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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
red region denotes vegetation cover, so it also indicates there
were non-vegetation in the two regions.
Figure 7. The classification Figure 8. NDVI image
image of vegetation
5. COMPARE UFCLS METHOD WITH CSMA
Constrained spectral mixture analysis (CSMA) was supposed
by Liu Zhengkai et.al(1996). Using the CSMA algorithm, we
can solve the linear spectral mixture model (1) through gradient
iteration. For the two constraints, ASC and ANC, adding merit
functions to the object function is applied in CSMA. So the
constrained object function is defined as
=|E|?- A1g(F)+A22(F) (8)
where lE | 2 denotes 2-norm in the error matrix E, Le., the least
squares error, and g,(F) and g(F) are the merit functions of
ASC and ANC respectively. Here A, and A, are constants;
when they are given very large values, the minimum of e is the
minimum of IE] 2 under the two constraints of ASC and ANC.
So the iterative equation is presented as follows
a
2 0
ius aon ijv Sece uan DE
X, og sully
n
where ot denotes the abundance fraction of the n-th
endmember in the A-th iteration, and 6 is the iterative step,
which is generally given a small value in the range of 0 to 1.
We applied the CSMA method to estimate the abundance
fractions of the six endmembers in the study area of experiment
1 (Fig.l). The classification result of the endmember m, is
presented in Fig.4(c). Compared it with NDVI (Fig.4(b)), it is
shown that their similarities are not better than that of the m,
generated by UFCLS and NDVI, especially in the bottom of the
image there are some distinct differences. And it did not
classified the shade areas correctly as the UFCLS did, in Fig.
4(a) and 4(c) denoted by the circles.
Considering the consumption of the computing time, the
UFCLS is also better than the CSMA. The latter consumed nine
minutes to process the data of 51x51 pixels, but the former
consumed less than one minute. The endmember signature
matrix M is required when using the CSMA method, so it does
nothing if the endmember signature matrix M is unknown. The
values of the three parameters, 8, A, and A; in the equation (9),
are obtained by repeating to do experiments, here 6=8x10""
S/(3n+1 ), A,= 6nx10° and A57 nx10*. The E, generated by the
CSMA, i.e., the average value of relative error, defined by E;* *
] L
=) (E DU , n denoting the total of spectral bands, was
isi
18.5%, and that of the UFCLS was only 1.695.
6. CONCLUSION AND DISCUSSION
The UFCLS method has been used for the inversion of linear
spectral mixture model. The pixels classification was done
through estimating the abundance fractions of endmembers.
And the results indicated its effects are good. In our
experiments the results of classification were verified only by
the NDVI image, so the verification will be done by the
measurement data of the land cover in the next study.
Compared the pixels classification results using the UFCLS
with that of using the CSMA, it was shown that the former is
better than the latter whether considering the effects of
classification or the consumptive computing time. If the values
of the three parameters, 6, A, and A; in the CSMA, are adjusted
farther, the effects of classification will be improved and the
consumptive time will be shorten. However, maybe this is just
its disadvantage, because it is very difficult to find the proper
values of these parameters.
The classification errors in the shade areas were increasing
whether using the UFCLS or using the CSMA, which indicates
the shade should be selected as an endmember in the inversion
of the linear spectral mixture model.
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