Boundary Detection Jue Wang and Runhe Zhang

May 17, 2004 UCLA EE206A In-class presentation 2 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 3 Boundary detection using static nodes 1. K. Chintalapudi and R. Govindan, “Localized edge detection in sensor fields,” in Ad-hoc Networks Journal, 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 4 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 5 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 6 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 7 Performance Percentage Missed Detection Errors: fraction of sensors which lie within the radius of tolerance (S true ) but were not marked as edge sensors (S det ). e m =|S true - S det | / |S true | False Detection Errors: This represents the fraction of nodes that declared themselves to be edge sensors but should not have (S det -S true ) among the rest of (S-S true ) sensors. e f =|S det -S true | / (N-|S true |) Mean Thickness ratio: Let t(S,E) be the mean distance of all the sensors in set S to the edge E. e t = (t(S det,E)-t(S true )) / t(S true,E)

May 17, 2004 UCLA EE206A In-class presentation 8 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 9 The statistical approach

May 17, 2004 UCLA EE206A In-class presentation 10 The statistical approach - Example n + the number of 1 valued predicates n - the number of 0 valued predicates Choice of gamma 0 depends on R/r and the performance requirements

May 17, 2004 UCLA EE206A In-class presentation 11 The statistical approach - Performance

May 17, 2004 UCLA EE206A In-class presentation 12 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 13 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 14 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 15 Simulation and Performance – 1

May 17, 2004 UCLA EE206A In-class presentation 16 Simulation and Performance – 2

May 17, 2004 UCLA EE206A In-class presentation 17 Simulation and Performance – 3

May 17, 2004 UCLA EE206A In-class presentation 18 Simulation and Performance - 4

May 17, 2004 UCLA EE206A In-class presentation 19 Conclusion Three approaches for boundary detection Three measurements for performances Trade offs between energy - performances

May 17, 2004 UCLA EE206A In-class presentation 20 Boundary detection using mobile nodes 1. D. Marthaler and A. L. Bertozzi, “Tracking environmental level sets with autonomous vehicles," UCLA Computational and Applied Mathematics Reports, April D. Marthaler and A. L. Bertozzi, “Collective motion algorithms for determining environmental boundaries," UCLA Computational and Applied Mathematics Reports, April A. L. Bertozzi, M. Kemp, and D. Marthaler, “Determining environmental boundaries: Asynchronous communication andphysical scales," UCLA Computational and Applied Mathematics Reports, March 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 21 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 22 Algorithm Anti-collision / inflation mechanism Motion related to sensing Motion related to communication and cooperation

May 17, 2004 UCLA EE206A In-class presentation 23 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=-(C o -C) 2, C o 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 24 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.

May 17, 2004 UCLA EE206A In-class presentation 25 Example

May 17, 2004 UCLA EE206A In-class presentation 26 Virtual contour Take consideration of the location of other nodes that forms virtual contour. Alpha, beta are some constant

May 17, 2004 UCLA EE206A In-class presentation 27 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

May 17, 2004 UCLA EE206A In-class presentation 28 Effective of surfacing time (1)

May 17, 2004 UCLA EE206A In-class presentation 29 Effective of surfacing time (2)

May 17, 2004 UCLA EE206A In-class presentation 30 Effective of surfacing time (3)

May 17, 2004 UCLA EE206A In-class presentation 31 Effective of surfacing time (4)

May 17, 2004 UCLA EE206A In-class presentation 32 Effective of initialization

May 17, 2004 UCLA EE206A In-class presentation 33 Effective of position noise

May 17, 2004 UCLA EE206A In-class presentation 34 Summary and Future Work Using PDE to solve the boundary detection problem Multiple boundaries Moving boundaries Without knowledge of gradient

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