In this talk I will discuss the application of techniques from algebraic geometry and numerical linear algebra to computer vision, in particular structure from motion and multiple view geometry. The problems will be motivated by a system that estimates the motion of a single moving camera based on video input. The system will be shown processing in real-time. The front end of the system is a feature tracker. Robust estimates of the camera motion are produced from the feature tracks using a the geometric hypothesize-and-test architecture RANSAC.

For RANSAC to operate on a particular geometry problem, a hypothesis-generator that solves a minimal instance of the problem is needed. I will outline algebraic geometry techniques with which we have managed to solve several previously unsolved minimal problems, and assess the difficulty of many more. The solved problems include relative orientation from six points with fixed but unknown focal length (to appear at CVPR), relative orientation from six points with a non-central camera and several problems of non-central cameras moving planarly. We have also with these techniques found a new version of the five-point relative orientation algorithm. Moreover, we have solved the problem of optimal triangulation in three views.

This problem is of a slightly different flavor, where the solutions to the polynomial formulation are stationary points of the cost function. We have also managed to apply these techniques to problems outside computer vision, in particular to relative orientation of microphones and speakers.

Before joining UK, he was a researcher in the Vision Technologies Laboratory, Sarnoff Corporation, Princeton, and Visual Technology, Ericsson Research, Stockholm, Sweden. His research interests include computer vision, computer graphics, structure from motion, multiple view geometry, Bayesian formulations, tracking, recognition, image and video compression. He is a member of the IEEE and American Mensa.