Natural Phenomena Visualization using Unstructured Grid

An international network of possible project partners will be established at the workshop. The main goal is to establish a future project team combining researchers from Austria and Slovakia (and other countries) where we will profit from the synergy of rich experience of TU Vienna in visualization and long-lasting tradition in applied mathematics and geometry at Comenius University Bratislava. A subtitle of future project might be Applied mathematics and geometry for multidimensional exploration of physical, environmental, and medical datasets.

We plan to address universal methods for environmental data visualization and exploration. The key problem is to preserve important features and this requires the optimal dataset representation using optimal structuring of scattered data.

The problem of optimal triangulation doesn’t have final theoretical and practical solutions. In this applied mathematical research field many problems are open, the most challenging one is the Minimum Weight Triangulation (MWT) – stated in 1979. The objective of this research cooperation is to use geometrically based reconstruction to reconstruct physical, environmental and medical multidimensional data sets with feature preserving triangulation meshes and to visualize them.

MWT is an open problem of computational geometry. Except of the theoretical challenge it has several utilization areas in natural and computer sciences. A short list of application area of the proposed research area follows.

Except of feature preserving multidimensional triangulations the selection of the quality preserving function is also important. These functions describe how the important features are represented in the data.

Appropriate tools are necessary for quality measurement in each application area (for example for application area of image reconstruction for measuring of radiometric quality are used perceptual metrics). Their design as the determination of the optimum means improvement towards an optimal reconstruction. In other words, it is possible to separate heuristics from the cost functions, and consider them as relatively independent layers. Adaptation of cost functions of heuristics can mean experimental founding of higher quality results.

The existing numerical techniques and the solutions from image processing field doesn’t yield as strong feature preserving property as our approach, which is based on the generalization of data-dependent triangulations described by Nira Dyn in 1991.

The described theoretical tools are of fundamental importance in current research and we plan to establish a bilateral (OEAD) or multilateral (Visegrad Plus) project team. To achieve this we plan to organize the workshop

Natural Phenomena Visualization using Unstructured Grid

of possible partners of TU Vienna and UK Bratislava. The list of invited partners is based on the CESCG 2005 participating universities. CESCG is our multilateral international student seminar - http://www.cg.tuwien.ac.at/studentwork/CESCG/.

The invited candidates for partners include:

The networking seminar will be organized in Budmerice Castle on Wednesday, May 11th, 2005 afternoon for those who will be interested. There we will discuss the theoretical possibilities and grant schemes. Afterwards, we will establish a website to support the online networking. In the meantime, preparatory team members will visit Vienna and Bratislava universities to detailise project structure and collect exploration worth datasets from environmental, medical, and physics researchers and other partners.

The initiating team consists from Master Edi Groeller, Werner Purgathofer, Michi Wimmer, and Ivan Viola, at the Vienna side. From Bratislava, there will be Andrej Ferko, Stanislav Stanek, Elena Sikudova and Zsolt Toth.

Physical, environmental, and medical multidimensional data sets are hard to explore and visualize. We intend to compose, during 2005, a team which will be competitive in getting bilateral (OEAD/SAIA), multilateral (Visegrad Plus) and European level grants for sustainable cooperation.