Direct mesh: A multiresolution approach to terrain visualization

Terrain can be approximated by a triangular mesh consisting millions of 3D points. Multiresolution triangular mesh (MTM) structures are designed to support applications that use terrain data at variable levels of detail (LOD). Typically, an MTM adopts a tree structure where a parent node represents a lower-resolution approximation of its descendants. Given a region of interest (ROI) and a LOD, the process of retrieving the required terrain data from the database is to traverse the MTM tree from the root to reach all the nodes satisfying the ROI and LOD conditions. This process, while being commonly used for multiresolution terrain visualization, is inefficient as either a large number of sequential I/O operations or fetching a large amount of extraneous data is incurred. Various spatial indexes have been proposed in the past to address this problem, however level-by-level tree traversal remains a common practice in order to obtain topological information among the retrieved terrain data. A new MTM data structure called direct mesh is proposed. We demonstrate that with direct mesh the amount of data retrieval can be substantially reduced. Comparing with existing MTM indexing methods, a significant performance improvement has been observed for real-life terrain data.

A hierarchical latent variable model for data visualization

Visualization has proven to be a powerful and widely-applicable tool the analysis and interpretation of data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach first on a toy data set, and then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines and to data in 36 dimensions derived from satellite images.