Target Enumeration via Euler Characteristic Integrals

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 m...

Target Enumeration via Euler Characteristic Integrals I: Sensor Fields

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 dense field of sensors, each of which measures the number of targets nearby but not 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 m...

Target Enumeration in Sensor Networks via Integration with Respect to Euler Characteristic

We solve the problem of counting the total number of observable targets (e.g., persons, vehicles, etc.) in a region based on local counts performed by a network of sensors, each of which measures the number of targets nearby but not their identities nor any positional information. We formulate several such problems based on the types of sensors and mobility of the targets. The main contribution...

Euler Enumeration and Beyond

This paper surveys recent results for flag enumeration of polytopes, Bruhat graphs, balanced digraphs, Whitney stratified spaces and quasi-graded posets.

Exponentiation and Euler Characteristic