Base Paper Discussion: A Hopfield Neural Network for Image Change Detection

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Base Paper DiscussionA Hopfield Neural Network
for Image Change Detection

• Phillip Anderson
• ENEE434, Spring 2007
• Professor Newcomb

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Image Change Detection

• Goal identify the set of pixels that are
  significantly different between the last image
  and a previous reference image
• Examples
• Video frames (surveillance footage)
• Satellite images (environmental, political)
• Industrial automation (quality control)

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Image Change Detection Historical Perspective

• Temporal Difference Models Simple, sometimes
  effective- Sensitive to noise, lighting
• Significance and Hypothesis Tests Models Less
  sensitive to variations in lighting, noise in
  image- Complicated, very computationally
  intense
• Vector and Shading Models Decreased
  noise/lighting sensitivity- Difficult to
  automate (empirical)
• Clustering Models Increased noise rejection,
  accuracy- Complicated requires a longer series
  of images

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Motivation for Neural Network Implementation

• Problems with previous systems
• May require empirical adjustments
• Limited by inherent assumptions
• Some require a larger image sequence
• Noise rejection is generally sub-optimal
• Neural network implementation combines strong
  points of several approaches

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Benefits of Neural Network Implementation

• Based on a probabilistic approach
• Decision about a pixel based on
• data consistency from difference image
• contextual consistency from neighbors
• self-data about the individual pixel
• Output strength of change in each pixel

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Hopfield Network

• Analog Hopfield (more resistant to local minima)
• One node for each pixel in the difference image
• Node state holds changed/unchanged info
• Network seeks to minimize the Energy Function

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Network Parameters

• Layer weights contextual information
• Stability requires symmetric weighting
• Biases self-data information
• Input to node i given by
• Activation function hyperbolic tangent,

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Energy Function

• General form
• Integral term has little contribution to
  stability dropped
• layer (interconnection) weight
• current state of node
• node bias
• What does this equation represent?
• Contributions from
• Data consistency,
• Contextual consistency,
• Self-data,

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Data Consistency

• Probabilistic Model
• Expectation Maximization, or EM method
• Estimate mean variance for two sets (unchanged
  and changed pixels)
• To initialize EM method
• Threshold difference image (diagram, above right)
• Define two groups, based on pixel intensities
• EM method converges on actual group definitions
  (diagram, below right)

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Contextual Consistency

• Relationship between pixel and nearest neighbors
• In terms of node states
• Equation
• Maximum when all 9 states are the same minimum
  when center state opposes edge states

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Numerical Representation of Data/Contextual
Consistency

• How to apply these to the energy function?
• Goal Both consistencies high gt energy low (and
  v.v.)
• Data Consistency
• Contextual Cons.
• Combined Energy Equation (first term in final
  equation)

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Self-data and Final Energy Equation

• Self-data node with high probability of being
  changed should reflect that fact in the state
  value
• Combine the three data sources to obtain
• Compare with general form (previously given)
• Result equations for connection weights and
  input bias!

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Putting it all together Functional Summary

• Hopfield Network seeks to minimize the energy
  function
• Energy function expressed through interconnection
  weights and biases
• Solution means that the network outputs (node
  states) correspond to the differences between the
  images

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Initialization Process

• Calculate thresholds (as shown in previous
  slide)
• Load initial state values
• Compute connection weights and biases with EM
  method
• Iterate
• For each node, compute u(t) using Runge-Kutta
  method
• Update node state accordingly
• Continue looping until states have stabilized

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Paper Results - Outdoors
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Paper Results Indoors
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Comparative Tests

• Hopfield (HNN) compared with six other change
  detection algorithms
• MTD Modified Temporal Difference
• LIU Shading Model
• MAP Statistical Model
• SKI Vector/Shading Model
• CAR Cluster Statistical Model
• BRU Contextual, no Self-Data

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Base Paper Conclusions

• Iterative methods (HNN, BRU) offer improved
  performance
• Initialization can be important, but is not
  decisive
• HNN/BRU still stabilize HNN is quicker
• Time complexity of iterative methods is extremely
  high
• May not always be practical
• Real-time applications require parallelism
• HNN is the most robust against noise

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Simulation

• Major obstacle Probabilistic model
• EM method is extremely involved
• Implementation requires background knowledge of
  probability distributions
• Good news initialization isnt critical!