We study the topological construction called Mapper in the context of simply connected domains, in particular on images. The Mapper construction can be considered as a generalization for contour, split, and joint trees on simply connected domains. A contour tree on an image domain assumes the height function to be a piecewise linear Morse function. This is a rather restrictive class of functions and does not allow us to explore the topology for most real world images. The Mapper construction avoids this limitation by assuming only continuity on the height function allowing this construction to robustly deal with a significant larger set of images. We provide a customized construction for Mapper on images, give a fast algorithm to compute it, and show how to simplify the Mapper structure in this case. Finally, we provide a simple procedure that guarantees the equivalence of Mapper to contour, join, and split trees on a simply connected domain.
The Shape of an Image: A Study of Mapper on Images
Alejandro Robles, Mustafa Hajij, and Paul Rosen
International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP) 2018
Scalar fields are used to describe a variety of data from photographs, to laser scans, to x-ray, CT or MRI scans of machine parts and are invaluable for a variety of tasks, such as fatigue detection in parts. Analyzing scalar fields can be quite challenging due to their size, complexity, and the need to understand both local and global details in context. Join trees are a data structure used to capture the geometric properties of scalar fields, including local minima, local maxima, and saddle points. Unfortunately, computing these trees is expensive, and their incremental construction makes parallel computation nontrivial. We introduce an approach that combines three strategies, pruning, spatial-domain parallelization, and value-domain parallelization, to parallelize join tree construction using OpenCL. The resulting implementation shows a significant speedup, making computation of trees on large data practical on even modest commodity hardware.
A hybrid solution to parallel calculation of augmented join trees of scalar fields in any dimension
P Rosen, J Tu, LA Piegl
Computer-Aided Design and Applications 15 (4), 610-618
The advancement of technology and its application to the field of education has caused many to re-examine the merits and pitfalls of cyberlearning environments. Though there is a wealth of research both for and against its mainstream use, there is a consensus that much work remains to be done in key areas such as collaboration, course content, personal learning environments, and engagement. CAD and cyberlearning share a common goal: to communicate information effectively. Unfortunately, many aspects well understood in CAD have been overlooked in online education. In this paper, ten key challenges and their implications for CAD cyber education are discussed. The purpose of this paper is not to provide a dismal outlook for cyberlearning, but to incite discussion, research, and development into these areas with the anticipation of a viable and attractive alternative to traditional classroom education.
Ten challenges in CAD cyber education
ZJ Beasley, LA Piegl, P Rosen
Computer-Aided Design and Applications 15 (3), 432-442
At the IEEE Vast Challenge 2017, held on October 1, 2017 in Phoenix, Arizona, the USF Department of Computer Science and Engineering student team of Sulav Malla, Anwesh Tuladhar, and Ghulam Jilani Quadri received an Honorable Mention. Their submission to the IEEE VAST Challenge was among 56 other entries.
According to the VAST Challenge website, “The Visual Analytics Science and Technology (VAST) Challenge is an annual contest with the goal of advancing the field of visual analytics through competition. The VAST Challenge is designed to help researchers understand how their software would be used in a novel analytic task and determine if their data transformations, visualizations, and interactions would be beneficial for particular analytic tasks. VAST Challenge problems provide researchers with realistic tasks and data sets for evaluating their software, as well as an opportunity to advance the field by solving more complex problems.”
Link to the original article
In visualization education, both science and humanities , the literature is often divided into two parts: the design aspect and the analysis of the visualization. However, we find limited discussion on how to motivate and engage visualization students in the classroom. In the field of Writing Studies, researchers develop tools and frameworks for student peer review of writing. Based on the literature review from the field of Writing Studies, this paper proposes a new framework to implement visualization peer review in the classroom to engage today’s students. This framework can be customized for incremental and double-blind review to inspire students and reinforce critical thinking about visualization.
Leveraging Peer Review in Visualization Education: A Proposal for a New Model
A. Friedman, P. Rosen
IEEE 2017 Pedagogy of Data Visualization Workshop
Correlation is a powerful measure of relationships assisting in estimating trends and making forecasts. Its use is widespread, being a critical data analysis component of fields including science, engineering, and business. Unfortunately, visualization methods used to identify and estimate correlation are designed to be general, supporting many visualization tasks. Due in large part to their generality, they do not provide the most efficient interface, in terms of speed and accuracy for correlation identifying. To address this shortcoming, we first propose a new correlation task-specific visual design called Correlation Coordinate Plots (CCPs). CCPs transform data into a powerful coordinate system for estimating the direction and strength of correlation. To extend the functionality of this approach to multiple attribute datasets, we propose two approaches. The first design is the Snowflake Visualization, a focus+context layout for exploring all pairwise correlations. The second design enhances the CCP by using principal component analysis to project multiple attributes. We validate CCP by applying it to real-world data sets and test its performance in correlation-specific tasks through an extensive user study that showed improvement in both accuracy and speed of correlation identification.
Correlation Coordinate Plots: Efficient Layouts for Correlation Tasks
H Nguyen, P Rosen
International Joint Conference on Computer Vision, Imaging and Computer Graphics
This paper revisits a more than half a century old problem: slice a free-form object into layers for manufacturing. A point based approach is taken that would have been prohibitive even a decade ago. Due to modern hardware, plenty of storage and a plethora of software packages, the time has come to ditch complicated and error prone numerical code and deploy a simple point based method to achieve robustness and accuracy that have been lacking for a very long time.
Point cloud slicing for 3-D printing
W Oropallo, LA Piegl, P Rosen, K Rajab
Computer-Aided Design and Applications 15 (1), 90-97
Student Ashley Suh was awarded a $3,000 stipend for her research project, “Using Persistent Homology to Drive Interactive Graph Drawing,” from the Collaborative Research Experience for Undergraduates (CREU). In addition to this, she will receive up to $1,500 for student travel and/or research supplies. The proposal for funding was submitted by Dr. Paul Rosen, who will be Suh’s faculty mentor throughout her research.
Suh and Rosen’s project involves working to develop a new method for drawing and interacting with graphs, such as for a social network. The challenge with many graphs is that their highly interconnected nature causes them to look like a hairball when drawn. Their project uses a technique called “persistent homology” to identify important structures in the data. Those structures are then interactively selected and used to “pull apart” the hairball, enabling clearer analysis of the graph.
The CREU program is sponsored by the Computing Research Association Committee on the Status of Women in Computing Research (CRA-W). Its intention is, according to their website, “to increase the number of women and underrepresented groups enrolled undergraduate studies in the fields of computer science and computer engineering by exposing them to the joy and potential of research.” The criteria for choosing which projects are funded include the stipulation that the project must “enable student empowerment, leadership development, confidence building, and skill building.”
Link to the original article
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