[+] Team 1: Structural Defect Localization from Propagating Wavefield Data
- Mentor Gabriela Martínez, University of Minnesota, Twin Cities
- Mark Eisen, University of Pennsylvania
- Mengjie Pan, Bryn Mawr College
- Zachary Siegel, Pomona College
- Sara Staszak, Macalester College
Faculty Advisor: Alicia Johnson, Department of Mathematics, Statistics and Computer Science, Macalester College
Problem Poser: Jarvis Haupt, Electrical and Computer Engineering, University of Minnesota
Non-destructive testing (NDT) describes a host of techniques designed to interrogate properties of the material without causing material damage. NDT techniques based on guided acoustic waves have become popular due to their sensitivity to a variety of damage types and their ability to identify defects located far from available actuation and sensing points.
In traditional implementations, guided waves are generated and received by transmitter-receiver pairs distributed over and affixed to the test material. The signatures of wave scattering caused by material defects are captured along the transmitter-receiver path, and the positions of defects can be inferred. Recently, a new and powerful class of laser-enabled inspection methodologies have emerged. Scanning Laser Doppler Vibrometers (SLDV’s) provide precise measurements across the entire material domain (rather than a collection of paths). The data produced by SLDV’s enables high-resolution reconstruction of the propagating wavefield, which may be used for subsequent processing, visualization, or inference.
In this project we will develop techniques for inferring the locations of structural defects and anomalies from this type of spatio-temporal propagating wavefield data. We will use emerging techniques from the theory of compressive sensing and sparse representations to identify locations of potential defects or anomalies. We will evaluate our techniques on simulated and real SLDV data.
Required Background: linear algebra, statistics, Matlab experience
Useful Background: Fourier Representations, Norms and Vector Spaces, Signal Processing, Machine Learning, Optimization
[+] Team 2: Recognizing and Segmenting Barcodes in Images
- Mentor Geordie Richards, University of Minnesota, Twin Cities
- Mikaela Cashman, Coe College
- Keenan Hawekotte, Nebraska Wesleyan University
- Elizabeth Newman, Haverford College
- Dung (Bill) Nguyen, Bard College
Faculty Advisor: Thomas Hoft, Department of Mathematics, University of St Thomas
Problem Poser: Fadil Santosa, Institute for Mathematics and its Applications, University of Minnesota
Bar codes are ubiquitous -- they are used to identify products in a store, parts in a warehouse, and books in a library, etc. They contain information that are critical in supply chains, manufacturing, and monitoring. Modern handheld bar code scanners are camera-based. These include specially built scanners, multipurpose devices, and smart phones. To encourage their adoption, scanners need to be easy to use. Much of the burden of information processing of bar codes must rely on mathematical algorithms that are efficient and robust.
In this project, we will develop a technique that first determine if a bar code is present in an image. If a bar code is detected, it must then draw a bounding box around the bar code. These steps represent the critical initial stages of image processing in a scanner, and are usually followed by a decoding algorithm. We will explore existing methods from image processing including machine learning and transform methods, as well as developing new approaches that specifically take advantage of the structures of bar code images.
Required background: differential equations, Fourier series, Matlab experience. Useful background: machine learning, wavelet theory, signal processing, image processing.
[+] Team 3: Defending against Intruders in Polygonal Environments
- Mentor Jane Butterfield, University of Minnesota, Twin Cities
- Lindsay Berry, The University of Texas at Austin
- Zachary Keller, University of Minnesota, Twin Cities
- Alana Shine, Pomona College
- Junyi Wang, Macalester College
Faculty Advisor: Andrew Beveridge, Department of Mathematics, Statistics and Computer Science, Macalester College
Problem Poser: Volkan Isler, Department of Computer Science and Engineering, University of Minnesota
Our research problem will model the control of an autonomous team of robots who are defending against one or more intruders. Current research focusses on a wide variety of these "good guy versus bad guy" games. There are many variants of these games based on the objectives of the agents, the environment (e.g., a polygon, graph), information available to the players (e.g., can they see each other at all times?), motion constraints (e.g., a car chasing an evader cannot turn arbitrarily). Examples include pursuit-evasion (aka cops and robbers) where the good guys must catch the bad guy; the firefighter problem, where the good guys must contain a dispersive fire; and spies and revolutionaries, where the good guys must prevent a meeting of the bad guys.
We will investigate one of these games in a polygonal environment, a typical setting for robotics applications. Inspired by recent results on graphs and large scale networks, we will prove analogous results in this geometric setting.
Required background: discrete mathematics, with advanced study of graph theory or combinatorics.
Useful background: algorithms, computational geometry.
