Next: Selection of the
right
Up: Texture Distance
Previous: Parametric
approaches:
Non parametric models for the texture are expressed in terms of
histograms.
Some of the well known dissimilarity measures for histograms are the
following.
- Minkowski-form distance is defined based on the
norm:
 |
(9) |
where
and
are the two distributions
and
.
computes
the city block or Manhattan
distance,
is the Euclidean distance and finally
measures
the maximal difference.
where
is the mean histogram.
The main disadvantage of
distance is that it yields
inaccurate
results with low number of observations. Moreover no bin in the
histograms
can have zero counts.
- The Kullback-Leibler divergence (KL) is regarded as a measure of
the
extent to which two probability density functions agree and is
expressed
as:
 |
(12) |
it can be shown that
.
For two discrete
distribution the
integration becomes a summation over the bins of
and
.
where
is a
matrix
and
is the similarity
coefficient between indices (bins)
and
.
is given
by
and
and
denotes the similarity between bins
and
.
- The Earth Mover's Distance (EMD): This distance considers each
value
of one distribution as a quantity to be moved (earth) to the other
distribution (holes). The EMD is thus defined as the minimum cost
of transferring one distribution to another one. The computation of
EMD comes from a well-known transportation problem [3,4].
The advantage of EMD is that it works on distributions with a different
number of bins.
Next: Selection of the
right
Up: Texture Distance
Previous: Parametric
approaches:
Ali Shahrokni
2004-06-21