P. David, V. Idasiak, F. Kratz Laboratoire Vision et Robotique, UPRES EA 2078

1. A Sensor Placement Approach for the Monitoring of Indoor Scenes • P. David, V. Idasiak, F. Kratz • Laboratoire Vision et Robotique, UPRES EA 2078 • ENSI de Bourges - Université d'Orléans • 10 boulevard Lahitolle, 18020 Bourges Cedex, France

2. SUMMARY • Background • Problem Definition • Reused Works • Modelling Method • Genetic Algorithm • Case Study • Conclusion & Future Works

3. BACKGROUND • Development of a new human presence sensor • Creating a sensor simulator for the product being designed: • Testing design choices • Proving the performances of the system • Helping the deployment of the system • Finding guidelines for the implantation

4. BACKGROUND

5. PROBLEM DEFINITION • Sensor placement in indoor scene (housing, office) • Graduated importance for the monitored area • Avoiding to monitor parts of the scene • Selection of sensors (type, settings, capabilities) • Limited places for the sensors • Limited number of sensors  The problem is to find the best sensors placement and selection to cover a scene with limited resources and heterogeneous goals.

6. REUSED WORKS 1/2 • Mainly inspired by works on video surveillance: • Similar goals (monitoring the activity of human) • Same kind of observed scenes • Basis brought by Erdem & Sclaroff [16]: • Method to convert a coverage problem as a linear programming problem • Finding solution for an entire monitoring of a room with a minimum number of cameras • Easy to reuse and enhance way of modelling

7. REUSED WORKS 2/2 • Weaknesses of Erdem & Sclaroff ’s solution: • Not considering aspects as price and energy consumption of the camera network • Considering only camera sensor, only one type of camera • Considering only the research of the total monitoring of the scene • Not considering priorities between different zones, or zones to avoid • Not considering balancing the efficiency and the cost of the sensor networks

8. Modelling Method EXPECTED DATA • Input data: • Geometry of the scene • Geometry of the furnishing • Usable sensors and possible location • Monitoring objectives • Output data: • Selection of sensors • Indicators (ex: coverage, cost)

9. Modelling Method TO A RESOLUTION PROCESS 1/2 • First Mathematical Formulation: • Minimize f(x) = cT x • With respect to A x ≥ b • ub  x lb • x is a binary vector • ub and lb are respectively a vector of 0 and a vector of 1 • Easy to optimise with a Branch and Bound algorithm • Build matrix A and vectors b and x to represent the problem

10. Modelling Method TO A RESOLUTION PROCESS 2/2 • The vector x is the solution: the selected sensors • The vector b represents the constraints: the scene description • The matrix A allows to compute the effectiveness of a given sensor network • The function f is to be minimized: the price of the network (hardware price + energy cost) • x is a selection vector giving the indices of the selected sensors • A is the concatenation of all the vectors representing the information provided by each sensor, presented in the same shape as b

11. Modelling Method SCENE DESCRIPTION 1/2 • The basic vector b is constructed as follows: • The scene is sampled in a list of point numbered with growing indices. • The number of points gives the vector size. • All elements are set to 0. • If a point belongs to the zone that we want to monitor the corresponding element of b is set to 1.

12. Modelling Method SCENE DESCRIPTION 2/2 • For a more complex model including importance graduation we suggest to add a second vector giving the level of priority (Є ) for the detection.

13. Modelling Method SENSOR DESCRIPTION 1/3 • To characterize a sensor we need to know its efficient zone geometry and its implantation point. • This description can be completed by the tracked flow and the measure’s reliability. • The first step is to identify the geometry of the efficient zone of the computed sensor. • The second step is to compute this zone by ray tracing • Then the vector representing the sensor is computed • The efficient zone is the zone in which the sensor can provide information on the measured flow

14. Modelling Method SENSOR DESCRIPTION 2/3 0 0 .. . 0 0 1 1 . . 0 1 1

15. Modelling Method SENSOR DESCRIPTION 3/3 • The vectors of each sensor are concatenated in the A matrix so that A x is the vector representing a sensor network selected by x. • A x is therefore the list of points viewed by the network • In order to deal with more complex aspects as reliability, it is possible to compute a second vector indicating for each point the reliability of the measure given by a sensor. • The employed reliability law should be of any form describing a spatial distribution. (ex: Linear, exponential)

16. Modelling Method THE COST FUNCTION • The function is a simple vector multiplication. We created a vector which indicates the cost of the installation and exploitation of each sensor. • By multiplying this vector by the selection vector we obtain the cost of the network. This cost is then to be minimized to find the best solution

17. Modelling Method PROBLEM DESCRIPTION ≥

18. Modelling Method A FIRST SOLUTION Example of solution with a Branch and Bound Algorithm

19. Modelling Method FIRST OBSERVATIONS • + Easy to compute • + Easy to solve with a Branch and Bound algorithm • + Taking into account price constraint, placement constraint. • + Give the guidelines to create a more complex data structure • Many parameters are not optimised (financial and technical efficiency) • Complex constraints as priorities in the monitoring are not tackled • Use of genetic algorithm with a stronger data structure

20. Genetic Algorithm EXPECTED ADVANTAGES • The use of genetic algorithms is justified by the following points: • Optimise heterogeneous properties of the system (ex: cost, efficiency, redundancy) • Taking into account heterogeneous constraints (ex: zone to monitor, to avoid, cost limitation) • Those algorithms allow us to find solutions respecting more complex wishes than finding a system monitoring a complete scene whatever its price. • This gives results more accurate for real exploitation

21. Genetic Algorithm ENHANCE DATA STRUCTURE • Computing new matrices similar to the A and Scene matrices. • Inserting priority of observation in a second Matrix representing the scene. • Adding a second column for each sensor in the sensor Matrix A, indicating the viability of the measure given in the designated point. • Associating complex cost involving energy consumption, maintenance cost and hardware price.

22. Genetic Algorithm BASIC FITNESS FUNCTION val  0 for i=0..NbPoint if Scene ( i ) > 0 if (A  x)( i ) ≥ Scene ( i ) val  val + 100 / sum(Scene ) if (A  x)( i ) < 0 val  val – 100 if sum( x ) > MaxSens val  val – 100 val  val + Cov  ( NbSens – sum( x ) )

23. Case Study THE MONITORED SCENE

24. Case Study POSSIBLE SENSORS LOCALISATION

25. Case Study RESULTS

26. CONCLUSION & FUTURE WORKS • First development of our placement tool. • Use genetic algorithm to provide a more realistic optimisation. • Possibility to model more complex implantation policies. • Taking into account the third dimension of the scene (Full 3D or using 3 parallel planes at significant heights). • Adding zone of perturbation for several types of sensors (US, PIR, …).

27. CONCLUSION & FUTURE WORKS • Implementing a GUI allowing to load plans of the scene and to choose the shape and parameters of the fitness function. • Integrating the final tool in a complete simulation tool. • Integrating, in the results, the enhancement brought by data fusion methods. • Integrating the resolution of the measure to know what kind of treatment could be performed on every point of the scene. • Repeating experiences in various environments to extract general guidelines of placement.

28. TYPES OF SENSORS