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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