Define and Construct an Enhanced Graph Representation for Multiscale Vector Field Data Summarization

NSF IIS 1352722

PI: Guoning Chen;

Participants: Marzieh Berenjkoub, Wei Cao, Xifeng Gao, Shuyu Xu, Lei Zhang

Project Description

Vector field data analysis is indispensable for many applications in science and engineering, ranging from climate study, physics, chemistry, automobile design, to medical practice. Most existing analysis techniques for vector field data are not scalable to the real-world data with ever-increasing sizes and complexity. More importantly, the inherent limited visual perception channel largely constrains the ability to understand the complex geometric and physical behaviors of vector fields as a whole or in detail. To address these challenges, this project investigates a graph-based vector field data reduction for the subsequent extraction of a multiscale vector field data summary. In addition to the construction of the enhanced graph representation, a number of novel vector field analysis techniques are developed to enrich the current state-of-the-art of the vector field analysis and visualization.

Key Outcomes

This project has resulted in the following significant results:

1) An Image-Space Morse Decomposition (ISMD) Framework

We proposed the ISMD that effectively resolves the granularity issue of the conventional Morse decomposition computation andvisualization. This ISMD framework also provides the foundation for the investigation of the enhanced directed graph for the representation of the vector field. In particular, the flux and probability information of the flow can be computed via the finer sampling strategy in the image-space, and encoded as the weights on the directed edges. In addition, the computation of ISMD can be parallelized, facilitating the processing of large-scale data. This ISMD framework has been applied to the processing of a number of 2D real-world vector field data stemming from the applications, such as automobile and engine design, aircraft design, mechanical engineering, climate study, and oceanography.

2) 3D Flow Structure Extraction and Visualization

We introduced a number of techniques to help users extract meaningful structure from 3D piecewise linear vector fields. Specifically, we developed a first framework to perform Morse decomposition computation on 3D piecewise linear defined on regular grids. The framework enables the computation of the hierarchical structure of the flow and the search of an ideal integration time for the computation of the Morse decomposition.

3) An Accumulative Attribute based Flow Analysis Framework

We integrate various local attributes along the individual integral curves (streamlines, pathlines, or streak lines) seeded densely in the domain, and assign the accumulated values of the integral curves to their corresponding seeding positions. This gives rise to a scalar field, i.e., the attribute field. We show that this attribute field(s) encodes certain amount of information relevant to the global flow behaviors, which can be used to indicate the existence of a number of important flow features, such as steady vector field topology, singularity paths, flow separation structure, boundary features, and vortices. Furthermore, the gradient of this scalar field can reveal some abrupt change in the flow behavior. This framework has been applied to the data provided by the domain experts, including Dr. David Thompson and Dr. James Liburdy. Both experts think the obtained results are very interesting and are asking for trying more of their data.

4) A Robustness-based Simplification Framework for Vector Fields

Based on the recently introduced robustness measurement, we develop a new simplification framework. This simplification does not require the computation of vector field topology as a pre-processing step, which may be compromised by numerical inaccuracy. Our new framework also takes into account the vector field magnitude in the simplification, an important physical property of the flow that is often ignored by the topology-based method. In addition, the new framework can handle more complicated simplification scenarios that the other methods may fail. We have applied it to a number of synthetic and real-world vector field data to demonstrate its effectiveness. We are now extending this framework for the processing of 2D time-dependent vector fields and 3D volumetric vector fields.etric vector fields.

5) An Analysis and Visualization Framework for Meshless Vector Field Data

The goal of this sub-project is to develop a set of analysis tool to analyze and SPH simulation results as well as enhancing their visualization. We have extended a number of analysis techniques that were once developed for the mesh-based vector field data to the meshless setting (i.e., particles), including FTLE, asymmetric tensor field analysis, and our rotation-based analysis (see above). We have also applied this suit of meshless analysis techniques to a number of SPH free surface fluid simulations. The results highlight a number of interesting underneath fluid behaviors that are not easy to observe using the existing visualization and rendering methods. These analysis results can also be used to guide the placement of more particles to the regions of interest while reducing the particles in other regions, leading to more effective adaptive SPH simulation framework.

6) Structure Control and Optimization for 3D Structured Meshing

Meshing is an indispensable step for many critical scientific computation. The quality of the meshes, especially structured-meshes often determines the speed and accuracy of the computation. The existing literature lacks a thorough understand of the role of the structure of a given 3D structured mesh in determining the quality of the generated meshes for the subsequent computations, as well as a comprehensive suite of techniques to control and optimize this structure. To address that, our team introduced a first technique that enables the simplification of the structure of a given structured mesh and a first technique that empowers the user the ability of prescribing the desired structure for the generated meshes. These initial results open a door for the future investigation of the structure (or topology) of higher-order tensor fields (e.g., 3D frame fields) and its effective control, which will find broader applications in the areas of geometric modeling, geometry processing, mechanical engineering, material engineering, architecture, and medicine.

In addition to the above key outcomes, the grant has also been used to partially support the research on the visual analytic technique for multivariate spatial data.

Software and Datasets

Forthcoming...

Acknowledgment

We would like to thank Dr. James Liburdy from Oregon State University for providing the OSU wind tunnel data and the velocity fields of the flow in the porous medium, Dr. Jackie Chen for the combustion data, and Dr. Mathew Maltude for the ocean data.

This work is supported by the National Science Foundation under Grant IIS-1352722. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).