(Joint work with Federico Iuricich, Riccardo Fellegara, Paola Magillo, Kenneth Weiss)

The huge size of available datasets describing terrains or 3D scalar fields (e.g. temperature, pressure, etc. over the surface of the Earth) requires efficient and effective spatial representations as well as powerful and compact morphological descriptors.
 

In the first part of the talk, Ms. DeFloriani will give examples of spatial representations focusing on two recent contributions of our research on efficient spatial data structures for gridded terrains and for tetrahedral meshes used for the discretization of 3D scalar fields.  In particular, she will describe the Sparse Terrain Pyramid, which is a compact multi-resolution representation for terrain datasets obtained as a subset of those representations lying on a regular grid that has been extended to gridded volume datasets.  Next, she will describe the Stellar  Tree, a new compact spatio-topological data structure for triangulated terrains  and tetrahedralized volume datasets, that is based on a spatial subdivision  of the mesh domain, naturally geared to parallel and distributed computation.
 

In the second part of the talk, Ms. DeFloriani will present the results of her research on morphological descriptors for terrains, which are subsequently extended to volume data sets. She will first discuss a morphological descriptor, based on discrete Morse theory and on a discrete gradient field, for Triangulated Irregular Networks (TINs). The discrete gradient field can be computed directly from the elevation values given at the vertices of the TIN, and it can be simplified in order to eliminate critical points that arise on account of noise or that correspond to uninteresting morphological features. With the same intent, DeFloriani and her team developed a new technique for eliminating flat edges from a TIN in a morphologically consistent way, as a preprocessing step for performing morphological computations on a terrain. She will briefly show how to generalize these descriptors and their computation algorithms to volume data, i.e., unstructured tetrahedral meshes discretizing the domain of a 3D scalar field.