Thematic Einstein Semester on
Geometric and Topological Structure of Materials
Summer Semester 2021
Speaker
Erin Wolf Chambers (Saint Louis U)
Title
Applications of topology and geometry to root analysis
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.
Contact
tes-summer2021@math.tu-berlin.de