Multi-dimensional trees for controlled volume rendering and compression

This paper explores the use of multi-dimensional trees to provide spatial and temporal efficiencies in imaging large data sets. Each node of the tree contains a model of the data in terms of a fixed number of basis functions, a measure of the error in that model, and a measure of the importance of the data in the region covered by the node. A divide-and-conquer algorithm permits efficient computation of these quantities at all nodes of the tree. The flexible design permits various sets of basis functions, error criteria, and importance criteria to be implemented easily. Selective traversal of the tree provides images in acceptable time, by drawing nodes that cover a large volume as single objects when the approximation error and/or importance are low, and descending to finer detail otherwise. Trees over very large datasets can be pruned by the same criterion to provide data representations of acceptable size and accuracy. Compression and traversal are controlled by a user-defined combination of modeling error and data importance. For imaging decisions additional parameters are considered, including grid location, allowed time, and projected screen area. To analyse results, two evaluation metrics are used: the first compares the hierarchical model to actual data values, and the second compares the pixel values of images produced by different parameter settings.