Interdisciplinary Distinguished Lecturer: Yuliy Baryshnikov

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Target Enumeration Via Euler Characteristic Integrals

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

Yuliy Baryshnikov spoke on Friday, May 2nd, 2008 at 12:00AM in Engineering Building II, Room 1230

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 theory—integration with respect to Euler characteristic—to yield complete solutions to
these problems.