2. Context in Image Classification
a. Lower Order Markov Chains3. Context in Text Recognition
b. Hilbert Space Filling Curves
c. Markov Meshes
d. Dependence Trees
a. A Quick Bit on Compound Decision Theory
b. Dictionary Look-up Methods
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:
.
This will be used in the
next section as the discriminant function when dictionary
look-up methods are used for text recognition.
Previous : 3.
Context in Text Recognition
Next: 3b.
Dictionary Look-up Methods