Coverage Estimation in Heterogeneous

Visual Sensor Networks

Mahmut Karakaya and Hairong Qi

Advanced Imaging & Collaborative Information Processing Laboratory

Electrical Engineering and Computer ScienceUniversity of Tennessee, Knoxville

Int. Conf. on Distributed Computing in Sensor Systems May 16th, 2012

Multi-Camera Systems vs. VSN 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.

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

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

MSP

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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.

Challenges in VSNs

[1] Estrin, 2002

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Target Detection Models

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.

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.

Coverage in Sensor Networks

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* Figure courtesy of Huang and Tseng (2003)

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

Visual Coverage Estimation

• To reach a desired visual coverage, camera positions may not be predetermined due to

– Random deployment – Impractical to

manipulate sensor locations.

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• 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.

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Visual Coverage Estimation Occupancy Map vs. Certainty Map

: The visual coverage probability that exactly k nodes cover a specific grid point in the sensing field todetermine target existence or non-existence.𝑷 (𝒌 )=∫𝑷 (𝒌 ,𝑸 ) 𝒇 (𝑸 )𝒅𝑸

Occupancy Map Based Certainty Map Based

• 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.

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Occupancy Map based Coverage Estimation

𝑷 (𝒌 )=∫𝑷 (𝒌 ,𝑸 ) 𝒇 (𝑸 )𝒅𝑸

Visual Coverage Estimation without Visual Occlusion

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• 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.

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Visual Coverage Estimation without Visual Occlusion (cont.)

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

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

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

Visual Coverage Estimation in Heterogeneous VSNs• In more realistic scenario:

– Heterogeneous visual sensor deployment,– Heterogeneous target existence

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Heterogeneous Visual Sensors Nodes Heterogeneous Targets

12Introduction Collaborative Target Fault Tolerance, Detection Visual Coverage Experimental Conclusion

Localization and Correction Estimation Results

Heterogeneous Visual Sensor Deployment• 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

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

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Heterogeneous Sensor Deployment without Visual Occlusions

The probability that a detectability area A1 contains exactly i many

Type I sensors nodes from a Poisson process

The number of combinations

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

The probability that A2 contains exactly j-i many

Type II nodes

The probability of that k-m many Type

II sensor facing towards the center

of A2

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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.

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• 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,𝑷 (𝒌 )=∫∫𝑷 (𝒌 ,𝑸𝟏𝑸𝟐 ) 𝒇 (𝑸𝟏 ) 𝒇 (𝑸𝟐 )𝒅𝑸𝟏  𝒅𝑸𝟐

Heterogeneous Sensor Deployment with Visual Occlusions

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Heterogeneous Sensor Deployment with Visual Occlusions

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Heterogeneous Target Existence

• Two types of targets with different target density and target radius.

– Type I : – Type II :

• : 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,𝑷 (𝒌 )=∫∫𝑷 (𝒌 ,𝒒𝟏𝒒𝟐 ) 𝒇 (𝒒𝟏 ) 𝒇 (𝒒𝟐 )𝒅𝒒𝟏  𝒅𝒒𝟐

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

sensor density λs

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

The number of combinations

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.,

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 Estimation19

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 .

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Effect of Target Related Parameters

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Comparison of theoretical values and simulation results corresponding to target related parameters, • Different numbers of targets, • Different sensing target radius.

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.

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Thank you

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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

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