Critical region analysis of scalar fields in arbitrary dimensions

The exploration of multidimensional scalar fields is commonly based on the knowledge of the topology of their isosurfaces. The latter is established through the analysis of critical regions of the studied fields. A new method, based on homology theory, for the detection and classification of critical regions in multidimensional scalar fields is proposed in this paper. The use of computational homology provides an efficient and successful algorithm that works in all dimensions and allows to generalize visual classification techniques based solely on the notion of connectedness which appears insufficient in higher dimensions. We present the algorithm, discuss details of its implementation, and illustrate it by experimentations in two, three, and four dimensional spaces.

• Type: Journal
• Year: 2010
• Where: VDA
• Authors: Madjid Allili, Marc Ethier, Tomasz Kaczynski
• Keywords: Critical Regions, Multidimensional Scalar Fields, VDA 2010, Visual Classification Techniques, Visualization