Jan Segert joined the mathematics faculty of the University of Missouri in 1990. He was a Bantrell Fellow in mathematical physics at the California Institute of Technology (Caltech) from 1987 to 1990, where he first started working with Wolfram Mathematica. He holds a bachelor's degree from UCLA and a PhD from Princeton University. He has also worked on scientific computing projects at the Stanford Linear Accelerator Center (SLAC) and the Princeton Plasma Physics Lab (PPPL). His primary interest is application of geometrical and topological methods to theoretical and mathematical physics. He has recently become interested in applying these techniques to the analysis of large datasets, including images and videos.
Project: Classifier for Spatial Orientations of a 3D Object
This project is about designing an exploration/demo to teach students how to collect, process and visualize real-time data using Mathematica and mBot robots. This is illustrated through a scenario of a robot placed in an unknown environment, used to discover and plot a map in real-time using an ultrasonic/color sensor's readings.
Goal of the project:
To train a neural network to identify spatial rotations from images of a 3D object.
Summary of work:
The initial step was to train a simple classifier to detect planar (2D) rotations of a planar object (triangle). The main part of work was training a classifier to detect nonplanar rotations of an imaged 3D object (Iron Man helmet). Most of the work focused on the special case of nonplanar rotations about the vertical axis in the image plane.
Results and future work:
Identifying planar rotations of a triangle is as easy as pie. Nonplanar rotations about a fixed axis can be identified reasonably well, with a little thought about fine-tuning networks. Identifying arbitrary nonplanar rotations will require future work, but in principle should work as well as the case of fixed rotation axis.