Browsing by Author "Rosen, Paul"

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    Persistent Homology and the Discrete Laplace Operator For Mesh Similarity
    (The Eurographics Association, 2020) Hajij, Mustafa; Zhang, Yunhao; Liu, Haowen; Rosen, Paul; Ritsos, Panagiotis D. and Xu, Kai
    We use persistent homology along with the eigenfunctions of the Laplacian to study similarity amongst geometric and combinatorial objects. 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.
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    TopoLines: Topological Smoothing for Line Charts
    (The Eurographics Association, 2020) Rosen, Paul; Suh, Ashley; Salgado, Christopher; Hajij, Mustafa; Kerren, Andreas and Garth, Christoph and Marai, G. Elisabeta
    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.