Visualizing time-varying features with TAC-based distance fields

To analyze time-varying data sets, tracking features over time is often necessary to better understand the dynamic nature of the underlying physical process. Tracking 3D time-varying features, however, is non-trivial when the boundaries of the features cannot be easily defined. In this paper, we propose a new framework to visualize time-varying features and their motion without explicit feature segmentation and tracking. In our framework, a time-varying feature is described by a time series or Time Activity Curve (TAC). To compute the distance, or similarity, between a voxel's time series and the feature, we use the Dynamic Time Warping (DTW) distance metric. The purpose of DTW is to compare the shape similarity between two time series with an optimal warping of time so that the phase shift of the feature in time can be accounted for. After applying DTW to compare each voxel's time series with the feature, a time-invariant distance field can be computed. The amount of time warping required for each voxel to match the feature provides an estimate of the time when the feature is most likely to occur. Based on the TAC-based distance field, several visualization methods can be derived to highlight the position and motion of the feature. We present several case studies to demonstrate and compare the effectiveness of our framework.