Wavelet-based multiresolution with n√2 subdivision

Multiresolution methods are a common technique used for dealing with large-scale data and representing it at multiple levels of detail. We present a multiresolution hierarchy construction based on (n)root2 subdivision, which has all the advantages of a regular data organization scheme while reducing the drawback of coarse granularity. The (n)root2-subdivision scheme only doubles the number of vertices in each subdivision step regardless of dimension n. We describe the construction of 2D, 3D, and 4D hierarchies representing surfaces, volume data, and time-varying volume data, respectively. The 4D approach supports spatial and temporal scalability. For high-quality data approximation on each level of detail, we use downsampling filters based on n-variate B-spline wavelets. We present a B-spline wavelet lifting scheme for (n)root2-subdivision steps to obtain small or narrow filters. Narrow filters support adaptive refinement and out-of-core data exploration techniques.