Image Processing Reference
In-Depth Information
Fig. 3.4. Four images
A
1
,
A
2
,
A
3
,
A
4
, clockwise from the
top left
, are to be compared with
each other by using the triangle inequality and the scaling rule of the norms. The pairwise
quotients
Q
suggest that
A
1
is most likely obtained from
A
2
by a positive multiplicative
constant
i.e., those that are obtained by positive scaling. Furthermore, in case
α
is negative
Q
will not be reliable at all because it will not only be less than 1, but it might
even vanish, i.e., when
α
=
1. We stress therefore that
Q
illustrates the triangle
inequality and the scaling, but that it cannot be used as a means to test all types of
image similarities.
−
3.4 Scalar Products
The norms are useful to measure distances. Next, we present another tool that is
useful for “navigation” in abstract vector spaces. This is the
scalar product
which
will be used to measure the “angles” between vectors in vector spaces. A scalar
product is a particular operation between two vectors that results in a scalar (real or
complex) that “somehow” represents the angle
ϕ
between the two vectors involved
in the product. The symbol of this operation is written as:
u
,
v
(3.23)
