Topology-based Feature Definition and Analysis

Topology-based Feature Definition and Analysis Gunther H. Weber Computational Research Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA 94720 Peer-Timo Bremer Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Box 808, L-422, Livermore, CA 94551 Attila Gyulassy and Valerio Pascucci Scientific Computing and Imaging Institute, University of Utah, 72 S Central Campus Drive, Salt Lake City, UT 84112 Abstract. Defining high-level features, detecting them, tracking them and deriving quantities based on them is an integral aspect of modern data analysis and visualiza- tion. In combustion simulations, for example, burning regions, which are characterized by high fuel-consumption, are a possible feature of interest. Detecting these regions makes it possible to derive statistics about their size and track them over time. How- ever, features of interest in scientific simulations are extremely varied, making it chal- lenging to develop cross-domain feature definitions. Topology-based techniques offer an extremely flexible means for general feature definitions and have proven useful in a variety of scientific domains. This paper will provide a brief introduction into topolog- ical structures like the contour tree and Morse-Smale complex and show how to apply them to define features in different science domains such as combustion. The overall goal is to provide an overview of these powerful techniques and start a discussion how these techniques can aid in the analysis of astrophysical simulations. Introduction Extracting quantitative measurements from scientific data is becoming an increasingly important aspect of visual data analysis. For this purpose, defining and extracting fea- tures plays a key role in the analysis process. Examples for features of interest (see Figure 1) include burning regions in combustion simulations, bubbles in the mixing layer of a Rayleigh-Taylor instability or filament structures in a porous medium. Once features are detected and extracted, one can derive quantitative measurements such as feature count (number of burning regions or bubbles) or their size distribution and track their evolution over time. In the following, we concentrate on defining features for scalar fields, i.e., a function that assigns a scalar value to each location in the domain. For scalar fields, two classes of feature definition are particularly ubiquitous: threshold- based features and gradient-based features. Threshold-based features, such as burning regions in a combustion simulation, which can be identified by thresholding the fuel consumption rate, are based on absolute value. They are also closely related to iso-