1. 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

2. 2 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

3. 3 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! Today’s Multi-Camera Installations Today’s Multi-Camera Installations

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

5. 5Solution 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

6. 6 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]

7. 7 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

8. 8Outline Setup Local processing Camera Model Selection Metric Placement Selection Simulation Results

9. 9Setup Cameras pointing horizontally, placed around a room Positions and orientations of cameras are known to some accuracy Prior statistics about the position of the object available No occlusions Prior for object to localize

10. 10 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!

11. 11 Camera Measurement Model v 1 and v 2 independent, have zero means Assume d >> prior , replace by (known) mean: Projective model: Linear model Object x Camera position error Read noise, camera angle error Focal length Perspective model:

12. 12 Selection Metric Could use linear estimation to locate object So, choose MSE of best linear estimate of location as metric for selection 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 cam i x1x1 zizi x2x2

13. 13 Assume diagonal object prior covariance The MSE for the best LE reduces to: MSE of Linear Estimate

14. 14Placement Only terms to consider Assume: Centered prior Circular Room Cameras pointing to center Minimize MSE over NN 22 11

15. 15 Symmetric Case  vi =  v,  = 1 Minimize:  Many optimal solutions, e.g., clusters of cameras doing locally optimal thing  Solution: N unit vectors arranged to sum to zero and

16. 16 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]

17. 17Selection Non-centered prior is OK Any room shape is OK Cameras already placed and fixed Positions and orientations are known to some accuracy Prior for object to localize 11 22 NN

18. 18Selection MSE(S) is given by: Combinatorial optimization problem --

19. 19 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

20. 20 MC Simulation Results 30 total cameras

21. 21Conclusions 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

22. 22 Thank You