Carola Wenk

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  Applications of persistent homology to low-dimensional data
  Carola Wenk

  Persistent homology is commonly applied to study the shape of high dimensional data sets. In this talk we consider two low-dimensional data scenarios in which both geometry and topology are of importance. We study 2D and 3D images of prostate cancer tissue, in which glands form cycles or voids. Treatment decisions for prostate cancer patients are largely based on the pathological analysis of the geometry and topology of these data. As a second scenario we consider the comparison of road networks.

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  Geometric algorithms for shapes and trajectories
  Carola Wenk

  This talk will give an introduction to geometric algorithms for comparing and matching discrete geometric shapes such as point sets, polygonal curves, and graphs. We will study distance measures for shapes, approaches for matching shapes under transformations, and algorithms for reconciling sets of shapes by constructing simpler representative shapes. We will consider theoretical results as well as real-world applications including biomedical imaging and GPS trajectory analysis.