Activity Detection in Videos

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Activity Detection in Videos

• Riu Baring
• CIS 8590 Perception of Intelligent System
• Temple University
• Fall 2007

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Outline

• Background
• Related Work
• The Model
• Normal Count
• Event Count

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Activity Detection Problems

• A process like e.g., traffic flow, crowd
  formation, or financial electronic transactions
  is unfolding in time. We can monitor and observe
  the flow frequencies at many fixed time points.
  Typically, there are many causes influencing
  changes in these frequencies.

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Causes for Change

• Possible causes for change include
• a) changes due to noise i.e., those
  best modeled by e.g., a Gaussian error
  distribution.
• b) periodic changes i.e., those
  expected to happen over periodic intervals.
• c) changes not due to either of the
  above these are usually the changes we would
  like to detect.

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An Example Building Data

• 3 months of people count
• 30 minutes
• Calit2 UC Irvine Campus

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Another Example Traffic Data

• 6 months of estimated vehicle count
• Every 5 minutes
• Glendale on-ramp to 101N, Los Angeles

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More Examples

• Detecting Events, which are not pre-planned,
  involving large numbers of people at a particular
  location.
• Detecting Fraudulent transactions. We observe a
  variety of electronic transactions at many time
  intervals. We would like to detect when the
  number of transactions is significantly different
  from what is expected.

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Related Work

• Keogh et al. KDD 02
• Quantize real-valued time-series into finite set
  of symbols
• Then use a Markov model to detect surprising
  patterns in the symbol sequence
• Guralnik and Srivastava KDD 99
• Iterative likelihood-based method for segmenting
  a time-series into homogeneous regions
• Salmenkivi and Mannila (2005)
• Segmenting sets of low-level time-stamped events
  into time-periods of relatively constant
  intensity using a combination of Poisson models
  and Bayesian estimation methods
• Kleinberg KDD 02
• method based on an infinite automaton could be
  used to detect bursty events in text streams

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Related Work

• All approaches share a common goal
• detection of novel and unusual data points or
  segments in time-series.
• None focuses on detection of bursty events
  embedded in time series of counts that reflect
  the normal diurnal and calendar patterns of human
  activity.

GOAL To automatically detect the presence of
unusual events in the observation sequence.
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Background

• Markov-modulated Processes (Scott, 1998)
• Analysis of Web Surfing Behavior (Scott and
  Smyth, 2005)
• Telephone Network Fraud Detection (Scott, 2000)
• Ihler et al (KDD 2006) developed a framework for
  building a probabilistic model of time-varying
  counting process in which a superposition of both
  time-varying but regular (periodic) and aperiodic
  processes were observed.

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Method I

• A Baseline Model
• Where
• Threshold
• Adequate for
• Events interspersed in the data are sufficiently
  few
• Events are sufficiently noticeable.

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Method I

• Baseline Model
• Ideal Model

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Method I

• False Positive, Persistence, and Duration

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Method II Ideal Model
Observed Count
Event Count (Unobserved )
Normal Count (Unobserved)
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Normal Count
Modeling Periodic Count Data
d(t) 1, , 7 Sunday 1,
h(t) interval i.e. half-hour
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Periodic Components
Poisson Process Rate
Day Effect
Time of Day Effect
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Event Count The Process NE

• Events signify times during which there are
  higher frequencies which are not due to periodic
  or noise causes. We can model this by
  introducing a binary latent process z(t) and
  assuming z(t)1 for such events and z(t)0 if
  not.
• P(z(t)1z(t-1)0) 1-z00
• P(z(t)0z(t-1)0) z00
• P(z(t)1z(t-1)1) z11
• P(z(t)0z(t-1)1) 1-z11
• i.e., if there is no event at time t-1, the
  chance of an event at time t is 1-z00

Modeling Rare Persistent Events
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Graphical Model
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Priors for event probabilities

• Beta distributions priors for the zs.
• and z11 analogously.
• This characterizes the behavior of the
  underlying latent process. The hyperparameters
  a,b are designed to model that behavior.

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Priors for event probabilities

• Recall that N0(t) (the non-event process)
  characterizes periodic and noise changes. The
  event process NE(t) characterizes other changes.
• NE(t) is 0 if z(t)0 and Poisson with rate ?(t)
  if z(t)1.
• So, if there is no event, N(t)N0(t). If there
  is an event, the frequency due to periodic or
  noise changes is N(t)N0(t)NE(t)
• The rate ?(t) is itself gamma with parameters aE
  and bE. Hence (by conjugacy) it is marginally
  negative binomial (NB) with p(bE/(1bE) and
  nN(t).

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Gibbs Sampling

• Gibbs sampling works by simulating each
  parameter/latent variable conditional on all the
  rest.
• The ?s are parameters and the zs,Ns are the
  latent variables.
• The resulting simulated values have an empirical
  distribution similar to the true posterior
  distribution. It works as a result of the fact
  that the joint distribution of parameters is
  determined by the set of all such conditional
  distributions.

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Gibbs Sampling

• Given z(t)0 and the remaining parameters, Put
  N0(t)N(t) and NE(t)0.
• If z(t)1, simulate NE(t) as negative binomial
  with parameters, N(t) and bE/(1bE). Put
  N0(t)N(t)-NE(t).
• To simulate z(t), define

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More of Gibbs Sampling

• Then, if the previous state was 0, we get

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Gibbs Sampling (Continued)

• Having simulated z(t), we can simulate the
  parameters as follows
• Where Nday denotes the number of day units in
  the data, Nhh denotes the number of hh
  periods in the data.

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Result Building Data
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Result Freeway Traffic Data
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Result 2600 frames
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Discussion

• Poisson process (nonhomogeneous).
• Able to detect activity at the expected frame.

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Future Work

• Histogram of direction implementation

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References

• A. Ihler, J. Hutchins, and P. Smyth, Adaptive
  event detection with time-varying Poissons
  process, KDD 2006.
• S. L. Scott and P. Smyth, The Markov modulated
  Poisson process and Markov Poisson cascade with
  applications to web traffic data, Bayesian
  Statistics, vol. 7, pp. 671-680, 2003.
• S. L. Scott, Detecting network intrusion using a
  Markov modulated nonhomogeneous Poisson process,
  http//www-rcf.usc.edu/sls/mmnhpp.ps.gz, 2004.
• S. L. Scott, Bayesian methods and extensions for
  the two state Markov modulated Poisson process,
  Ph.D. dissertation, Harvard University, Dept. of
  Statistics, 1998.