Environmental Engineering Reference
In-Depth Information
superior to unsupervised projections based on global statistics
(Section 4.3.1.1). For feature selection thousands of spectral
features are calculated based on all spectra contained in the
image spectral library. Since the pairwise maximum likelihood
classification uses covariance statistics, it is capable of integrating
features of different scales. These features include band ratios,
absorption depths as well as means, standard deviations and
coefficients of polynomial fits.
The feature selection process results in a set of spectral
features for each class pair allowing its optimal separation. After
parameterizing the pairwise classifiers, the final material decision
is made by applying a MIN-MAX operation. First, the minimum
probability is selected for each class and second, the pixel is
assigned to the material characterized by the highest minimum
probability. Once the classifier has been established, it can be
applied to any HyMap-like hyperspectral image dataset in order
to identify the specific endmembers. For this purpose a user-
defined threshold is applied to the obtained class probabilities.
This way, the developed endmember detection method reduces
the effort for collecting ground truth information.
and a list of possible endmember combinations are introduced
into neighborhood-oriented iterative linear spectral unmixing
(Roessner
et al
., 2001). The iterative unmixing procedure starts
at pixels that are adjacent to the previously identified spec-
trally pure pixels (seedlings). These seedlings represent potential
endmembers forming the mixed pixel spectrum. Depending on
their number and spatial configuration in relation to unknown
mixed pixels (neighborhood analysis), different combinations are
tested successively according to their likelihood based on a list
of possible endmember combinations. During further unmixing
iterations the endmember information of previously unmixed
pixels is also considered in the analysis of neighboring mixed
pixels. This way, the iterative unmixing procedure leads to spatial
growing of the unmixing results around seedling pixels. The
process is repeated until no more pixels are left which can be
unmixed in a meaningful way. The result of the spectral mixture
analysis consists of a multi-band image whereas each band rep-
resents one surface material containing the fractional abundance
of this endmember for each pixel.
4.3.2.2
Classification of spectrally
pure pixels
4.4
Results and discussion
of their potential for urban
analysis
The endmember pixels identified in the first processing step only
represent a small percentage of all image pixels. The remaining
majority can be subdivided into spectrally pure and mixed pixels
whereas it is assumed that the spectral signal of the pure ones
is caused by a single material covering the whole pixel. In case
of mixed pixels the spectral signal results from a combination
of several materials occurring within one pixel. The second pro-
cessing step aims at optimal separation between these two groups
including the identification of the respective surface material
for the spectrally pure ones. For this purpose an algorithm has
been developed which is based on the maximum likelihood clas-
sification. The already identified endmembers serve as training
information for the classifier after they have been further subdi-
vided into representative subclasses by a cluster algorithm based
on reflectance data in order to accommodate the high spectral
variability of urban surface materials in the image data. In the
result, the classifier is parameterized with the mean and covari-
ance statistics of Gaussian distributed subclasses. The separation
between pure and mixed pixels builds on the fact that in feature
space mixed pixels are located further away from the class centers
compared with spectrally pure pixels. Hence, the Mahalanobis
distance threshold is used to exclude mixed pixels from the clas-
sification process. This threshold is calculated for each subclass
based on the training pixels and one global user-defined param-
eter for the rejection of a certain percentage of distant pixels. The
combined identification results of the first and second processing
step represent the total number of spectrally pure pixels. They
serve as seedling pixels for the third processing step analyzing the
remaining mixed pixels.
Figure 4.4(b-d) depicts exemplary results of the developed auto-
matedurbanmaterialmapping systemin comparison to aHyMap
true color composite (Fig. 4.4a) for a 2
2
.
5kmsubsetcon-
taining a part of the inner city of Berlin, Germany. The area
is characterized by different urban structure types dominated
by industrial areas, perimeter block development, single family
homes and mid-rise dwellings development. For a classification-
like representation of the results the dominating endmember
(Fig. 4.4b) has been derived for each pixel based on the 45
abundance layers representing the surface materials automat-
ically detected in the study area. This map is complemented
by Fig. 4.4c showing the endmember with the second high-
est abundance for each mixed pixel. For visualization purposes
these surface materials have been further aggregated into the
mapping categories contained in the legend for the maps in
Fig. 4.4(b and c). The numbers in brackets indicate the number
of surface materials (level 4 of Table 4.1) aggregated into the
respective categories. These mapping results are supplemented
by a grayscale image depicting the fraction of the dominating
endmember ranging between 50 and 100% (Fig. 4.4d).
Despite thematic aggregation of the mapping categories, the
large spatial heterogeneity of surface materials is well visible in
the mapping result. Although the developed approach operates
on a per-pixel basis, the shapes of the real-world objects are well
preserved. This is due to the large number of material classes and
the lownumber of unclassified pixels (coded black) amounting to
less than three percent. The grayscale image of Fig. 4.4d indicating
the fractional abundance of the dominating endmember shows
that about 60% of the 3-4 m resolution image data of the test
area are covered by mixed pixels. Areas dominated by small-sized
objects are depicted in various shades of gray indicating a large
number of mixed pixels. They can clearly be distinguished from
areas characterized by large homogeneous objects consisting
of several pure pixels framed by mixed pixels (e.g., industrial
×
4.3.2.3
Neighborhood-oriented iterative
linear spectral unmixing
A special spectral mixture analysis similar to the MESMA
approach has been developed that includes additional opti-
mization strategies in order to reduce the number of possible
endmembers per pixel. For this purpose spectrally pure seedlings
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