The Use of Context in Pattern Recognition

 
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1. Introduction

2. Context in Image Classification

a. Lower Order Markov Chains
b. Hilbert Space Filling Curves
c. Markov Meshes
d. Dependence Trees
3. Context in Text Recognition
a. A Quick Bit on Compound Decision Theory
b. Dictionary Look-up Methods


4. Conclusions

References

 

3.  Context in Text Recognition

a. Compound Decision Theory Toussaint

Compound decision theory is a tool that can be used in order to determine discriminant functions based on features which are extracted.  This can be done for text or words which need to be identified or classified.  What this means is that based on bunch of features which are extracted which word has the most likelihood of occurring based on our discriminant function.

So consider a line of text with N characters.  Consider that each character yields a feature vector .  If  is the conditional probability that the feature vectors  is the sequence of identities  taking on the values of a certain class  is the feature vector and  is the value of the pattern class.

If we know  to be the a priori probability of all N characters.  We want to classify the text by choosing the sequence of characters that has the maximum a posterior probability given by .  Bayes'' rule tells us that 

.

P(X) is independent of the sequence , and therefore we only need to maximize the discriminant function .
 

To simplify  we can assume independence among the feature vectors .  This means that the shape of the letter that we are scrutinizing is only dependent on the shape itself and not on the shape of the letters around it.  Using this assumption and taking logarithms the discriminant function reduces to:

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This will be used in the next section as the discriminant function when dictionary look-up methods are used for text recognition.
 

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