Q. Explain the following measures for matching: (June 00)
Minkowski metric
Mahalanobis distance
Product moment correlation
Minkowski metric
Minkowski metric is a general distance measure metric. It
satisfies the following assumption-
For all elements x, y, z, of the set E, the function d is
a metric if and only if a. d(x, x) = 0
b. d(x, y) ³ 0
c. d(x, y) = d(y, x)
d. d(x, y) £ d(x, z) + d(z,
y)
It is given by
For the case p = 2, this metric is the familiar Euclidean
distance. When p = 1, dp is the so-called absolute
or city block distance.
Mahalanobis distance
In some cases, the representation variables should be treated
as random variables. Then one requires a measure of the distance
between the variates, their distributions, or possibly between
a variable and distribution. One such measure is the Mahalanobis
distance, which gives a measure of the separation between
two distributions. Given the random vectors X and Y let C
be their covariance matrix. Then the Mahalanobis distance
is given by
where the prime (') denotes transpose (row vector) and C-1
is the inverse of C . The X and Y vectors may be adjusted
for zero means by first subtracting the vector means ux
and uy
Product moment correlation
It is another popular probability measure. It is given by
where Cov and Var denote covariance and variance respectively.
The correlation r, which ranges between -1 and +1, is a measure
of similarity frequently used in vision applications.
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