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Coverage Estimation in Heterogeneous Visual Sensor Networks. Mahmut Karakaya and Hairong Qi Advanced Imaging & Collaborative Information Processing Laboratory Electrical Engineering and Computer Science University of Tennessee, Knoxville

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coverage estimation in heterogeneous visual sensor networks

Coverage Estimation in HeterogeneousVisual Sensor Networks

Mahmut Karakaya and Hairong Qi

Advanced Imaging & Collaborative Information Processing Laboratory

Electrical Engineering and Computer Science

University of Tennessee, Knoxville

Int. Conf. on Distributed Computing in Sensor Systems

May 16th, 2012

multi camera systems vs vsn
Multi-Camera Systems vs. VSN

MSP

  • Visual Sensor Platforms
    • Small size and low cost.
    • Imaging, on-board processing, wireless communication.
  • Collaboration in sensor networks is necessary
    • To compensate for the limitations of each node,
    • To improve the accuracy and robustness.

CMUcam

* Photo Courtesy of www. mobese.iem.gov.tr, of Rowe et al. (2007

  • Multi-camera system applications ranging from security monitoring to surveillance.
  • Deployment of many expensive and high-resolution cameras in large areas.
  • Not scalable and subjective to decisions of human operators, unaffordable to deploy many cameras
    • high cost of installation and system maintenance.
challenges in vsns
Challenges in VSNs
  • Huge data volume of camera
    • Limited energy source
    • Low-bandwidth communication
    • Local processing vs. computational cost
    • Directional sensing characteristic
    • Limited Field of View (FOV)
    • FOV < 180o.
  • Visual occlusion
    • Capture a target only when
      • in the field of view
      • no other occluding targets
    • Not possible to cover all targets in a crowded environment by a single camera.

[1] Estrin, 2002

target detection models
Target Detection Models

Progressive Certainty Map:Union of the non-occupied areas in the 2D visual hull.

  • Resolving on non-existence information
  • Focused on: How many sensors declares target non- existence at a single grid point.

Traditional: Intersections of the back-projected 2D visual cones of the targets.

  • Resolving on existence information
  • Focused on: How many sensors detects target existence at a single grid point.
coverage in sensor networks
Coverage in Sensor Networks
  • In Scalar Sensor Networks:
  • Based on the total number of nodes that captures an arbitrary target within their circular sensing range.
  • In Visual Sensor Networks:
  • More challenging because of unique features of cameras
    • Directional sensing characteristic
    • Presence of visual occlusion

* Figure courtesy of Huang and Tseng(2003)

visual coverage estimation
Visual Coverage Estimation
  • Sensor related parameters should be decided before deployment.
    • Number of sensors, sensing range, field of view.
  • Visual coverage in a crowded area depending on
    • Sensor density and deployment
    • Target density and distribution.
  • To reach a desired visual coverage, camera positions may not be predetermined due to
      • Random deployment
      • Impractical to manipulate sensor locations.
visual coverage estimation occupancy map vs certainty map
Visual Coverage Estimation Occupancy Map vs. Certainty Map

Occupancy Map Based Certainty Map Based

: The visual coverage probability that exactly k nodes cover a specific grid point in the sensing fieldto

determine target existence or non-existence.

occupancy map based coverage estimation
Occupancy Map based Coverage Estimation
  • Free sight vs. Partial appearance
    • If free sight available:
    • If partial appearance: is random variable that depends on the location of occluding targets.
    • Then, derivation of becomes too complex.
visual coverage estimation without visual occlusion
Visual Coverage Estimation without Visual Occlusion
  • If the radius of targets is infinitely small, i.e.,, we can ignore the visual occlusion.
  • A sensor node covers a specific grid point of the sensing field, if
    • The node is located in a circular area A with radius ρ centered at the corresponding grid point (x, y)
    • Oriented towards the circle center.
visual coverage estimation without visual occlusion cont
Visual Coverage Estimation without Visual Occlusion (cont.)

The probability of k many sensor node facingtowards the center of detectability area, A, i.e.,

The probability of not facing the node towards the center of A.

The probability that a detectability area A contains exactly j sensor nodes from a Poisson process with sensor density λs, i.e., where .

