Boundary Detection

Jue Wangand

Runhe Zhang

May 17, 2004 UCLA EE206A In-class presentation

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Outline

Boundary detection using static nodes Boundary detection using mobile nodes

Applications: Dark / Light (without Gradient) Chemical Spills (without Gradient) Temperature (with Gradient)

May 17, 2004 UCLA EE206A In-class presentation

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Boundary detection using static nodes1. K. Chintalapudi and R. Govindan,

“Localized edge detection in sensor fields,” in Ad-hoc Networks Journal, 2003.

2. J. Cortés, S. Martinez, T. Karatas, and F. Bullo, “Coverage control for mobile sensing networks,” IEEE Transactions on Robotics and Automation, vol. 20, no. 2, 2004.

May 17, 2004 UCLA EE206A In-class presentation

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Model

Nodes arbitrary deployed, know their location (x,y) by a localization system.

Interior of the phenomenon (I) Exterior of the phenomenon (E) Ideal Edge: set of all points (x,y), such that

every non-empty neighborhood of (x,y) intersects with both I and E

May 17, 2004 UCLA EE206A In-class presentation

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Model

Edge Sensor In the interior of the phenomenon Lies within a pre-specified distance r of

the ideal edge (r: tolerance radius)

May 17, 2004 UCLA EE206A In-class presentation

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Robustness and Performance

Robustness Intrinsic error Sensor calibration error Threshold settings

Performances Trade off between energy and accuracy Quality of the result: thickness of edge

May 17, 2004 UCLA EE206A In-class presentation

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Performance

Percentage Missed Detection Errors: fraction of sensors which lie within the radius of tolerance (Strue) but were not marked as edge sensors (Sdet). em=|Strue - Sdet| / |Strue|

False Detection Errors: This represents the fraction of nodes that declared themselves to be edge sensors but should not have (Sdet-Strue) among the rest of (S-Strue) sensors.ef=|Sdet-Strue| / (N-|Strue|)

Mean Thickness ratio: Let t(S,E) be the mean distance of all the sensors in set S to the edge E.et= (t(Sdet,E)-t(Strue)) / t(Strue,E)

May 17, 2004 UCLA EE206A In-class presentation

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Three approaches to localized edge detection Statistical approach Approach from image processing Approach from pattern recognition

Sensor gets it’s own information and probe the information within its probing radius (R)

Intuitively, larger R/r yields better performances

May 17, 2004 UCLA EE206A In-class presentation

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The statistical approach

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The statistical approach - Example

n+ the number of 1 valued predicates

n- the number of 0 valued predicates

Choice of gamma0 depends on R/r and the performance requirements

May 17, 2004 UCLA EE206A In-class presentation

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The statistical approach - Performance

May 17, 2004 UCLA EE206A In-class presentation

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Image Processing Approach

Basic Idea: using high-pass filter to retain high frequencies, i.e., abrupt changes such as edges present in the image and removes all the uniformities.

Treat sensor as pixel.

May 17, 2004 UCLA EE206A In-class presentation

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Pattern Recognition approach (classifier-based) Relies on the information provided by

sensors in the interior I being ‘significantly’ different from that by sensors in the exterior E

‘Similar’ data lie in same subnet and ‘dissimilar’ data lie in different subset.

A successful partition implies the presence of edge.

May 17, 2004 UCLA EE206A In-class presentation

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Pattern Recognition Approach - Example Classifier: Line

L(a,b,c)=ax+by+c=0 such that all sensors with 1 are on one side of the line and those with 0 lie on the other side.

A localized edge detection scheme based on a linear classifier is: if this line passes within a distance of r from the sensor, the partition is accepted as valid and the edge is deemed as an edge sensor

May 17, 2004 UCLA EE206A In-class presentation

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Simulation and Performance – 1

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Simulation and Performance – 2

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Simulation and Performance – 3

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Simulation and Performance - 4

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Conclusion

Three approaches for boundary detection Three measurements for performances Trade offs between energy - performances

May 17, 2004 UCLA EE206A In-class presentation

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Boundary detection using mobile nodes1. D. Marthaler and A. L. Bertozzi, “Tracking environmental level

sets with autonomous vehicles," UCLA Computational and Applied Mathematics Reports, April 2003.

2. D. Marthaler and A. L. Bertozzi, “Collective motion algorithms for determining environmental boundaries," UCLA Computational and Applied Mathematics Reports, April 2003.

3. A. L. Bertozzi, M. Kemp, and D. Marthaler, “Determining environmental boundaries: Asynchronous communication andphysical scales," UCLA Computational and Applied Mathematics Reports, March 2004.

4. A. Savvides, J Fang, and D. Lymberopoulos, “Using mobile sensing nodes for dynamic boundary estimation," Yale University,Electrical Engineering Department Report, 2004.

May 17, 2004 UCLA EE206A In-class presentation

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Introduction

Locating the boundary of a physical phenomenon using multiple vehicles

Platform features Ability of each agent to perform a ‘move to’ function, to

move to a specified new position on command Ability of each agent to obtain position information about

other agents A sensor for determining environmental concentration at

the agent’s location and a method for estimating the local gradient concentration

May 17, 2004 UCLA EE206A In-class presentation

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Algorithm

Anti-collision / inflation mechanism Motion related to sensing Motion related to communication and

cooperation

May 17, 2004 UCLA EE206A In-class presentation

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Estimation of local gradient of the environmental concentration

C(x,y): the concentration function of the environment at robot’s position V=(x,y)

P(x,y)=f(C(x,y)) that achieves a minimum at the boundary of the environmental concentration. E.g. P=-(Co-C)2, Co is boundary concentration.

results in a gradient descent toward a local minimum of the function P.

Motion related to sensing

May 17, 2004 UCLA EE206A In-class presentation

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Motion related to sensing (cont.)

Results in a composite motion of an agent toward the boundary plus motion along level curves of the concentration function of C.

Omega determines the speed at which the agent traverses the boundary once it arrives there.

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Example

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Virtual contour

Take consideration of the location of other nodes that forms virtual contour.

Alpha, beta are some constant

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Algorithm (cont.)

The nodes exchange their location information only at ‘surface time’ intervals.

Effective of Surface time Effective of Initial position Effective of Position noise

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Effective of surfacing time (1)

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Effective of surfacing time (2)

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Effective of surfacing time (3)

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Effective of surfacing time (4)

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Effective of initialization

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Effective of position noise

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Summary and Future Work

Using PDE to solve the boundary detection problem

Multiple boundaries Moving boundaries Without knowledge of gradient

Thank you