Image Processing Reference
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based analysis approaches focusing on the urban environment. Authors like Phinn
et al. ( 2002 ) have shown that such an approach can be successfully transferred to
an analysis at subpixel level. Hyperspectral data are well
suited for applying such methods, as their spectral informa-
tion content allows the discrimination of diverse materials in
a pixel. This paragraph provides an overview on the analy-
sis of urban areas with methods capable to quantify material
components at a sub-pixel level, commonly referred to as
spectral mixture analysis (SMA) or spectral unmixing .
A straightforward unmixing procedure is a linear spec-
tral unmixing approach. In a simplifying approach, pixel reflectance is supposed to
depend on a linear combination of a limited set of pure urban surface components
(or endmembers) and can hence be decomposed by calculating the respective frac-
tional component abundances.
For statistical reasons, the maximum number of possible endmembers depends
on the dimensionality of the data set and the spectral contrast of the individual
endmembers. It will usually be close to the independent feature space bands (repre-
sented, for example, by an MNF-transformation). Potentially, this leads to uncer-
tainties in the unmixing process and to unexplained surface components not
represented by a limited number of endmembers. The unexplained components are
accounted for by band-wise residuals; residuals may be summarized as root mean
squared error (RMSE). The RMSE is particularly relevant in highly diverse urban
areas to keep track of uncertainties in the data analysis. A second indicator is that the
resulting fraction image for every endmembers contains positive values only. Every
unmixing model should sum to unity, which is mathematically also possible with
endmember abundances below zero or above 100%. Largely positive fractions indi-
cate the validity of the unmixing, as the mathematical solution represents physically
meaningful results (Fig. 9.6 ).
Assuming that suitable spectra are available in a spectral library, one way to
overcome this limitation is to employ multiple endmember models, i.e. to use indi-
vidual endmember combinations depending on the respective components present
in every individual pixel. It may, for example, be adequate to model a pixel in a
homogeneous industrial area with two endmembers only, e.g. concrete and asphalt.
Heterogeneous urban areas such as many residential quarters may result in pixels
Spectral mixture
analysis is a well
adapted concept
to work with
spectral high
resolution data
Fig. 9.6 Results from a linear spectral unmixing with five endmembers: Vegetation, soil, con-
crete, asphalt, clay shingle. Here: R-G-B vegetation-concrete-clay shingle (water along the left-
image border is masked)
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