classes is difficult to discriminate using a common
remotely sensed image with a small number of
bands. So far, research in wetland vegetation
classification has not been intensively studied the
mutually overlapping and continuously changing
vegetation distributions due to the lack of
established method (Yamagata, 1995). However
from the wetland ecosystem conservation planning
and the global warming model perspective,
wetland vegetation classification has become an
urgent research theme.
3-2-1. Procedure of unmixing
The process of unmixing by subspace method
applied to CASI image is as follows.
1) Nine pure pixels (end member points) for
each unmixing class were selected as the
training data based on the knowledge of field
surveys.
2) Using training vectors, the class correlation
matrix @is calculated by equation (6).
3) The eigen value problem using the class
correlation matrix @ is solved to determine
the subspaces for each class.
4) The projection of pixel vector of CASI image
on the class subspace is calculated using
equation (12) .
5) The projection (component of unmixing) for
each class was normalized to (0,1) and
mapped to an image.
3-2-2 Unmixing methods for comparison.
The following 3 conventional unmixing methods
are used for the comparison to the new method:
1) Least squares method : Assuming a linear
mixing model, area fractions of each class are
determined by a least squares model using
the training data.
2) Quadratic programming : Adding a condition
that the area fractions add up to 1 to a linear
mixing model, a least squares solution is
obtained by the quadratic programming
method.
3) Orthogonal subspace projection method
First, the projection of the mixel vector onto
the orthogonal complement space spanned by
the class vectors of the other classes is
computed. The inner product of this projected
vector and the class vector is calculated
(Harsanyi and Chang, 1994).
3-2-3 Results of unmixing.
The result of unmixing by the subspace method
applied to the CASI image of Kushiro mire is
shown in Figure 4. The result of unmixing by
conventional least squares, quadratic
programming and orthogonal subspace projection
methods are shown in Figure 5, 6 and 7
respectively. Here the unmixed vegetation classes
are Yoshi (Phragmites.: Reed), Hannoki (A/nus.:
Alder) Mizugoke(Shagnum.: Moss), Isotsutsuzi
(Ledum), Suge(Carex.: Sedge).
By comparing the quantitative classification
accuracy of unmixing by the subspace method
with the other methods, and investigating the
correspondence between the actual vegetation
distribution from field surveys, the following
results were obtained:
1) In figure 4, it is seen that the subspace
method highlighted the reed contaminated
with sedge as Sedge class.
2) With Sedge class, by comparing figure 4 and 6,
subspace method delineated accurately the
ground pattern of sedge class as well as
quadratic programming.
3) Only quadratic programming (Figure 6)
delineated the Moss and Ledum class that are
spectrally very similar (Figure 3). This result
may be due to the constraint of quadratic
programming, ie. it tries to enhance the
subtle spectral difference between classes to
increase membership difference.
4) Alder class was accurately delineated only by
quadratic programming (Figure 6).
5) Water and Road classes were delineated
accurately by all methods.
3-2-4 Evaluation of unmixing methods
Based on the results obtained above, an
evaluation of the unmixing methods can be
summarized as follows},
1) Spectrally distinct classes such as road, Water,
Sedge (Figure 3) are well unmixed by
subspace method (Figure 4).
2) Spectrally similar classes such as Ledum and
Moss (Figure 3) are unmixed sufficiently only
by quadratic programming (Figure 6).
3) The result achieved by orthogonal subspace
projection method (Figure 7) is entirely the
same as the least square method (Figure 4).
4) Quadratic programming (Figure 6) shows the
most accurate pattern of unmixing across all
classes, however it is the most time
consuming to implement. The subspace
method is a very fast algorithm owing to
many fast and stable eigen value problem
algorithms. Unmixing is performed by a
1 Here, these evaluation are all of qualitative nature.
This is because the evaluation of unmixing is
impossible unless we conduct a through survey of
continuous distribution of all vegetation types.
784
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996
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