Critical region analysis of scalar fields in arbitrary dimensions
Madjid Állili, Marc Ethier, Tomasz Kaczyński · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009
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.