Applied & Computational Mathematics seminar: Emerging Methods in Pattern and Shape Analysis

Speaker:  Zachary Grey, NIST

Title:  Emerging Methods in Pattern and Shape Analysis

Abstract:   Image segmentation yields massive ensembles of curves—often thousands or tens of thousand per data set—that encode shape information essential for scientific inference. We present a new pattern‑recognition framework that couples these curve ensembles with efficient inference tools. By approximating the eigenspaces of composite integral operators, we obtain discrete, dual representations of curves at quadrature nodes. Projecting these approximations onto matrix manifolds produces separable shape tensors that decompose each curve into a rigid‑invariant generalized linear‑scale component and a complementary nonlinear undulation component. Applying the method to thousands of segmented curves from paired images, we extract data‑driven features from the shape tensors and feed them into an explainable binary classifier based on product Maximum Mean Discrepancy. The approach builds interpretable feature spaces in seconds, requires no labeled data, and reveals subtle differences that evade visual inspection.

Bio: Before joining NIST, Dr. Grey spent several years at Rolls‑Royce Corporation, culminating as the Robust Design Technical Lead responsible for the design and analysis of gas‑turbine flow‑path components. His industry experience, combined with deep expertise in optimization, applied mathematics, and aerospace engineering, underpins his current research program. At NIST, Dr. Grey develops model‑based dimension‑reduction and manifold‑learning methods that enable transparent, interpretable AI/ML solutions for imaging, signal‑processing, geometric, and optimization challenges. His work bridges rigorous mathematical theory with practical data‑driven applications, offering new pathways for explainable machine‑learning technologies.

Time:  Friday, April 17, 1:30pm – 2:30pm
Place:  Exploratory Hall, room 4106