Title Hierarchical Representation of Time-varying Volume Data with 4th-root-of-2 Subdivision and Quadrilinear B-spline Wavelets (In Proceedings) Proceedings of Tenth Pacific Conference on Computer Graphics and Applications - Pacific Graphics 2002 Lars Linsen, Valerio Pascucci, Mark A. Duchaineau, Bernd Hamann, Ken Joy S. Coquillart, H.-Y. Shum, S.-M. Hu 2002 IEEE Computer Society Press Multiresolution methods for representing data at multiple levels of detail are widely used for large-scale two- and three-dimensional data sets. We present a four-dimensional multiresolution approach for time-varying volume data. This approach supports a hierarchy with spatial and temporal scalability. The hierarchical data organization is based on $\sqrt[4]{2}$ subdivision. The $\sqrt[n]{2}$-subdivision scheme only doubles the overall number of grid points in each subdivision step. This fact leads to fine granularity and high adaptivity, which is especially desirable in the spatial dimensions. For high-quality data approximation on each level of detail, we use quadrilinear B-spline wavelets. We present a linear B-spline wavelet lifting scheme based on $\sqrt[n]{2}$ subdivision to obtain narrow masks for the update rules. Narrow masks provide a basis for out-of-core data exploration techniques and view-dependent visualization of sequences of time steps.