Object%20Identification:%20A%20Bayesian%20Analysis%20with%20Application%20to%20Traffic%20Surveillance

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Object Identification A Bayesian Analysis with
Application to Traffic Surveillance

• By Timothy Huang and Stuart Russell
• University of California at Berkeley

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• Object Identification
• Object Recognition
• Is there difference in practice?

A and B are the same object?
A
?
?
?
.....
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• 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
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• Given
• Interested in

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Application to traffic surveillance
Find average travel time, origin/destination
counts
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• Instead of modeling trajectories
• Matching observations is less general than
  modeling trajectories

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S is the set of all possible matchings
is a uniform prior on S
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Assumption
Computationally expensive
(n-1)! matchings to consider
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For each feature,
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In particular
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System learns parameters online
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Exponential forgetting
controls how fast we forget
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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)

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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

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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

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

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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