Feature tracking and viewing for time-varying data sets
Han‐Wei Shen, Guangfeng Ji · 2006
Feature tracking plays an important role in understanding time-varying data sets since it allows scientists to focus on regions of interest and track their evolution and interaction over time. In this work, we first present an efficient algorithm to track time-varying isosurface and interval volume features using isosurfacing in higher dimensions. Instead of extracting these isosurface or interval volume features separately from multiple time steps and computing the spatial correspondence between them, our algorithm extracts the correspondence directly from the higher dimensional geometry and allows more efficient feature tracking. We further show that the correspondence relationship for time-varying isosurfaces can only change at critical isovalues in R3 or R4. Based on the observation, we present a method to pre-compute the correspondence relationship at a preprocessing stage. At run time, isosurface tracking can be efficiently performed by simple table lookup operations with minimal overhead. For complex data sets, the previous feature tracking methods cannot guarantee the globally best matching because these methods use local matching criteria and track features independently in the local neighborhood. To amend the problem, we propose a novel global tracking technique to track features, which defines the globally best match as the one with a minimal overall matching cost. Noticing the deficiencies of previous tracking criteria, we use the Earth Mover's Distance as a better metric to measure the matching cost. We also propose an efficient branch-and-bound algorithm to search the global minimal cost. In addition to tracking features, another important problem is how to view the time-varying features effectively. Due to the time-varying nature, animation remains the most general and common way to show how time-varying features evolve over time. A key issue of generating a good animation is to select ideal views through which the user can perceive the maximum information of the time-varying features. In this work, an algorithm is also presented to select dynamic views. We first propose an improved view selection method for static data, which measures the quality of a static view by analyzing the opacity, color and curvature distributions of the feature rendering images from the given view. A dynamic programming approach is used to select dynamic views. The process maximizes the information perceived from the time-varying features based on the constraint that the view should show smooth changes of direction and near-constant speed. Our feature tracking and viewing algorithms provide the user with a more effective and efficient way to study the time-varying features, and allow the user to gain more insight into the time-varying data sets.