The number of combinations of k-node subset from a j-node set

visual coverage estimation in heterogeneous vsns
Visual Coverage Estimation in Heterogeneous VSNs

Heterogeneous Visual Sensors Nodes

Heterogeneous Targets

  • In more realistic scenario:
    • Heterogeneous visual sensor deployment,
    • Heterogeneous target existence
heterogeneous visual sensor deployment
Heterogeneous Visual Sensor Deployment

The probability that a detectability area contains exactly i many Type I sensor nodes and m of them can cover the corresponding grid point

The probability that a detectability area contains exactly j-i many Type II sensor nodes and k-m of them can cover the corresponding grid point

Introduction Collaborative Target Fault Tolerance, Detection Visual Coverage Experimental Conclusion

Localization and CorrectionEstimation Results

  • Two types of sensor nodes with different sensor density, sensing radius, and angle of view.
    • Type I :
    • Type II :
  • The probability that exactly k sensor nodes cover a specific grid point of the sensing field
  • Heterogeneous Sensor Deployment without Visual Occlusions
  • Heterogeneous Sensor Deployment with Visual Occlusions
heterogeneous sensor deployment without visual occlusions
Heterogeneous Sensor Deployment without Visual Occlusions

The probability of that k-m many Type II sensor facing towards the center of A2

The probability that A2contains exactly j-i many Type II nodes

The probability of that m many Type I sensor facing towards the center of A1

The number of combinations

The probability that a detectability area A1contains exactly i many Type I sensors nodes from a Poisson process

visual coverage estimation with visual occlusion
Visual Coverage Estimation with Visual Occlusion

In an environment with crowded targets,

  • Target radius r becomes a finite value, i.e.,
  • Visual occlusions cannot be ignored.

To cover a specific grid point of the sensing field,

  • The node is located in the circle,
    • Oriented towards the grid point,
  • All targets be outside of the occlusion zone between the grid point and the sensor node.
heterogeneous sensor deployment with visual occlusions
Heterogeneous Sensor Deployment with Visual Occlusions
  • Q : The probability of covering a specific grid point of the sensing field depends on
    • To be within the FOV of the sensor,
    • No visual occlusion
  • : The visual coverage probability that exactly k nodes cover a specific grid point of the sensing field,
heterogeneous target existence
Heterogeneous Target Existence
  • : The probability that no Type I target in the occlusion zone,
  • : The probability that no Type II target in the occlusion zone
  • : The visual coverage probability
  • that exactly k nodes cover a specific grid point of the sensing field,
  • Two types of targets with different target density and target radius.
    • Type I :
    • Type II :
heterogeneous target existence1
Heterogeneous Target Existence

The probability of that having no Type I target in the occlusion zone, Ao1 i.e.,

The probability of that having no Type II target in the occlusion zone,Ao2 i.e.,

The probability of that i many sensor node facing towards the center of A, i.e.,

The number of combinations

The probability that a detectability area A contains exactly j many sensors nodes from a Poisson process with sensor density λs

experiments for visual coverage estimation
Experiments for Visual Coverage Estimation
  • Simulation setup: 40mx40m area, 10 targets, r=0.5m-2m, 30 sensor nodes, ρ=10m-15m and FOV=45o-60o.
  • Two sets of experiment to compare the simulation results and theoretical values to validate the theoretical derivation of visual coverage probability.
  • Visual Coverage Estimation without/with boundary effect
    • The effects of two groups of parameters
      • Sensor node related parameters
        • Number of Sensors,
        • Sensor Range,
        • Angle of View
      • Target related parameters.
        • Number of Targets,
        • Target radius
  • Minimum Sensor Density Estimation
effect of sensor related parameters
Effect of Sensor Related Parameters
  • Comparison of theoretical values and simulation results corresponding to sensor node related parameters,
  • Different numbers of sensor nodes,
  • Different sensing range,
  • Different angle of views .
effect of target related parameters
Effect of Target Related Parameters
  • Comparison of theoretical values and simulation results corresponding to target related parameters,
  • Different numbers of targets,
  • Different sensing target radius.
conclusion
Conclusion
  • A closed form solution for the visual coverage estimation problem in the presence of visual occlusions among crowded targets in a VSN.
  • Deployment of sensors follows a stationary Poisson point process.
  • Derivation of the visual coverage estimation possible by modeling the target detection algorithm based on the target non-existence information.
  • Heterogeneous sensor nodes or heterogeneous targets are likely to appear in the sensing field.
  • Comparison of the simulation results and the theoretical values,
    • Validate of the proposed close form solution of visual coverage estimation
    • Show effectiveness of our model to be deployed in practical scenarios.
boundary effect
Boundary Effect

Sensor nodes close to the boundary might cover outside of sensing region.

The grid points close to the boundary have a partial detectability area,

Therefore, visual coverage probability, P(k) depends on the location in the sensing field.

Let u and v denote the minimum distances from a grid point in a corner sub-region AC