Advanced Computer Vision

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Advanced Computer Vision
An efficient implementation of Reids Multiple
Hypothesis Tracking Algorithm and Its evaluation
for the purpose of visual tracking I. Cox and S. 
Hingorani Presented by Carlos Busso
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Overview

• Motivation
• Multiple Hypothesis Tracking (MHT)
• Practical Implementation
• Experiments and results
• Conclusion

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Motivation

• Tracking can be divided in two main steps
• Prediction
• Data association (object/measurement matching)
• In the matching step, ambiguities may arise
• One measure match more than one object
• One object match more than one measurement
• Occluded object
• Spurious measurements
• Appearance of new objects
• Objects cease to exist
• Features to track are corners automatically
  extracted using a variant of the Lucas and Kanade
  algorithm

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Motivation

• Easy solution Nearest Neighbor
• Good if consecutive frames do not have big
  differences
• Partial occlusions and background changes
  decreases performance
• Multiple Hypothesis Tracking Algorithm
• Provide a good solution to solve
  objects/measurements ambiguities
• Track Initiation
• Track Termination
• Track Continuation
• Explicit modeling of spurious measurements
• Explicit modeling of uniqueness constrain

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Multiple Hypothesis Tracking
Come back to 1979...

• Presented by Donald B. Reid in the context of
  multi-target tracking
• Each hypothesis represents a different set of
  assignment of measurements to features
  (collection of disjoint tracks)
• A tree structure is used, in which each global
  hypothesis generated child hypotheses
• Each child hypothesis together with its parent
  hypothesis represent one possible interpretation
  of all past measurement
• Considerations
• The hypotheses are represented by ambiguity
  matrixes
• Each measurement may be a feature, a new
  feature, noise, deleted feature or occluded
  features
• Mahalonobis distance is used

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Multiple Hypothesis Tracking

• Outlines of the basic Operation

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Multiple Hypothesis Tracking

• Measurement of the hypotheses
• They use statistical measures to evaluate how
  good are the hypotheses
• Three terms
• First term Conditional probability of the
  measurement Z(k)
• Second term Conditional probability of the
  assignment ?
• Third term Conditional probability of parent
  hypotheses T

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Multiple Hypothesis Tracking

• Assumptions
• Measurements are Gaussian distributed
• Number of false alarms and new features are
  Poisson distributed
• The implementation is straightforward
• However the complexity is exponential, see next
  slide

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Multiple Hypothesis Tracking
t t1 t2
t3 t4
Impractical for real applications
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Practical Implementation
Review the paper contribution

• The paper describes an efficient implementation
  of an MHT algorithm
• Several strategies were jointly employed in order
  contain the growth of the hypothesis
• Track Trees
• Spatially disjoint Hypothesis Trees
• Generating the k-best Hypotheses
• N-scan-back
• Ratio Pruning

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Practical Implementation

• Track Trees
• Idea duplicate path must be removed
• The same track may appear in more than one global
  hypothesis
• Track tree provides considerable saving

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Practical Implementation

• Track Trees

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Practical Implementation

• Spatially disjoint Hypothesis Trees
• Idea tracks in a global hypothesis tree must
  compete for the same measurements
• Track are partitioned into separate clusters
• Track in a cluster compete for common
  measurements
• The combinatorial problem associated with forming
  global hypotheses is significantly reduced
• Cluster may be merged or split

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Practical Implementation

• Spatially Disjoint Hypothesis Three

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Practical Implementation

• Generating the k-best Hypotheses
• Idea select only the k-best hypotheses without
  enumerate all possible global hypotheses.
• Enumeration of all hypotheses is impractical
• They use Murty algorithm to optimally determine
  the k-best assignments
• Formulated as linear assignment problem
• The number of linear assigment is linear in k
  (Polynomial time)
• The algorithm avoid solving duplicate assignments
• In the paper k was set to 300

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Practical Implementation

• Generating the k-best Hypotheses

e.g k4
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Practical Implementation

• N-scan-back
• Idea Any ambiguity at time k is resolved by time
  kN
• The branch with higher probability is conserved
  and the other are pruned
• Below the decision node there is a degenerated
  tree of depth N
• N must be set low enough
• If N0, the algorithm is similar to Nearest
  Neighbor
• Results suggest N3

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Practical Implementation

• N-scan-Back

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Practical Implementation

• Ratio Pruning
• Idea Hypotheses with low probability compared to
  other competing hypotheses can be removed
• The maximum number of hypotheses is limited by
  k-best hypotheses algorithm
• Some of these hypotheses can have low probability
• A threshold is set to prevent hypotheses from
  being considered if the ratio of their
  probability to that of the best hypothesis became
  too small

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Practical Implementation

• Ratio pruning

e.g K-best hypotheses4 Ratio pruning 0.1
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Practical Implementation

• Other considerations
• They use linear Kalman filter for prediction
• Features to track are corners automatically
  extracted using a variant of the Lucas and Kanade
  algorithm
• Track initiation There are no prediction for
  measurements in the first frame, their need to be
  considered a new track or spurious measurement
• Mahalanobis test with a cross correlation test to
  prevent nonsense matches (color is first used
  here)

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Experiments and Results

• You can clearly see.

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Experiments and Results
MHT
Nearest Neighbor
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Experiments and Results
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Conclusion

• Features matching is a not trivial issue. The
  paper described a good solution for complex
  scenarios
• The algorithm is robust to errors in the motion
  model
• Occlusions, noise, start and end of features are
  successfully and naturally handled by the
  algorithm
• The computation complexity is the biggest
  drawback of the algorithm
• The computation complexity depends on the number
  of features (therefore on the scene)
• In one video it took 1.5 second per frame, in the
  other 3.06
• MIPS R4400 150 MHz