Characterizing urban subpixel composition using spectral mixture analysis - Urban Remote Sensing: Monitoring, Synthesis and Modeling in the Urban Environment - page 110

For two-endmember models, the resulting shade-normalized
fraction is 1.0. Shade normalization allows comparison of mod-
eled fraction estimates with measures derived from other data
sources or from other dates (Powell et al ., 2007; Myint and
Okin, 2009).

QuickBird imagery (Small and Lu, 2006; Myint and Okin, 2009).
In situ data have also been used to evaluate continuous vegetation
fractions estimated from multispectral data (Smith et al ., 1990;
Elmore et al ., 2000), though in urban environments physical
access to many areas may be restricted and thereby limit the
feasibility of collecting field data.
Commonly, modeled and reference fractions are compared
using correlation analysis; a scatter plot of modeled vs. reference
fractions is generated for a given material class, and the ''good-
ness'' of the correlation is assessed in terms of the slope, intercept,
and coefficient of determination ( R 2 ) or correlation coefficient
(Pearson's r ) of the relationship. If the fractions were perfectly
modeled,thebest-fitregressionlinewouldhaveaslopeequal
to one and an intercept equal to zero. Other measures used to
evaluate the accuracy of fraction estimates include RMS error,
mean absolute error (MAE), and bias. RMS error is calculated
between the modeled and reference fractions for a given material
class (e.g., Wu and Murray, 2003); MAE is the average absolute
residual between modeled and reference fractions; and bias is the
average residual, indicating trends of over- or underestimation
(Schwarz and Zimmermann, 2005; Powell et al ., 2007; Weng
et al ., 2008).
To compare modeled and reference fractions, most studies
average fraction values over a region, either a window of pix-
els (e.g., 3

8.2.5 Model complexity

An additional product that can be generated from MESMA is
a map of per-pixel model complexity by generating a thematic
layer that represents the number of endmembers included in the
overall best-fit model for each pixel. The number of endmembers
required to adequately model a pixel is a measure of the spectral
complexity of the land cover in the pixel's IFOV. Small (2005)
noted that spectral heterogeneity at scales of 10-20 m may be
''the most characteristic feature'' of urban land cover globally.
Characterizing the spectral complexity of a landscape, therefore,
may facilitate the delineation of built-up areas from undevel-
oped categories of land cover (Small, 2005). In a study of a
rapidly urbanizing region of the Brazilian Amazon, Powell and
Roberts (2008) found that model complexity is correlated with
the degree of human impact on a landscape: four-endmember
models corresponded to built-up (urban) land cover, three-
endmember models corresponded to disturbed land cover, and
two-endmember models corresponded to natural land cover.
Thus, maps of model complexity can serve as a summarymeasure
of human impact.

3) or an area that corresponds to the reference
sampling unit. Pixel-to-pixel comparison of urban landscapes is
problematic for several reasons. First, because of the high spec-
tral and spatial variability, a small error in georegistration can
result in significantly different subpixel compositions (Clapham
Jr., 2003; Small and Lu, 2006; Powell et al ., 2007). Second, the
signal recorded at the sensor for a given pixel is influenced
by the spectral properties of the surrounding pixels due to
the MTF of the sensor (Forster, 1983; Townshend et al ., 2000;
Small, 2001). Third, the process of averaging fractions over larger
areas generally reduces variance that may be caused by signal
noise or geolocation error (Woodcock and Strahler, 1987; Powell
et al ., 2007). Therefore, averaging endmember fractions over
zones can generate more robust estimates of land-cover compo-
sition. One of the strengths of SMA is that sub-pixel fractions are
ratio data, and aggregating fraction values generates statistically
valid results (Clapham Jr., 2003).

×

8.2.6 Accuracy assessment

One measure of model fit is generated by the SMA algorithm
itself - RMS error. However, a limitation of SMA is that RMS
error only measures model fit, but provides no information
on fraction accuracy. It is possible, therefore, that a model
could fit the data very well but use an incorrect combination of
endmembers (Sabol et al ., 1992; Roberts et al ., 1998b). Therefore,
assessing accuracy of SMA results cannot depend on RMS error
alone, and an independent dataset is required for validation.
Accuracy assessment is not only a quantitative measure of the
quality of the final product, but also serves as an important
intermediate step to assess the appropriateness of endmembers
and guide refinement of allowed model combinations, model
constraints, and selection rules (Fig. 8.3, Step 5).
Some applications of SMA use fractional abundance images
as input to traditional classifiers (e.g., maximum likelihood)
and generate maps of land-use/land-cover classes. In this case,
accuracy assessment is usually applied to the final classified
image using a standard error matrix and accuracy measures
such as overall, User's, and Producer's accuracy (e.g., Roberts
et al ., 2002; Weng and Lu, 2009). However, if the final product
of SMA is the set of fractional abundance images themselves, the
most common form of accuracy assessment involves compar-
ing modeled fractions with reference fractions, usually derived
from finer spatial resolution imagery, e.g., aerial photography
(Rashed et al ., 2003; Wu and Murray, 2003; Rashed, 2008), aerial
videography (Powell et al ., 2007; Powell and Roberts, 2008), or

8.3 Two case studies

This section presents an overview of several MESMA products
and applications in the context of two case studies: the first
characterizes the evolution of urban land cover on the Brazil-
ian ''arc of deforestation'' and the second quantifies vegetation
cover in a temperate Western US city. Rather than recount
every detail of each study, these examples are meant to high-
light the flexibility of MESMA in characterizing the fundamental
components of urban landscapes. These examples also illus-
trate the difficulty of fully automating or generically applying
MESMA; rather, determination of the most appropriate strategy
for endmember selection and the most effective model param-
eters requires iterative assessment by the analyst (Powell and
Roberts, 2008).