Target enumeration via euler characteristic integrals

Yuliy Baryshnikov, Robert Ghrist

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)825-844
Number of pages20
JournalSIAM Journal on Applied Mathematics
Issue number3
StatePublished - 2009
Externally publishedYes


  • Enumeration
  • Euler characteristic
  • Integration
  • Sensor network

ASJC Scopus subject areas

  • Applied Mathematics


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