skip to main content


Search for: All records

Creators/Authors contains: "Wenk, Carola"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Comparing two road maps is a basic operation that arises in a variety of situations. A map comparison method that is commonly used, mainly in the context of comparing reconstructed maps to ground truth maps, is based ongraph sampling. The essential idea is to first compute a set of point samples on each map, and then to match pairs of samples—one from each map—in a one-to-one fashion. For deciding whether two samples can be matched, different criteria, e.g., based on distance or orientation, can be used. The total number of matched pairs gives a measure of how similar the maps are.

    Since the work of Biagioni and Eriksson [11, 12], graph sampling methods have become widely used. However, there are different ways to implement each of the steps, which can lead to significant differences in the results. This means that conclusions drawn from different studies that seemingly use the same comparison method, cannot necessarily be compared.

    In this work we present a unified approach to graph sampling for map comparison. We present the method in full generality, discussing the main decisions involved in its implementation. In particular, we point out the importance of the sampling method (GEO vs. TOPO) and that of the matching definition, discussing the main options used, and proposing alternatives for both key steps. We experimentally evaluate the different sampling and matching options considered on map datasets and reconstructed maps. Furthermore, we provide a code base and an interactive visualization tool to set a standard for future evaluations in the field of map construction and map comparison.

     
    more » « less
    Free, publicly-accessible full text available May 3, 2025
  2. Free, publicly-accessible full text available March 1, 2025
  3. This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral component of visualization and analysis pipelines. Although not all topological features present in data are of equal importance. To date, the default definition of feature importance is often assumed and fixed. This work shows how proven explainable deep learning approaches can be adapted for use in topological classification. In doing so, it provides the first technique that illuminates what topological structures are important in each dataset in regards to their class label. In particular, the approach uses a learned metric classifier with a density estimator of the points of a persistence diagram as input. This metric learns how to reweigh this density such that classification accuracy is high. By extracting this weight, an importance field on persistent point density can be created. This provides an intuitive representation of persistence point importance that can be used to drive new visualizations. This work provides two examples: Visualization on each diagram directly and, in the case of sublevel set filtrations on images, directly on the images themselves. This work highlights 
    more » « less
    Free, publicly-accessible full text available October 22, 2024
  4. This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral component of visualization and analysis pipelines. Although not all topological features present in data are of equal importance. To date, the default definition of feature importance is often assumed and fixed. This work shows how proven explainable deep learning approaches can be adapted for use in topological classification. In doing so, it provides the first technique that illuminates what topological structures are important in each dataset in regards to their class label. In particular, the approach uses a learned metric classifier with a density estimator of the points of a persistence diagram as input. This metric learns how to reweigh this density such that classification accuracy is high. By extracting this weight, an importance field on persistent point density can be created. This provides an intuitive representation of persistence point importance that can be used to drive new visualizations. This work provides two examples: Visualization on each diagram directly and, in the case of sublevel set filtrations on images, directly on the images themselves. This work highlights real-world examples of this approach visualizing the important topological features in graph, 3D shape, and medical image data. 
    more » « less
    Free, publicly-accessible full text available October 22, 2024
  5. Moring, Pat ; Suri, Subhash (Ed.)
    Free, publicly-accessible full text available July 28, 2024
  6. The Fréchet distance is often used to measure distances between paths, with applications in areas ranging from map matching to GPS trajectory analysis to hand- writing recognition. More recently, the Fréchet distance has been generalized to a distance between two copies of the same graph embedded or immersed in a metric space; this more general setting opens up a wide range of more complex applications in graph analysis. In this paper, we initiate a study of some of the fundamental topological properties of spaces of paths and of graphs mapped to R^n under the Fréchet distance, in an eort to lay the theoretical groundwork for understanding how these distances can be used in practice. In particular, we prove whether or not these spaces, and the metric balls therein, are path-connected. 
    more » « less
    Free, publicly-accessible full text available July 31, 2024
  7. Free, publicly-accessible full text available July 31, 2024
  8. Morin, Pat ; Suri, Subhash (Ed.)
    Let γ be a generic closed curve in the plane. Samuel Blank, in his 1967 Ph.D. thesis, determined if γ is self-overlapping by geometrically constructing a combinatorial word from γ. More recently, Zipei Nie, in an unpublished manuscript, computed the minimum homotopy area of γ by constructing a combinatorial word algebraically. We provide a unified framework for working with both words and determine the settings under which Blank’s word and Nie’s word are equivalent. Using this equivalence, we give a new geometric proof for the correctness of Nie’s algorithm. Unlike previous work, our proof is constructive which allows us to naturally compute the actual homotopy that realizes the minimum area. Furthermore, we contribute to the theory of self-overlapping curves by providing the first polynomial-time algorithm to compute a self-overlapping decomposition of any closed curve γ with minimum area. 
    more » « less
  9. Morin, Pat ; Suri, Subhash (Ed.)
    Free, publicly-accessible full text available July 28, 2024
  10. Blank, in his Ph.D. thesis on determining whether a planar closed curve $\gamma$ is self-overlapping, constructed a combinatorial word geometrically over the faces of $\gamma$ by drawing cuts from each face to a point at infinity and tracing their intersection points with $\gamma$. Independently, Nie, in an unpublished manuscript, gave an algorithm to determine the minimum area swept out by any homotopy from a closed curve $\gamma$ to a point. Nie constructed a combinatorial word algebraically over the faces of $\gamma$ inspired by ideas from geometric group theory, followed by dynamic programming over the subwords. In this paper, we examine the definitions of the two words and prove the equivalence between Blank's word and Nie's word under the right assumptions. 
    more » « less