Date: 28 November 2007, 15.00
Venue: EM2.33
Name: Dr. A. Duci, University of Rostock, Germany
We present and study a family of metrics on the space of compact subsets of $\real^N$ (that we call ``shapes''). These metrics are ``geometric'', that is, they are independent of rotation and translation; and these metrics enjoy many interesting properties, as, for example, the existence of minimal geodesics. We view our space of shapes as a subset of Banach (or Hilbert) manifolds: so we can define a ``tangent manifold'' to shapes, and (in a very weak form) talk of a ``Riemannian Geometry'' of shapes. Some of the metrics that we propose are topologically equivalent to the Hausdorff metric; but at the same time, they are more ``regular'', since we can hope for a local uniqueness of minimal geodesics. We also study properties of the metrics obtained by isometrically identifying a generic metric space with a subset of a Banach space toobtain a rigidity result.their state vectors in data with false alarms and missed detections. These techniques have a wide range range of applications within electrical engineering and can be deployed on many different types of sensors.Target tracking algorithms are an essential building block of systems that perform functions such as surveillance, guidance or obstacle avoidance. Tracking algorithms take their input measurements from sensors which provide the signals such as radar, sonar or video. The measurements are taken at regular intervals and the task is to estimate the state of a target at each point in time, such as its position, velocity or other attribute. Successive estimates provide the tracks which describe the trajectory of a target. Whilst these techniques are attracting international attention within the engineering academia and in industry, they is relatively unknown within the mathematics and statistics community.