Advancements in the acquisition and modeling of flow fields result in unsteady volumetric flow fields of unprecedented quality. An important example is found in the analysis of unsteady blood-flow data. Preclinical research strives for a better understanding of correlations between the hemodynamics and the progression of cardiovascular diseases. Modern-day computer models and MRI acquisition provide time-resolved volumetric blood-flow velocity fields. Unfortunately, these fields often remain unexplored, as high-dimensional data is difficult to conceive. We present a spatiotemporal, i.e., four-dimensional, hierarchical clustering, yielding a sparse representation of the velocity data. The clustering results underpin an illustrative visualization approach, facilitating visual analysis. The hierarchy allows an intuitive level-of-detail selection, largely retaining important flow patterns. The clustering employs dissimilarity measures to construct the hierarchy. We have adapted two existing measures for steady vector fields for use in the spacetime domain. Because of the inherent computational complexity of the multidimensional clustering, we introduce a coarse hierarchical clustering approach, which closely approximates the full hierarchy generation, and considerably improves the performance. The resulting clusters are visualized by representative patharrows, in combination with an illustrative anatomical context. We present various seeding approaches and visualization styles, providing sparse overviews of the unsteady behavior of volumetric flow fields.
Pelt, van, R. F. P., Jacobs, S. S. A. M., Haar Romenij, ter, B. M., & Vilanova, A. (2012). Visualization of 4D blood-flow fields by spatiotemporal hierarchical clustering. Computer Graphics Forum, 31(3), 1065-1074. https://doi.org/10.1111/j.1467-8659.2012.03099.x