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Activity Detection in Videos. Riu Baring CIS 8590 Perception of Intelligent System Temple University Fall 2007. Outline. Background Related Work The Model Normal Count Event Count. Activity Detection Problems.

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activity detection in videos

Activity Detection in Videos

Riu Baring

CIS 8590 Perception of Intelligent System

Temple University

Fall 2007

outline
Outline
  • Background
  • Related Work
  • The Model
  • Normal Count
  • Event Count
activity detection problems
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.
causes for change
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.

an example building data
An Example: Building Data
  • 3 months of “people count”
  • 30 minutes
  • Calit2 UC Irvine Campus
another example traffic data
Another Example: Traffic Data
  • 6 months of estimated vehicle count
  • Every 5 minutes
  • Glendale on-ramp to 101N, Los Angeles
more examples
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.
related work
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
related work1
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.

background
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.
method i
Method I
  • A Baseline Model
    • Where
  • Threshold
  • Adequate for:
    • Events interspersed in the data are sufficiently few
    • Events are sufficiently noticeable.
method i1

Chicken and Egg

Method I
  • Baseline Model
  • Ideal Model
method i2

Baseline Model

Baseline Model – Lower Threshold

Method I
  • False Positive, Persistence, and Duration
method ii ideal model
Method II – Ideal Model

Observed Count

Event Count (Unobserved )

Normal Count (Unobserved)

normal count

Modeling Periodic Count Data

Normal Count

d(t) = {1, …, 7}

Sunday = 1, …

h(t) = interval

i.e. half-hour

periodic components
Periodic Components

Poisson Process Rate

Day Effect

Time of Day Effect

event count the process n e
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)=1|z(t-1)=0)= 1-z00;
  • P(z(t)=0|z(t-1)=0)= z00;
  • P(z(t)=1|z(t-1)=1)= z11;
  • P(z(t)=0|z(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

priors for event probabilities
Priors for event probabilities
  • Beta distributions: priors for the z’s.

and z11 analogously.

This characterizes the behavior of the underlying latent process. The hyperparameters a,b are designed to model that behavior.

priors for event probabilities1
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 γ(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 γ(t) is itself gamma with parameters aE and bE. Hence (by conjugacy) it is marginally negative binomial (NB) with p=(bE/(1+bE) and n=N(t).

gibbs sampling
Gibbs Sampling
  • Gibbs sampling works by simulating each parameter/latentvariable conditional on all the rest.
  • The λ’s are parameters and the z’s,N’s 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.
gibbs sampling1
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/(1+bE). Put N0(t)=N(t)-NE(t).
  • To simulate z(t), define
more of gibbs sampling
More of Gibbs Sampling
  • Then, if the previous state was 0, we get:
gibbs sampling continued
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.
discussion
Discussion
  • Poisson process (nonhomogeneous).
  • Able to detect activity at the expected frame.
future work
Future Work
  • Histogram of direction implementation
references
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.