Pattern Recognition with N-Tuple Systems

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Pattern RecognitionwithN-Tuple Systems

• Simon Lucas
• Computer Science Dept
• Essex University

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Overview

• Standard Binary n-tuple
• Dealing with grey-levels
• Continuous n-tuple
• Bit-plane decomposition
• Dealing with sequences
• Scanning N-Tuple
• Future Directions

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N-Tuple Systems

• Bledsoe Browning (late fifties)
• Sample a pattern at m sets of n-points per set
• Use each sample set to represent a memory address
• Have an n-tuple bank for each pattern class
• Simple training
• Note address occurrences for each class

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What to store

• Various options
• 1-bit address occurred or not
• Freq weighted count number of occurs
• Prob. use count to estimate probability
• 1-bit version saturates
• Usually better to use probabilistic version (ML
  estimate)

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N-Tuple Architecture
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Standard N-Tuple Features

• Superfast training
• As fast as you can read the data in!
• Superfast recognition (ditto)
• Simple
• Applicable to binary images

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Grey-level
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Threshold?
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Niblack?
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Beavis?
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Continuous N-Tuple

• Samples grey-level image directly
• Pre-compiles samples into LUTs
• Fills LUT entries with ABS distance to closest
  sampled point
• Recognition speed not compromised
• BUT slower to train
• Memory problems
• Not probabilistic
• Sensitive to spurious training data!

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Continuous N-Tuple Results
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Bit-Plane Decomposition

• Alternative to continuous n-tuple
• Uses a combination of binary n-tuple classifiers
• One for each bit-plane (so 8 for 256-grey level)
• Good results reported
• Speed sacrifice

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Scanning N-Tuple Classifier(SNT)

• Introduced in 1995 (Lucas, Lucas Amiri)
• Since investigated by other research groups (IBM,
  Kaist, Kent, Athens)
• In a recent study was one of the best classifiers
  on UNIPEN dataset
• Simple modification of n-gram model
• An n-gram with gaps!!!

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Scanning N-Tuple

• Chain code image
• Scan sampler along chain code
• Estimate weights of address occurrences
• Classify by summing weights for each class
• Softmax function -gt posterior probability
• Train
• DEMO!

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Recent Work

• Extensive evaluation (IBM)
• Directional bit-plane decomposition (Kent)
  (smaller tables)
• Mixture models for table compression (IBM, KAIST)
• Clustering (Athens)
• Discriminative Training (Essex)
• Better accuracy (why????)

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Terminology

• m frequency count
• l log likelihood weights
• a class activation vector
• y output vector (posterior prob.)
• t target vector

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Likelihood Score for Class k given Sequence s
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Softmax Function

• Interpret as posterior probability y_k

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Maximum Likelihood Est.
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Discriminative Training

• Maximise probability of correct classification
• Minimise cross-entropy

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Cross Entropy Error Term
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Weight Update Rule
If k true class
Apply weight updates
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Cross-Entropy v. ML
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Design Process
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MNIST Results
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Future Work

• Improve accuracy further
• Mixture Models
• Training data deformation models
• Better understanding of discrim v. ML
• Sparse (e.g. trie) SNT
• Optimal (all) threshold version for colour /
  grey-level images

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Why Mixture?To tell A from B !!!

• A
• 010111000101001
• 010110100010101
• 0101010001011
• 10100101010101
• 010101010001011
• 01010101001010101

• B
• 1111011101111101
• 00010001000001000
• 00001000100010001
• 11110111111011111
• .

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Why Opti-Thresh?
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Global Mean Threshold
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Optimally Thresholded Image
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Conclusions

• N-Tuple classifiers fantastic speed
• High degree of design skill needed to make them
  work well
• Compete with much more complex systems
• Interesting future work to be done!

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Further Reading

• Continuous n-tuple
• Simon M. Lucas , Face recognition with the
  continuous n-tuple classifier, Proceedings of the
  British Machine Vision Conference (1997) , pages
  222 -- 231 pdf
• Scanning n-tuple
• Simon M. Lucas and A. Amiri,, Statistical
  syntactic Methods for high performance OCR, IEE
  Proceedings on Vision, Image and Signal
  Processing (1996) , v. 143, pages 23 -- 30 pdf
  
• Simon M. Lucas , Discriminative Training of the
  Scanning N-Tuple Classifier, International
  Workshop on Artificial Neural Networks (2003) ,
  pages 222 -- 229 pdf (draft)
• Plus many more references in those papers
• Search Google for n-tuple and also for scanning
  n-tuple