arXiv subjects

Paul Rosen

Publications and source records attributed to Paul Rosen.

54 records · Page 3Linked to original sources

arXiv2020

An Efficient Data Retrieval Parallel Reeb Graph Algorithm

The Reeb graph of a scalar function defined on a domain gives a topologically meaningful summary of that domain. Reeb graphs have been shown in the past decade to be of great importance in geometric processing, image processing, computer graphics, and computational topology. The demand for analyzing large data sets has increased in the last decade. Hence the parallelization of topological computations needs to be more fully considered. We propose a parallel augmented Reeb graph algorithm on triangulated meshes with and without a boundary. That is, in addition to our parallel algorithm for computing a Reeb graph, we describe a method for extracting the original manifold data from the Reeb graph structure. We demonstrate the running time of our algorithm on standard datasets. As an application, we show how our algorithm can be utilized in mesh segmentation algorithms.

cs.CG↗

arXiv2020

Modeling the Influence of Visual Density on Cluster Perception in Scatterplots Using Topology

Scatterplots are used for a variety of visual analytics tasks, including cluster identification, and the visual encodings used on a scatterplot play a deciding role on the level of visual separation of clusters. For visualization designers, optimizing the visual encodings is crucial to maximizing the clarity of data. This requires accurately modeling human perception of cluster separation, which remains challenging. We present a multi-stage user study focusing on four factors---distribution size of clusters, number of points, size of points, and opacity of points---that influence cluster identification in scatterplots. From these parameters, we have constructed two models, a distance-based model, and a density-based model, using the merge tree data structure from Topological Data Analysis. Our analysis demonstrates that these factors play an important role in the number of clusters perceived, and it verifies that the distance-based and density-based models can reasonably estimate the number of clusters a user observes. Finally, we demonstrate how these models can be used to optimize visual encodings on real-world data.

cs.HC↗

arXiv2020

LineSmooth: An Analytical Framework for Evaluating the Effectiveness of Smoothing Techniques on Line Charts

We present a comprehensive framework for evaluating line chart smoothing methods under a variety of visual analytics tasks. Line charts are commonly used to visualize a series of data samples. When the number of samples is large, or the data are noisy, smoothing can be applied to make the signal more apparent. However, there are a wide variety of smoothing techniques available, and the effectiveness of each depends upon both nature of the data and the visual analytics task at hand. To date, the visualization community lacks a summary work for analyzing and classifying the various smoothing methods available. In this paper, we establish a framework, based on 8 measures of the line smoothing effectiveness tied to 8 low-level visual analytics tasks. We then analyze 12 methods coming from 4 commonly used classes of line chart smoothing---rank filters, convolutional filters, frequency domain filters, and subsampling. The results show that while no method is ideal for all situations, certain methods, such as Gaussian filters and Topology-based subsampling, perform well in general. Other methods, such as low-pass cutoff filters and Douglas-Peucker subsampling, perform well for specific visual analytics tasks. Almost as importantly, our framework demonstrates that several methods, including the commonly used uniform subsampling, produce low-quality results, and should, therefore, be avoided, if possible.

cs.HC↗

arXiv2020

Fast and Scalable Complex Network Descriptor Using PageRank and Persistent Homology

The PageRank of a graph is a scalar function defined on the node set of the graph which encodes nodes centrality information of the graph. In this article, we use the PageRank function along with persistent homology to obtain a scalable graph descriptor and utilize it to compare the similarities between graphs. For a given graph $G(V,E)$, our descriptor can be computed in $O(|E|α(|V|))$, where $α$ is the inverse Ackermann function which makes it scalable and computable on massive graphs. We show the effectiveness of our method by utilizing it on multiple shape mesh datasets.

cs.CG↗

arXiv2020

Leveraging Peer Feedback to Improve Visualization Education

Peer review is a widely utilized pedagogical feedback mechanism for engaging students, which has been shown to improve educational outcomes. However, we find limited discussion and empirical measurement of peer review in visualization coursework. In addition to engagement, peer review provides direct and diverse feedback and reinforces recently-learned course concepts through critical evaluation of others' work. In this paper, we discuss the construction and application of peer review in a computer science visualization course, including: projects that reuse code and visualizations in a feedback-guided, continual improvement process and a peer review rubric to reinforce key course concepts. To measure the effectiveness of the approach, we evaluate student projects, peer review text, and a post-course questionnaire from 3 semesters of mixed undergraduate and graduate courses. The results indicate that course concepts are reinforced with peer review---82% reported learning more because of peer review, and 75% of students recommended continuing it. Finally, we provide a road-map for adapting peer review to other visualization courses to produce more highly engaged students.

cs.HC↗

arXiv2020

Parallel Mapper

The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint trees. In this paper, we study the parallel analysis of the construction of Mapper. We give a provably correct parallel algorithm to execute Mapper on multiple processors and discuss the performance results that compare our approach to a reference sequential Mapper implementation. We report the performance experiments that demonstrate the efficiency of our method.

