Image Processing Reference
In-Depth Information
Chapter 9
Spatial Information in Fusion Methods
Spatial information is fundamental in image processing. Including it in fusion
methods is crucial and often requires specific developments to adapt the methods used
in other fields. One of the most common objectives of these developments it to ensure
that the decision is spatially consistent. For example, in multi-source classification,
the goal will be to avoid those points which are isolated or scattered in a homogenous
class to be assigned to a different class.
9.1. Modeling
Spatial information on the modeling level is generally implicit depending on what
level of representation is chosen. If we are reasoning on a pixel level, the information
contained in a pixel does not include any spatial information, so this information will
have to be added explicitly. The spatial context that is considered is most often the
local neighborhood of each point. A simple way of taking it into account is to define
the measure
M
i
(
x
) (see Chapter 1) based on the characteristics of
x
and of its neigh-
bors also. If we denote by
(
x
) the neighborhood of
x
(containing
x
), we will define
M
i
(
x
) as a function of the type:
M
i
(
x
)=
F
i
f
j
(
y
)
,y
V
(
x
)
,
∈V
[9.1]
where
f
j
(
y
) refers to the characteristics of
y
in the source
j
. This type of approach can
be seen as a spatial filtering problem. In the case of linear filtering,
F
is expressed as a
convolution and the convolution kernel defined on
is typically a Gaussian function
or a rectangular window. If the filtering is not linear, many solutions are suggested
V
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