Pattern Recognitionwith

N-Tuple SystemsSimon Lucas

Computer Science Dept

Essex University

Overview

• Standard Binary n-tuple

• Dealing with grey-levels– Continuous n-tuple– Bit-plane decomposition

• Dealing with sequences– Scanning N-Tuple

• Future Directions

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

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)

N-Tuple Architecture

Standard N-Tuple Features

• Superfast training– As fast as you can read the data in!

• Superfast recognition (ditto)

• Simple

• Applicable to binary images

Grey-level

Threshold?

Niblack?

Beavis?

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!

Continuous N-Tuple Results

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

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!!!

http://algoval.essex.ac.uk:8080/chaincodes/chicken.jsp

Scanning N-Tuple

0 2 3 2

•Chain code image

•Scan sampler along chain code

•Estimate weights of address occurrences

•Classify by summing weights for each class

•Softmax function -> posterior probability

•Train

•DEMO!

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????)

Terminology

• m – frequency count

• l – log likelihood weights

• a – class activation vector

• y – output vector (posterior prob.)

• t – target vector

Likelihood Score for Class k given Sequence s

Softmax Function

• Interpret as posterior probability y_k

Maximum Likelihood Est.

Discriminative Training

• Maximise probability of correct classification

• Minimise cross-entropy

Cross Entropy Error Term

Weight Update RuleIf k = true class

Apply weight updates

Cross-Entropy v. ML

Design Process

MNIST Results

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

Why Mixture?To tell A from B !!!A

010111000101001

010110100010101

0101010001011

10100101010101

010101010001011

01010101001010101

B

1111011101111101

00010001000001000

00001000100010001

11110111111011111

….

Why Opti-Thresh?

Global Mean Threshold

Optimally Thresholded Image

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!

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