cs.CV↗

arXiv2020

TopoLines: Topological Smoothing for Line Charts

Line charts are commonly used to visualize a series of data values. When the data are noisy, smoothing is applied to make the signal more apparent. Conventional methods used to smooth line charts, e.g., using subsampling or filters, such as median, Gaussian, or low-pass, each optimize for different properties of the data. The properties generally do not include retaining peaks (i.e., local minima and maxima) in the data, which is an important feature for certain visual analytics tasks. We present TopoLines, a method for smoothing line charts using techniques from Topological Data Analysis. The design goal of TopoLines is to maintain prominent peaks in the data while minimizing any residual error. We evaluate TopoLines for 2 visual analytics tasks by comparing to 5 popular line smoothing methods with data from 4 application domains.

cs.HC↗

arXiv2019

Persistent Homology Guided Force-Directed Graph Layouts

Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node arrangements that use local relationships in an attempt to reveal the global shape of the graph. However, clutter and overlap of unrelated structures can lead to confusing graph visualizations. This paper leverages the persistent homology features of an undirected graph as derived information for interactive manipulation of force-directed layouts. We first discuss how to efficiently extract 0-dimensional persistent homology features from both weighted and unweighted undirected graphs. We then introduce the interactive persistence barcode used to manipulate the force-directed graph layout. In particular, the user adds and removes contracting and repulsing forces generated by the persistent homology features, eventually selecting the set of persistent homology features that most improve the layout. Finally, we demonstrate the utility of our approach across a variety of synthetic and real datasets.

cs.GR↗

arXiv2019

Propagate and Pair: A Single-Pass Approach to Critical Point Pairing in Reeb Graphs

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.

cs.CG↗

arXiv2019

Topologically-Guided Color Image Enhancement

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.

cs.GR↗

arXiv2019

You Can't Publish Replication Studies (and How to Anyways)

Reproducibility has been increasingly encouraged by communities of science in order to validate experimental conclusions, and replication studies represent a significant opportunity to vision scientists wishing contribute new perceptual models, methods, or insights to the visualization community. Unfortunately, the notion of replication of previous studies does not lend itself to how we communicate research findings. Simple put, studies that re-conduct and confirm earlier results do not hold any novelty, a key element to the modern research publication system. Nevertheless, savvy researchers have discovered ways to produce replication studies by embedding them into other sufficiently novel studies. In this position paper, we define three methods -- re-evaluation, expansion, and specialization -- for embedding a replication study into a novel published work. Within this context, we provide a non-exhaustive case study on replications of Cleveland and McGill's seminal work on graphical perception. As it turns out, numerous replication studies have been carried out based on that work, which have both confirmed prior findings and shined new light on our understanding of human perception. Finally, we discuss how publishing a true replication study should be avoided, while providing suggestions for how vision scientists and others can still use replication studies as a vehicle to producing visualization research publications.

cs.HC↗

arXiv2019

Using Contour Trees in the Analysis and Visualization of Radio Astronomy Data Cubes

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.

astro-ph.IM↗

arXiv2019

Mesh Learning Using Persistent Homology on the Laplacian Eigenfunctions

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.

stat.ML↗

arXiv2018

Inferring Quality in Point Cloud-based 3D Printed Objects using Topological Data Analysis

Assessing the quality of 3D printed models before they are printed remains a challeng- ing 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 Analy- sis (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.

cs.GR↗

arXiv2018

Homology-Preserving Dimensionality Reduction via Manifold Landmarking and Tearing

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 generalized 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.

cs.CG↗

arXiv2017

The Shape of an Image: A Study of Mapper on Images

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.

cs.CV↗

arXiv2017

Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we propose a novel method using persistent homology to quantify structural changes in time-varying graphs. Specifically, we transform each instance of the time-varying graph into metric spaces, extract topological features using persistent homology, and compare those features over time. We provide a visualization that assists in time-varying graph exploration and helps to identify patterns of behavior within the data. To validate our approach, we conduct several case studies on real world data sets and show how our method can find cyclic patterns, deviations from those patterns, and one-time events in time-varying graphs. We also examine whether persistence-based similarity measure as a graph metric satisfies a set of well-established, desirable properties for graph metrics.

cs.GR↗

arXiv2012

Data management and analysis with WRF and SFIRE

We introduce several useful utilities in development for the creation and analysis of real wildland fire simulations using WRF and SFIRE. These utilities exist as standalone programs and scripts as well as extensions to other well known software. Python web scrapers automate the process of downloading and preprocessing atmospheric and surface data from common sources. Other scripts simplify the domain setup by creating parameter files automatically. Integration with Google Earth allows users to explore the simulation in a 3D environment along with real surface imagery. Postprocessing scripts provide the user with a number of output data formats compatible with many commonly used visualization suites allowing for the creation of high quality 3D renderings. As a whole, these improvements build toward a unified web application that brings a sophisticated wildland fire modeling environment to scientists and users alike.

physics.ao-ph↗