Target Enumeration Via Euler Characteristic Integrals

We solve the problem of counting the total number of observable targets (e.g.,
persons, vehicles, landmarks) in a region using local counts performed by a network of sensors,
each of which measures the number of targets nearby but neither their identities nor any positional
information. We formulate and solve several such problems based on the types of sensors and
mobility of the targets. The main contribution of this paper is the adaptation of a topological sheaf
integration theoryóintegration with respect to Euler characteristicóto yield complete solutions to
these problems.

Yuliy Baryshnikov

Professor of Mathematics and Electrical and Computing Engineering, University of Illinois

Date: May 2, 2008 at 12:00 PM

Location: Engineering Building II, Room 1230

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