never decay to zero. It follows that the time to warp a volume is proportional to the number of element pairs. An efficient C++ implementation, using incremental calculations, needs 160 minutes to warp a single volume with 30 element pairs on an SGI Indigo 2.
We have implemented two optimizations which greatly accelerate the computation of the warped volume , where we henceforth use to denote either or . First, we approximate the spatially non-linear warping function with a piecewise linear warp . Second, we introduce an octree subdivision over .