Structure-significant representation of structured datasets

Numerical simulation of physical phenomena is now an accepted way of scientific inquiry. However, the field is still evolving, with a profusion of new solution and grid-generation techniques being continuously proposed. Concurrent and retrospective visualization are being used to validate the results, compare them among themselves and with experimental data, and browse through large scientific databases. There exists a need for representation schemes which allow access of structures in an increasing order of smoothness (or decreasing order of significance). We describe our methods on datasets obtained from curvilinear grids. Our target application required visualization of a computational simulation performed on a very remote supercomputer. Since no grid adaptation was performed, it was not deemed necessary to simplify or compress the grid. In essence, we treat the solution as if it were in the computational domain. Inherent to the identification of significant structures is determining the location of the scale coherent structures and assigning saliency values to them [22], [23]. Scale coherent structures are obtained as a result of combining the coefficients of a wavelet transform across scales. The result of this operation is a correlation mask that delineates regions containing significant structures. A spatial subdivision (e.g., octree) is used to delineate regions of interest. The mask values in these subdivided regions are used as a measure of information content. Later, another wavelet transform is conducted within each subdivided region and the coefficients are sorted based on a perceptual function with bandpass characteristics. This allows for ranking of structures based on the order of significance, giving rise to an adaptive and embedded representation scheme. We demonstrate our methods on two datasets from computational field simulations. Essentially, we show how our methods allow the ranked access of significant structures. We also compare our adaptive representation scheme with a fixed blocksize scheme.