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 the specific problem of 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.
Here, we will focus on and discuss several 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.
Dr. Erin Wolf Chambers is a Professor and the Associate Chair at Saint Louis University in the Department of Computer Science, with a secondary appointment in the Department of Mathematics. Her research focus is on computational topology and geometry, with a more general interest in combinatorics and combinatorial algorithms. Complementing this work, she is also active in research projects to support and improve the culture and climate in computer science and mathematics, as well as to try to improve broader STEM educational experiences at all levels. She serves as a trustee for the Society of Computational Geometry and on the SafeTOC organizing committee, as well as being an editor for Journal of Computational Geometry and for the Journal of Applied and Computational Topology. She received her PhD in Computer Science from the University of Illinois at Urbana-Champaign in 2008, and was a Visiting Research Professor at Saarland University in summer 2011.