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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
Congalton that stats at least 50 samples and in large area at least
75-100 samples should be taken per class (Congalton, 1991).
In images with large fields, ie. image#1 and image#4 (Figure
1(a) and Figure 1(d)), the graphs show that these results have
tendency to overestimating actual overall accuracy. In fact in
images with large fields optimistic estimation of errors is
occurred. The reason for this matter is that in images with small
fields, distribution and dispersion of classes and consequently
errors in image is better and sampling with simple random
method is more suitable.
For comparing results of SRS method in the all synthetic
images, average and standard deviation of overall accuracies in
each sampling cases after stability were computed and results of
each three cases related to each image are averaged. The results
were graphically displayed in Figure 2. The y-axis in Figure
2(a) shows differences of means after stability with actual
overall accuracies and in Figure 2(b) shows standard deviations
from means and in Figure 2(c) shows standard deviations from
real values of overall accuracies. The x-axis shows image
numbers that image number 5 is the real TM image.
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image number image number
Figure 2. The difference of average overall accuracies after
stability with actual overall accuracies (a) and standard
deviations from means (b), and standard deviations from real
values (c), using SRS method (each sampling schema for each
sample size has been repeated 30 times and the results have
been averaged)
With respect to these graphs, the best results are related to
image #2 and image#3 with smaller difference of means (Figure
2(a)) and standard deviations (Figure 2(b) and Figure 2(c)).
Also with due attention to Figure 2(a) the overestimating in
image? and image£4 is distinctive. In addition to largeness of
difference values in these images in Figure 2(a), the value of
standard deviations from real overall accuracies in these two
images are clearly bigger than standard deviations from means
(Figure 2(b) and Figure 2(c)).
466 sou 600 700 800 900 1000
sample size (pixel)
Figure 3. Overall accuracies resulted from using SRS method
(each sampling schema for each sample size has been repeated
30 times and the results have been averaged) for 3 cases in the
real TM image
The results of SRS schema in real image has been graphed in
Figure 3 that it shows, the results go towards stability almost
after 50 samples for each class.
4.2 Experiment 42: Investigation of Stratified Random
Sampling (STRAT) Schema
With due attention to graphs of overall accuracies using STRAT
sampling schema in 3 cases, it was seen that with nearly 50
samples for each class, i.e. 500 samples in first three images
with 10 classes and almost 400 samples in image £4 and image
#5 with 9 classes, the results went towards stability, either for
larger images or smaller images. So, produced samples with this
sampling schema have better distribution in image relative to
SRS method, therefore, with fewer samples, good results are
achieved.
In the graph of image £4, continuously, the overestimating of
results was seen. Because this image is an image with large
fields and large size, that this sampling method can not sample
this image in a good way. But in image #1 in spite of having
large fields because of smallness of image size the results are
better. From this, it is concluded that the size of image is an
effective factor for STRAT method.
Also with comparing image #2 with image # 3 in Figure 4, it is
distinguishable that STRAT method has better results in images
with smaller image size used in this paper. The nearness of
means of overall accuracies to real amounts in image #2 (Figure
4(a)) that is smaller image in comparing to image #3, is better,
in spite of same distribution of fields and classes in image.
On the other hand with due attention to results of image #1 and
image #2 in Figure 4, the later has better results in mean of
overall accuracy (Figure 4.4(a)), but the former has better
standard deviation (Figure 4(b) and Figure 4(c)). Then results of
these two images with the same image size have not advantage
upon each other.
Totally, Stratified Random Sampling has better results in image
with smaller image size, and with considering results of real
image in Figure 4, this matter is well confirmed.
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image number b image number
image number
Figure 4. The difference of average overall accuracies after
stability with actual overall accuracies (a) and standard
deviations from means (b), and standard deviations from real
values (c), using STRAT method (each sampling schema for
each sample size has been repeated 30 times and the results
have been averaged)
The results of computing of overall accuracies with various
sample sizes using stratified sampling schema in real TM image
showed that the results go towards stability almost after 50
samples per class.
4.3 Experiment #3: Investigation of Systematic Sampling
(SYSTEM) Schema
Studying of graphs of STRAT method showed that in this
method (similar to STRAT method) the size of images is not an
important factor for stability of results. These graphs showed
that almost with more than 30 or 40 sample for each class,
stable results are acquired, i.e. some more quickly than two
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