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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