If we already have a prior distribution for one texture,
we can
estimate the posterior distribution of the texture descriptor elements
given the observed sequence of the data i.e.
.
For example
could be the mean and and covariance of
a given
region (Gaussian model for texture) or they can be the bins of
histogram
or the indices of a transition matrix in case of a
order
Markovian model of texture. This probability can be expressed using
Bayes rule as:
with being a normalization factor to make sure
that the probabilities
sum to
. The prior distribution determines the term
.
We can eliminate
from the likelihood term
since it doesn't have any effects on the probability of the observed
sequence.