Light- -weight Contour Tracking in weight Contour Tracking in - - PowerPoint PPT Presentation

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Light- -weight Contour Tracking in weight Contour Tracking in - - PowerPoint PPT Presentation

Light- -weight Contour Tracking in weight Contour Tracking in Light Wireless Sensor Networks Wireless Sensor Networks Xianjin Zhu Rik Sarkar Jie Gao Joseph S. B. Mitchell INFOCOM 08 1 Motivation Motivation Sensor network: sense


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Light Light-

  • weight Contour Tracking in

weight Contour Tracking in Wireless Sensor Networks Wireless Sensor Networks

Xianjin Zhu Rik Sarkar Jie Gao Joseph S. B. Mitchell

INFOCOM’ 08

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Motivation Motivation

  • Sensor network: sense and monitor the physical world

(temperature, traffic density, pollution level, etc).

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Motivation Motivation

  • Time-varying 2-D signal field
  • Example application scenario

– Chemical pollution

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Motivation Motivation

  • Time-varying 2-D signal field
  • Example application scenario

– Chemical pollution

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Motivation Motivation

  • Time-varying 2-D signal field
  • Example application scenario

– Chemical pollution

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SLIDE 6

Motivation Motivation

  • Time-varying 2-D signal field
  • Example application scenario

– Chemical pollution

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Motivation Motivation

  • Time-varying 2-D signal field
  • Example application scenario

– Chemical pollution

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SLIDE 8

Motivation Motivation

  • Time-varying 2-D signal field
  • Example application scenario

– Chemical pollution

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Motivation Motivation

  • Time-varying 2-D signal field
  • Example application scenario

– Chemical pollution

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Motivation Motivation

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  • Topological features are important
  • Queries:

– Is there a safe path from B to A? C to B? – Is a location surrounded by chemical contaminations?

A B C

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Contour tracking problem Contour tracking problem

  • Track contours at a threshold of

interest - below/above thresh (0/1).

  • Capture their topological features as

contours evolve over time

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1 1 1 1

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Related works Related works

  • Target tracking [Guibas 2002, Zhao et al. 2002,

Aslam et al. 2003, Liu et al. 2004, Kim et al. 2005, He et al. 2006, Shrivastava et al. 2006 ]

– Track individual targets – Few works on tracking a continuously deforming blob

  • r groups of targets
  • Boundary detection [Fekete et al. 2005, Wang et
  • al. 2006, Funke et al. 2006, Kroller et al. 2006]

– Can be used in static scenario – Periodically running boundary detection in dynamic scenario is inefficient.

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Our contributions Our contributions

  • Light-weight distributed algorithm to track time-

varying contours

  • Capture topological features
  • Low communication cost

– proportional to the change in the input

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Outline: our approach Outline: our approach

  • Network setting & concepts
  • Challenges
  • Contour tracking algorithm
  • Theoretical results
  • Simulation results

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Network setting & concepts Network setting & concepts

  • Binary sensor model:

– Color

  • BLACK: all neighbors high
  • WHITE: all neighbors low
  • GRAY: neither BLACK nor WHITE

(mixed high and low)

  • We want to track the Black boundaries.
  • Robustness: resilient to outliers and ambiguity.
  • Black regions and white regions are separated by gray.
  • Black regions are bounded by contours of threshold.

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Goal of the algorithm Goal of the algorithm

  • K-gray band:

– a set of gray nodes at most k-hop from BLACK region

  • Contour network: Graph to

capture topological features of contours

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Contour network k-gray band

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Goal of the algorithm Goal of the algorithm

  • Deformation retract:

– A thinner version in subspace, with same homotopy. There is a continuous deformation taking the space to the retract. – Contour network: skeleton of k-gray band

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Contour network k-gray band

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Challenges Challenges

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(ii) (iv)

  • Hard to tell if a contour network is valid from local view
  • Same contour topology may have multiple valid

deformation retract with totally different local view

(i) (iii)

?

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Challenges Challenges

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Network setting Goal

Naturally require distributed efficient algorithm global property Each sensor node only has local information Limited resources Maintain graphs with identical topological information

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Contour tracking algorithm Contour tracking algorithm

  • When change occurs:

– freeze the valid segments in the old contour graph – only repair the contour network where it is broken

  • Automaton runs at each sensor

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RED: a GRAY node on the contour network

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Contour Repair Contour Repair

  • The simplest case: repair of a single contour cycle

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Contour Repair Contour Repair

  • The simplest case: repair of a single contour cycle
  • Open red nodes take responsibility of repair

– Red nodes at edge of broken contour

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a

b Open red node

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Contour Repair Contour Repair

  • Which direction to send repair messages?

– sensor nodes have no sense of orientation

  • The k-hop neighbors of the closed red segments block

the propagation of repair messages.

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a

b

Open region

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Contour Repair Contour Repair

  • Simultaneous repair, merging and splitting

– May encounter multiple RED nodes, which RED node to connect to?

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Contour Repair Contour Repair

  • Simultaneous repair, merging and splitting

– May encounter multiple open RED nodes, which RED node to connect to? – Connect by a (non self-intersecting) spanning tree, e.g, the shortest path tree.

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a b c d

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Contour creation Contour creation

  • Triggered at some BLACK nodes

– have a GRAY neighbor but cannot see RED nodes in its k-hop neighborhood

  • GRAY neighbors start to create a new contour

– Select leaders within k-hop neighborhood – Form short chain with length > k – Start contour repair

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Summary of algorithm Summary of algorithm

  • Valid segments of contour network are still usable
  • Repair only happens where the contour network is broken

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  • Repair connects all red

nodes within a open neighborhood through a spanning tree.

  • Augmented algorithm

deals with small holes inside the k-gray band

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Theoretical results Theoretical results

  • Theorem: The contour network is a deformation retract
  • f the k-gray band, when the system stabilizes.
  • Sketch of proof:

– Existing contour network is a deformation retract of the segment

  • f k-gray band it resides in.

– Repaired new contour network is a deformation retract of open neighborhood. – The boundaries align correctly.

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a

b

a b c d

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Simulations Simulations

  • Setup:

– 4000 nodes distributed in a 500*500 field – Simulate dynamic changes among a sequence of stabilized states of a contour field – Changes happen in a random order between two stabilized states

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Simulations Simulations

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Two black regions move closer. Their gray bands meet each other and (multiple) “bridges” are built up. Black regions themselves merge together.

  • Contour merge/split
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Simulations Simulations

  • Nested contours

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Simulations Simulations

  • Contours pass through a hole

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Simulations Simulations

  • Multi-level contours

– Apply the single-level contour tracking algorithm at each level independently

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Simulation Simulation

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  • Communication cost:

– Proportional to number of changes

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Simulations Simulations

  • Video clips

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Conclusions Conclusions

  • A light-weight distributed algorithm that captures the

topological features of time-varying contours.

  • The communication cost is “output-sensitive”,

proportional to the amount of contour changes.

  • The algorithm provides a foundation for further

processing of spatial sensor data, e.g., contour compression and aggregation [Gandhi et al. 2007].

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Future Works Future Works

  • Explore the applications of contour tracking

– Real-time response and emergency rescue – Direct vehicles to alleviate traffic jam

  • Combine with our concurrent contour tree work

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Thank you ! Thank you !

  • Questions & Comments?

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