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Bayesian Analysis for Traffic Surveillance Object Identification

Study on object identification for traffic surveillance using Bayesian analysis. Focus on matching observations and computing probabilities for traffic trajectories. Results show high accuracy in link travel time predictions.

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Bayesian Analysis for Traffic Surveillance Object Identification

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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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