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Applications of Topology and Geometry to Root Analysis

Wednesday, October 27th, 4:10pm Tel Aviv time (3:10pm CET, 9:10am NY time)

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Erin Wolf Chambers, Saint Louis University

Abstract:

Analysis of 3d shapes is a core problem in many fields, and there are many
tools from topology and geometry that can provide insight and understanding. In
this talk, we focus on developing significance measures for 3d plant
structures, primarily root systems of plants. Our measures are based on the
medial axis transform, which plays a fundamental role in shape matching and
analysis, but is widely known to be unstable to even small boundary
perturbations. Methods for pruning the medial axis are usually guided by some
measure of significance, with considerable work done for both 2- and
3-dimensional shapes. Such significance measures can be used for identifying
salient features, and hence are useful for simplification, comparison, and
alignment. In this talk, we will present theoretical insights and properties of
commonly used significance measures, focusing on those in 2D and 3D that are
both shape-revealing and topology-preserving, as well as being robust to noise
on the boundary. We'll then discuss several methods that de-noise a shape and
identify topologically and geometrically prominent features, using both the
medial axis and other measures commonly used in topological data analysis. Our
methods are quite successful compared to the state of the art, and are
available in the package TopoRoot, an automatic pipeline for plant
architectural analysis from 3D Imaging.
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