University of Houston

Vector fields and its analysis play an important role in many scientific and engineering applications, ranging from automobile design, oceanography, climate study, to medicine. Due to the complex nature of flow fields and the data sizes, it is often difficult to obtain an efficient interpretation of the underlying dynamics of these flow data. Vector field topology that condenses the flow into its skeletal structure is a popular solution to address this challenge. It provides an intrinsic partition of the flow domain based on the different homogeneous flow behaviors at different regions. However, traditional vector field topology computation suffers from the issue of numerical instability, thus, the obtained results are typically not reliable. Recently, Morse decomposition has been introduced to address this numerical instability issue of the previous vector field topology extraction. The limitations of the original Morse decompositions are two-fold. First, the decomposition largely relies on the resolution of the underlying mesh, generating visualization with the serrated look. Second, its computation is expensive. In addition, it does not encode the flow uncertainty information, which may produce mis-leading results. To address these challenges, this project introduces an Image-Space Morse decomposition (ISMD) framework. This technique first converts the original flow defined on a triangle mesh into the pixel-based representation in an image plane using standard graphics hardware. The Morse decomposition is then computed under this image plane. This new framework not only mitigates the serrated boundary issue of the previous method with pixel-level accuracy but also enables a parallel implementation of the Morse decompositions using OpenMPI and CUDA, respectively. In addition, it allows us to visualize uncertainty and error introduced during the computation by computing an ensemble of the ISMDs of the same flow with different perturbations and integration errors. The developed techniques have been implemented in a visual analysis tool that can handle both 2D and 3D steady vector fields.