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Object Identification: A Bayesian Analysis with Application to Traffic Surveillance

Object Identification: A Bayesian Analysis with Application to Traffic Surveillance. By Timothy Huang and Stuart Russell University of California at Berkeley. Class 1. Class 2. Class k. A and B are the same object?. Object Identification : Object Recognition :

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Object Identification: A Bayesian Analysis with Application to Traffic Surveillance

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  1. Object Identification: A Bayesian Analysis with Application to Traffic Surveillance By Timothy Huang and Stuart Russell University of California at Berkeley

  2. Class 1 Class 2 Class k A and B are the same object? • Object Identification: • Object Recognition: • Is there difference in practice? A ? ? ? ….....

  3. k moving objects: trajectory of object i modeled by r.v. • Agent makes observations: is a prior on object trajectories is observation of some object

  4. Given • Interested in:

  5. Camera D Camera U Application to traffic surveillance Find: average travel time, origin/destination counts

  6. Instead of modeling trajectories: • Matching observations is less general than modeling trajectories

  7. S is the set of all possible matchings is a uniform prior on S

  8. Assumption: Computationally expensive: (n-1)! matchings to consider

  9. For each feature,

  10. Standard deviation and mean of predicted link travel times starting upstream in lane ending downstream in lane In particular:

  11. Appearance probability:

  12. Upstream Lane 1 Lane2 Lane 1 Downstream Lane2 System learns parameters online:

  13. matches lane lane time t Exponential forgetting: controls how fast we forget

  14. Matching • Aim: find pairs (a,b) s.t. • Formula computed in previously computationally intractable • Can find most probable complete matching in time by weighted bipartite matching • In best matching, is not necessarily high for all (a,b)

  15. “Leave one out” heuristic: • Upstream observations: Downstream observations: • Best assignment: with probability p • Forbid match and compute new best assignment with probability • If accept match (a,b) • Repeat for all matched pairs

  16. m upstream and n downstream observations • n dummy upstream and m dummy downstream observations • vehicle is “new”, i.e. entered below upstream camera • vehicle has left before downstream camera

  17. , probability to exit • , where is some coefficient and is prior appearance probability

  18. Results • With on-ramps and off-ramps 14% matched ---- 100% accuracy 80% matched ---- 50% accuracy • Without on-ramps and off-ramps 37% matched ---- 100% accuracy 80% matched ---- 64% accuracy • Link travel time --- accurate within 1% for 2 mile distance --- no bias based on speed

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