HMM-BASED PATTERN DETECTION

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HMM-BASED PATTERN DETECTION

• Image Processing and Reconstruction
• Winter 2002

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Outline

• Markov Process
• Hidden Markov Models
• Elements
• Basic Problems
• Evaluation
• Optimization
• Training
• Implementation
• 2-D HMM
• Application
• Simulation and Results

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Markov Process
S2

• Can be described at any time to
• be in one state among N distinct
• states
• Its probabilistic description
• just requires a fixed specification
• of current and previous states
• actual state at time t
• state transition probability
• Each state corresponds to a physical (observable)
  event
• Too restrictive for sophisticated applications

S3
S1
a31
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Extension to Hidden Markov Models

• A conditionally independent process on a Markov
  chain
• States correspond to clusters of context with
  similar distribution
• Elements of HMM
• State transition probability
• The observation symbol probability in each state
• The initial state distribution

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Fundamental Problems for HMM

• Evaluation
• the probability of the observation OO1O2OT
  given the model ?, P(O ?)
• Optimization
• Choosing optimal state sequence given the
  observation and the model ?.
• Training
• Estimating model parameters to maximize P(O ?)

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Evaluation the Model Forward-Backward Algorithm

• This calculation is on order of
• Forward-Backward Procedure with order of
• Forward variable
• Backward variable

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Optimal States Sequence Solution(s)

• One solution choose the states which are
  individually most likely.
• This optimal solution has to be a valid state
  sequence!!
• Vitterbi Algorithm find the single best state
  sequence that maximizes P(QO,?)

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Training the Model
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Continuous Observation Distributions

• In most of the applications (Speech, Image, ),
  observations can not be characterized as discrete
  symbols from finite alphabet and should be
  considered by probability density function (PDF).
• The most general representation of the PDF is a
  finite mixture of normal distributions with
  different means and variances for each state.
• Estimating mean and variance instead of
  estimating bj(k)

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Implementation Considerations

• Scaling Dynamic range of ? and ? will exceed the
  precision range of any machine
• Multiple observations for training
• Initial Estimation of HMM Parameters
• for convergence, good initial values of PDF are
  really helpful.
• Choice of Model, Number of states, Choice of
  observation PDF

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Two-Dimensional HMM

• Set of Markovian states within each super-state
• Transition probability
• Useful for segmentation

Sub-State
Si-1,j
Si,j
Si,j-1
Super-State
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Application Pattern Detection

• SNR-5
• SNR10

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Simulations

• Feature Vector DCT Coefficients or their
  averages over some of them
• Block Size 1616
• Both images in training set and test set have
  different rotation of jincs, but the distance
  and center of them are fixed.
• Running K-means Clustering Algorithm For initial
  estimation
• Comparing with template matching and Learning
  Vector Quantization

Average of Absolute value of the Coefficients
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Results and Conclusion!

• Detection Error