With the popularization of Topological Data Analysis, the Reeb graph has found new applications as a summarization technique in the analysis and visualization of large and complex data, whose usefulness extends beyond just the graph itself. Pairing critical points enables forming topological fingerprints, known as persistence diagrams, that provides insights into the structure and noise in data. Although the body of work addressing the efficient calculation of Reeb graphs is large, the literature on pairing is limited. In this paper, we discuss two algorithmic approaches for pairing critical points in Reeb graphs, first a multipass approach, followed by a new single-pass algorithm, called Propagate and Pair.
Propagate and Pair: A Single-Pass Approach to Critical Point Pairing in Reeb Graphs
J. Tu, M. Hajij, P. Rosen
International Symposium on Visual Computing
Enhancement is an important step in post-processing digital images for personal use, in medical imaging, and for object recognition. Most existing manual techniques rely on region selection, similarity, and/or thresholding for editing, never really considering the topological structure of the image. In this paper, we leverage the contour tree to extract a hierarchical representation of the topology of an image. We propose 4 topology-aware transfer functions for editing features of the image using local topological properties, instead of global image properties. Finally, we evaluate our approach with grayscale and color images.
Topologically-Guided Color Image Enhancement
J. Tu, P. Rosen
International Symposium on Visual Computing
Paul Rosen, Ph.D., assistant professor in Computer Science and Engineering received a National Science Foundation Faculty Early Career Development Program (CAREER) Award.
Rosen will use the award to investigate new methods for visualizing uncertainty using Topological Data Analysis. The approach will develop topology-based techniques for extracting features from ensembles and new visual analysis approaches for investigating those features.
Rosen and his research team will use their theoretic results to assist teams of biomedical engineers investigating conditions of myocardial ischemia and energy scientists at the National Renewable Energy Laboratory in building new tools to analyze uncertainties in their domains.
In addition, Rosen plans to work with students to develop intuitive methods of communicating uncertainties in data to laypeople.
The current generation of radio and millimeter telescopes, particularly the Atacama Large Millimeter Array (ALMA), offers enormous advances in observing capabilities. While these advances represent an unprecedented opportunity to facilitate scientific understanding, the increased complexity in the spatial and spectral structure of these ALMA data cubes lead to challenges in their interpretation. In this paper, we perform a feasibility study for applying topological data analysis and visualization techniques never before tested by the ALMA community. Through techniques based on contour trees, we seek to improve upon existing analysis and visualization workflows of ALMA data cubes, in terms of accuracy and speed in feature extraction. We review our application development process in building effective analysis and visualization capabilities for the astrophysicists. We also summarize effective design practices by identifying domain-specific needs of simplicity, integrability, and reproducibility, in order to best target and service the large astrophysics community.
Using Contour Trees in the Analysis and Visualization of Radio Astronomy Data Cubes
P Rosen, A Seth, B Mills, A Ginsburg, J Kamenetzky, J Kern, CR Johnson, B Wang
Topological Methods in Data Analysis and Visualization (TopoInVis)
This evidence-based practice paper employs a data-driven, explainable, and scalable approach to the development and application of an online peer review system in computer science and engineering courses. Crowd-sourced grading through peer review is an effective evaluation methodology that 1) allows the use of meaningful assignments in large or online classes (e.g. assignments other than true/false, multiple choice, or short answer), 2) fosters learning and critical thinking in a student evaluating another’s work, and 3) provides a defendable and non-biased score through the wisdom of the crowd. Although peer review is widely utilized, to the authors’ best knowledge, the form and associated grading process have never been subjected to data-driven analysis and design. We present a novel, iterative approach by first gathering the most appropriate review form questions through intelligent data mining of past student reviews. During this process, key words and ideas are gathered for positive and negative sentiment dictionaries, a flag word dictionary, and a negate word dictionary. Next, we revise our grading algorithm using simulations and perturbation to determine robustness (measured by standard deviation within a section). Using the dictionaries, we leverage sentiment gathered from review comments as a quality assurance mechanism to generate a crowd comment “grade”. This grade supplements the weighted average of other review form sections. The result of this semi-automated, innovative process is a peer assessment package (intelligently-designed review form and robust grading algorithm leveraging crowd sentiment) based on actual student work that can be used by an educator to confidently assign and grade meaningful open-ended assignments in any size class.
Designing Intelligent Review Forms for Peer Assessment: A Data-Driven Approach
Z Beasley, L Piegl, P Rosen
ASEE Annual Conference & Exposition, 2019
We use persistent homology along with the eigenfunctions of the Laplacian to study similarity amongst triangulated 2-manifolds. Our method relies on studying the lower-star filtration induced by the eigenfunctions of the Laplacian. This gives us a shape descriptor that inherits the rich information encoded in the eigenfunctions of the Laplacian. Moreover, the similarity between these descriptors can be easily computed using tools that are readily available in Topological Data Analysis. We provide experiments to illustrate the effectiveness of the proposed method.
Mesh Learning Using Persistent Homology on the Laplacian Eigenfunctions
Y Zhang, H Liu, P Rosen, M Hajij
International Geometry Summit (poster), 2019
Ghulam Jilani Quadri was awarded the Spirit of Innovation Scholarship. This scholarship recognizes graduate students in the Department of Computer Science and Engineering on the basis of merit.
Link to the original article
Assessing the quality of 3D printed models before they are printed remains a challenging problem, particularly when considering point cloud-based models. This paper introduces an approach to quality assessment, which uses techniques from the field of Topological Data Analysis (TDA) to compute a topological abstraction of the eventual printed model. Two main tools of TDA, Mapper and persistent homology, are used to analyze both the printed space and empty space created by the model. This abstraction enables investigating certain qualities of the model, with respect to print quality, and identifies potential anomalies that may appear in the final product.
Inferring Quality in Point Cloud-based 3D Printed Objects using Topological Data Analysis
P Rosen, M Hajij, J Tu, T Arafin, L Piegl
Computer-Aided Design and Applications 2019
This paper introduces and extension to our previous papers to handle anomalies in the point based object slicing method. The anomalies handled are point, line and plane touch cases as well as overlaps. These anomalies can cause major problems in any intersection procedure, yet, they are seldom discussed, let alone handled. It turns out that the point based approach is capable of handling these special cases with minor extensions.
Handling Anomalies in Object Slicing for 3-D Printing
W Oropallo, L Piegl, P Rosen, K Rajab
Computer-Aided Design and Applications, 2019
Dimensionality reduction is an integral part of data visualization. It is a process that obtains a structure preserving low-dimensional representation of the high-dimensional data. Two common criteria can be used to achieve a dimensionality reduction: distance preservation and topology preservation. Inspired by recent work in topological data analysis, we are on the quest for a dimensionality reduction technique that achieves the criterion of homology preservation, a specific version of topology preservation. Specifically, we are interested in using topology-inspired manifold landmarking and manifold tearing to aid such a process and evaluate their effectiveness.
Homology-Preserving Dimensionality Reduction via Manifold Landmarking and Tearing
L Yan, Y Zhao, P Rosen, C Scheidegger, B Wang
Visualization in Data Science (VDS at IEEE VIS 2018)