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Optimal Placement and Selection of Camera Network Nodes for

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					   Optimal Placement and
Selection of Camera Network
Nodes for Target Localization
   A. O. Ercan, D. B. Yang, A. El Gamal and
                 L. J. Guibas

             Stanford University
    Low vs. High Data Rate Sensors

   Recent work has focused on low data rate
    sensors, e.g. [Mainwaring’02]

   Video cameras, which have very high data rate,
    are needed in many applications
       Security
       Surveillance
       Healthcare
       Traffic monitoring



                                                     2
    Today’s Multi-Camera Installations
   Security/surveillance
   Use expensive cameras
   Analog and wired
   Video is shipped to
    monitors
   Observed by human
    operators
   Not scalable
   Extremely hard to interpret,
    and search data
       Slim chance of catching
        anything!

                                     3
           Imaging Sensor Networks
                                 Agilent ADCM
   Many low cost nodes
                                 2650
    combining:
       Sensing
       Processing
                                          8 mm
       Communication
   Networked
   Scalable, easy to deploy
   Automated monitoring
   Main challenge: limited BW
    and energy:
       Cannot send everything
       Cannot perform vision
        algorithms at nodes
                                                 4
                        Solution

   Task-driven approach:
       Network performs a task or answers a query
       Simple local processing to reduce data
       Nodes collaborate to perform the task


   Node selection:
       Measurements are highly correlated
       Select best subset of nodes for the task
       Reduces BW and energy usage greatly
       Makes the network scalable to many nodes

                                                     5
                    Selection Problem
   Formulation:
       Given N sensor nodes (already placed)
       Use metric:
       Find best subset of size k , i.e.,

   Previous work
       Sensor networks:
            Information theoretic quantities [Chu’01], [Doucet’02],
             [Ertin’03], [Wang’04]
            Coverage [Slijepcevic’01]
            Geometric quantities [Yang’04], [Isler’04]
            General utility functions [Byers’00], [Bian’06]
       Computer vision and graphics:
            Viewpoint selection [Roberts’98], [Wong’99], [Vazquez’01]   6
             Task: Target Localization
   Useful for:
       Tracking
       Surveillance
       Human-computer interaction
       Robotics
            Navigation
            Controlling an end-effector to perform
             delicate task
   We focus on camera selection to
    minimize 2-D localization error
       2-D location is most relevant in many
        tasks

                                                      7
                     Outline

   Setup
   Local processing
   Camera Model
   Selection Metric
   Placement
   Selection
   Simulation Results



                               8
                       Setup

   Cameras pointing
    horizontally, placed
    around a room
   Positions and orientations
    of cameras are known to
    some accuracy                Prior for
                                 object to
   Prior statistics about the   localize
    position of the object
    available
   No occlusions
                                             9
          Local Processing [Yang’04]
   Simple background subtraction to detect objects
   Resulting bitmap is summed vertically and thresholded
      Horizontal position is most relevant for 2D localization

      Reduces noise

   Resulting bits is called “scan-line”
   Center of the scan-line is sent to cluster head


                                                         Scan-line


                                                      A few
                                                      bytes!
                                                               10
     Camera Measurement Model

                      Object
                        x


                                                   Camera position error

      Focal length

                                                       Read noise, camera angle
Perspective model:                                     error

Assume d >> prior , replace by (known) mean:

Projective model:                                            Linear model




              v1 and v2 independent, have zero means                        11
               Selection Metric
          zi              Could use linear
                           estimation to locate object
                cami      So, choose MSE of best
x2
                           linear estimate of location
                           as metric for selection
     x1                   Actual localization need
                           not be performed using LE
                              Use MSE of LE for selection
                              Query the selected set of
                               cameras for measurements
                              Can utilize any localization
                               method suitable to non-
                               linear camera model


                                                        12
         MSE of Linear Estimate

   Assume diagonal object prior covariance



   The MSE for the best LE reduces to:




                                              13
               Placement

                    Assume:
     q2                  Centered prior
          q1             Circular Room
qN                       Cameras pointing to center

                    Minimize MSE over




                     Only terms to consider            14
                  Symmetric Case
   vi = v, a = 1
   Minimize:



 Solution: N unit vectors
  arranged to sum to zero


 Many optimal solutions,
  e.g., clusters of
                                   and
  cameras doing locally
  optimal thing                          15
                      General Case

   Minimize:


   Solution: N vectors of length       summing to

    offset from 0:

   Similar to “inverse kinematics”
    problem of robotics
       Solved using steepest descent
        [Welman’93]                                  16
                    Selection

   Non-centered prior is OK
                                           q1
   Any room shape is OK         q2
   Cameras already placed
    and fixed
   Positions and orientations        Prior for object
    are known to some                 to localize
    accuracy
                                      qN




                                                         17
                   Selection






   MSE(S) is given by:




   Combinatorial optimization problem --
                                            18
                 SDP Heuristic

   Drop the numerator
   Give weights              to cameras




   Solve dual problem using SDP [Poljak’95,Boyd’04]
   Plug dual optimal variables into the Lagrangian
   Find the set of weights that maximize it
   Set top k weights = 1 and rest to 0             19
           MC Simulation Results




   30 total cameras

                                   20
                      Conclusions
   Presented analytical approach for camera
    placement and selection for target localization
    in a camera network
   Placement: globally optimal solution is found
   Selection: SDP outperforms other heuristics
    and achieves close results to brute-force
    enumeration
   Selection approach suitable for implementation
    in a large sensor network
       Simple local processing at each node
       Small amount of data shipped around
       Selection performed at each cluster head
                                                      21
Thank You




            22

				
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posted:12/2/2011
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