Quantifying Visualizations for Reduced Modeling in Nonlinear Science: Extracting Structures from Data Sets

Visualization is the process of converting a set of numbers resulting from numerical simulations or experiments into a graphical image. However, the ultimate goal is to understand the underlying science. A crucial part is to identify and quantify "important" regions and structures. Computer vision (image understanding) seeks to do the same. In this paper, we discuss our visiometric approach to visualization, i.e., visualizing, identifying, and quantifying evolving amorphous regions in 3D data sets. Our methods incorporate ideas from computer vision, image processing, and mathematical morphology.