Environmental Engineering Reference
In-Depth Information
FIGURE 3.3
The processing chain proposed.
geodesic dilation of
X
with respect to
Y
until stability:
In fact, no spatial post-processing based on spectral classifica-
tion is able to capture all the details of a complex scene. This is due
to the very different scales of the objects. It is instead mandatory
to include spatial features within the actual classification pro-
cess. Thus, one proposed way forward is to insert the results of
the class-adaptive filtering step into a spatial analysis performed
using a segmentation algorithm, which could be scaled according
to the requirements of the scene and the sensor resolution. To
this aim, the seeds of the segmentation are extracted from the
refined class maps. Following this idea, in Fig. 3.3 it is shown that
the class-adaptive filtering step is followed by a seed extraction
and then fed into a segmentation algorithm. Seed extraction can
be performed using morphological operators as well, using a
minima imposition procedure. Similarly, the gradient informa-
tion required by the segmentation algorithm is provided by a
gradient computation based again on morphological operators.
In particular, minima imposition is performed in two steps.
First the pointwise minimum between the input image and the
marker image is computed. Then a reconstruction by erosion
is applied:
=
δ
(
i
Y
(
X
),
R
Y
(
X
)
(3.5)
where
i
is such that
δ
(
i
Y
(
X
)
=
δ
(
i
+
1
Y
(
X
).
●
Reconstruction by erosion. The reconstruction by erosion is
similarly defined as:
=
ε
(
i
Y
(
X
),
R
Y
(
X
)
(3.6)
where
i
is such that
ε
(
i
Y
(
X
)
=
ε
(
i
+
1
Y
(
X
).
●
Fillhole. The holes of a binary image correspond to the set
of its regional minima that are not connected to the image
border. Thus, filling the holes of a grayscale image means to
remove all minima not connected to the border:
R
X
(
X
m
),
=
FILL
(
X
)
(3.7)
where
X
m
(
x
)isequalto
X
(
x
)if
x
belongs to the border, and to
t
max
otherwise.
It is clear that away to implement a class-dependent procedure
based on morphological operators and with large robustness and
suitability is guaranteed by the possibility to choose the size
and shape of the structuring elements in each of the previously
mentioned steps in accordance with the mean size and shape
of the objects in the class. All these possibilities ensure to match
the scale of the spatial analysis performed by the filters with
the scales of the objects in each mapped class. Indeed, this has
been proposed by Soille (1996) and also exploited in a number
of stimulating papers, where the size and shape of different
elements of the scenes under test have been exploited to improve
substantially the mapping results. This is the case for instance
for Soille and Pesaresi (2002), where different examples are
proposed. A multi-scale approach using these operators, able
to adapt to different resolution and capture the characteristics
of multiple objects, is the so called Differential Morphological
Profile (DMP), introduced in Pesaresi and Benediktsson (2001).
Since this publication, DMPs have been considered as one of the
most promising approaches in spatial processing of urban scenes.
MI
(
X
)
=
R
(
X
+
1)
∧
X
m
(
X
m
),
(3.8)
where
X
m
(
x
)isequalto0if
x
belongs to amarker, and to
t
max
oth-
erwise. Gradient values are computed as the arithmetic difference
between the dilation and the erosion by the elementary SE:
−
ε
B
(
X
)
˜
=
δ
B
(
X
)
ρ
B
(
X
)
(3.9)
The segmentation algorithm exploited in this work is the
watershed segmentation algorithm. As is well known, the basic
idea of watershed segmentation is to consider the regions to be
extracted as catchment basins in topography (Lin
et al
., 2006).
The watershed lines are then the boundaries of these basins. If
one applies the watershed segmentation method directly to the
intensity image, we may not obtain meaningful segmentation
results for most images. Except for a few simple cases where
the target object is brighter than the background or vice versa,
watershed segmentation cannot be applied directly to raw images,
because of a severe over-segmentation.
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