Lab Papers (GRASP)

Document Type

Journal Article

Date of this Version

7-1-2009

Comments

Copyright 2009 SIAM.
Reprinted from:
Target Enumeration via Euler Characteristic Integrals Yuliy Baryshnikov and Robert Ghrist, SIAM J. Appl. Math. 70, 825 (2009), DOI:10.1137/070687293

Abstract

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.

Keywords

Euler characteristic, sensor network, enumeration, integration

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Date Posted: 17 September 2009

This document has been peer reviewed.