The topological notion of robustness introduces mathematically rigorous approaches to interpret vector field data. Robustness quantifies the structural stability of critical points with respect to perturbations and has been shown to be useful for increasing the visual interpretability of vector fields. However, critical points, which are essential components of vector field topology, are defined with respect to a chosen frame of reference. The classical definition of robustness, therefore, depends also on the chosen frame of reference. We define a new Galilean invariant robustness framework that enables the simultaneous visualization of robust critical points across the dominating reference frames in different regions of the data. We also demonstrate a strong connection between such a robustness-based framework with the one recently proposed by Bujack et al., which is based on the determinant of the Jacobian. Our results include notable observations regarding the definition of stable features within the vector field data.
Interpreting Galilean Invariant Vector Field Analysis via Extended Robustness
B Wang, R Bujack, P Rosen, P Skraba, H Bhatia, H Hagen
Topology-based Methods in Visualization (TopoInVis)
We present a new approach for accessing and visualizing point-based data in CAD applications. Instead of developing a traditional database around spatial data structures, our approach augments a data indexing engine to enable quick access to data. The primary advantage of an indexing engine is flexibility. The approach enables both range queries for accessing data spatially and resolution queries to access data at appropriate spatial resolutions. Our approach is robust to very large datasets, naturally supporting remote visualization and near-real-time input data streams. We demonstrate our approach on 2 large datasets, one 45M points, the other 53M points.
Using data indexing for remote visualization of point cloud data
P Rosen, LA Piegl
Computer-Aided Design and Applications 14 (6), 789-795
3-D printing, also known as additive manufacturing, has gained a lot of attention both within and outside CAD research. Even popular media have touted the technology as one of the game changer technologies of the 21st century. Simply stated, most printing devices add material to an unfinished part, layer by layer, until the entire object is completed. In order to make this happen, the object is sliced into thin layers which are produced and glued together. Since NURBS are the standard form of modeling tools, the process entails converting the NURBS into an STL model (piecewise triangular model) which is then sliced into a set of closed polygonal loops. In order to avoid the many problems with the STL-based slicing, in this paper we investigate a point cloud-based approach to direct slicing of NURBS based models. It uses the original NURBS model and converts the model into a point cloud, based on layer thickness and accuracy requirements, for direct slicing. The only major computational requirement is point evaluation which can be done error free and in an inexpensive manner. The generation of the point cloud is the main topic of this paper.
Generating point clouds for slicing free-form objects for 3-D printing
W Oropallo, LA Piegl, P Rosen, K Rajab
Computer-Aided Design and Applications 14 (2), 242-249
Paul Rosen, in collaboration with Primoz Skraba (Jozef Stefan Institute), Bei Wang (University of Utah), Guoning Chen (University of Houston), Harsh Bhatia (Lawrence Livermore National Laboratory), and Valerio Pascucci (University of Utah), was awarded the best paper award at the IEEE Pacific Visualization Symposium 2016 for their paper titled, “Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion”.
This IEEE sponsored international visualization symposium is held in the Asia-Pacific region, with the objective to foster greater exchange between visualization researchers and practitioners, and to draw more researchers in the Asia-Pacific region to enter this rapidly growing area of research.
More information on the IEEE Pacific Visualization Symposium can be found here.
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Paul Rosen and his PhD student from University of Utah, Hoa Nguyen, received two awards at the 2016 International Conference on Information Visualization Theory and Applications.
Paul Rosen and Hoa Nguyen received the Best Paper Award for their publication “Improved Identification of Data Correlations through Correlation Coordinate Plots”. They also received the Best PhD Project Award for “Data Scalable Approach for Identifying Correlation in Large and Multi-dimensional Data”. According to the conference awards page, “Papers receiving these awards were selected from a set of outstanding papers, based on the quantitative and qualitative classifications as well as comments provided by the program committee reviewers, their final classification as full paper and their oral presentation at the conference”.
More information on the awards, as well as previous award winners, can be found here.
Link to the original article
Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with a guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains non-trivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. We apply our method to synthetic and simulation datasets to demonstrate its effectiveness.
Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion
P Skraba, P Rosen, B Wang, G Chen, H Bhatia, V Pascucci
Transactions on Visualization and Computer Graphics
Paul Rosen along with Bei Wang (University of Utah), Chris Johnson (University of Utah), Jeff Kern (NRAO), and Betsy Mills (NRAO) received a 1-year ALMA Development Project grant from the National Radio Astronomy Observatory for $185k. The grant is titled “Feature Extraction and Visualization of AMLA Data Cubes through Topological Data Analysis”.
The project is a feasibility study for applying forms of data analysis and visualization never before tested by the ALMA community. Through contour tree-based Topological Data Analysis, we seek to improve upon existing data cube analysis and visualization. This will come in the form of improved accuracy and speed in finding features, which are robust to noise, and a better visual description of features once identified. We will build prototype software, which creates visualizations that help in characterizing and analyzing the spectra of complex spectral line sources within a given data cube.
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Paul Rosen along with Bei Wang (University of Utah) received a NSF grant with additional collaborative award for Carlos Scheidegger (University of Arizona) for 4 years totaling $1.03M. The grant is titled “III: Medium: Collaborative Research: Topological Data Analysis for Large Network Visualization.” Rosen’s portion of this grant, to be subcontracted from the University of Utah, is $325K.
This project leverages topological methods to develop a new class of data analysis and visualization techniques to understand the structure of networks. Networks are often used in modeling social, biological and technological systems, and capturing relationships among individuals, businesses, and genomic entities. Understanding such large, complex data sources is highly relevant and important in application areas including brain connectomics, epidemiology, law enforcement, public policy and marketing. The proposed research will be evaluated over multiple data sources, including but not limited to large social, communication and brain network datasets. Furthermore, the new approaches developed in this project will be integrated into growing data analysis curricula, shared through developing workshops, and used as topics to continue attracting underrepresented groups into STEM fields and computer science specifically.
For more information about the award, click here and for more information about the award with amendments, click here.
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Three dimensional printing has gained considerable interest lately due to the proliferation of inexpensive devices as well as open source software that drive those devices. Public interest is often followed by media coverage that tends to sensationalize technology. Based on popular articles, the public may create the impression that 3D printing is the Holy Grail; we are going to print everything as one piece, traditional manufacturing is at the brink of collapse, and exotic applications, such as cloning a human body by 3D bio-printing, are just around the corner. The purpose of this paper is to paint a more realistic picture by identifying ten challenges that clearly illustrate the limitations of this technology, which makes it just as vulnerable as anything else that had been touted before as the next game changer.
Ten challenges in 3D printing
W Oropallo, LA Piegl
Engineering with Computers 32 (1), 135-148
Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.
Robustness-based simplification of 2d steady and unsteady vector fields
P Skraba, B Wang, G Chen, P Rosen
IEEE transactions on visualization and computer graphics 21 (8), 930-944