3.1 Threshold Selection Using Ground Truth Data
We carried out the ground truth of several regions that
actually changed at time intervals of 4 years (1987-1991)
and located them in the image under consideration. After
that, we determine the threshold of the distance D so that
the area of change investigated by the ground truth is
successfully detected.
In this study, we selected three different areas of change:
1) newly developed residential area in the mountain,
2) newly constructed factory in the rice field, and
3) newly extended road in the rice field.
And then we computed the mean values of D, D;, Dj, Ds
for each of three areas, 1), 2) and 3). The threshold value of
D, Dy, was determined as D, = Min.{D;, D,, D3}-C, where
C is an arbitrary small value used for detecting the
localized pixel area of change in the image. As a result, we
found D, — 6.9 (multiplied by 10). Fig.4 is the image
showing the area of change. In Fig.4 white regions
represent the area of change.
3.2 Change Detection Using 2-Dim. Histograms
In the procedure for detemining the threshold described in
the previous section, the ground truth is needed to find some
areas that have actually changed. In this section we describe
a method for detecting the area of change automatically.
This method is based on the idea that some peaks
corresponding to the area of change will occur in a 2-
dimensional frequency distribution against two distance
variables, d; and d; (1j). For example, consider the land
use change of the vegetation field into the residential area.
In this case, the change of reflectance ratio in TM bands 1,
2 and 3 will occur in the areas where land use changed,
because for their spectral bands the reflectance of the
residential area is larger than that of the vegetation. If we
construct the frequency distribution against distance values
in two of three bands, it will have significant peaks at the
large distance value. This is the reason why we use a two
dimensional histograms.
We investigated the shape of histograms for all
combinations of TM bands (4C, = 15) to detect the area of
change. As a result of it, in all the histograms, more than
two significant peaks were found in the region where the
value of the distance is large. It will be, therefore, possible
to extract the area of change from the reflectance ratio
image if we can detect the pixels in the image that distribute
around the significant peaks in the histogram. However, it
is difficult to extract some peaks from the frequency
distribution automatically. For simplicity, we divided the
two bands distance space into two regions, Change Area
and Non-change Area, as follows:
Change Area is the outside of the ellipse defined as
2
dd;
dep te | (8)
aj. b
1
Where a; and b; are the values of d; and d; corresponding to
the valley (minimum between two peaks ) that occurs in
frequencies on each axis in band i and band j, respectively.
Non-change Area is the inside of the ellipse given by
Eq.(8).
In order to examine which combination of TM bands
provides better results in detecting the area of change, we
extracted the pixels from the paired images that correspond
to Change Area in each of all the histigrams and checkeÿ
whether the areas 1), 2) and 3) used as ground truth data in
the previous section 3.1 are successfully detected.
Consequently, we found the following results.
(1) The combinations of did», dod, d4d; provided better
results, because the land use in the study site mainly
changes from the agricultural field to the residential are
and road.
(2) It is difficult to detect the area of change fiom
histograms whose variables are taken as distance values
including bands 4 and 5, because most of the study site
consists of the vegetation field such as agricultural area and
forest, and so it is difficult to find small peaks in the
histogram.
(3) In the case that more than two valleys are found in the
histogram, we obtain better results if we select the distance
value corresponding to the second valley as aj or bj in
Eq.(8).
Fig.5 shows the frequency distribution in bands 3 and 7 and
Fig.6 is the image showing the area of change extracted
from the histogram in bands 3 and 7 (White regions
represent the areas of change.)
To compare with the results of the section 3.1, we also used
the ground truth data, 1), 2) and 3), given in the section 3.1.
Fig.7 shows the shape of the extracted area of change. As
seen from Fig.7, in the extraction of facory in the case 2),
the change detection algorithm described in this section is
superior to that in the section 3.1 because the shape of the
buildings appears clearly. In the case 3), the present
algorithm provides better results, as compared to the change
detection method described in the previous section because
the chain of pixels in the road is more smooth.
4. CONCLUSIONS
A new change detection method using the relative
atmospheric correction of multi-temporal Landsat TM
images was described. This method is based on the idea that
the surface reflectance ratio, A(t2)/A(t1), at two different
times, t1 and t2, is obtained from count levels, X(12) and
X(t1), of the corresponding pixel at two different image
and the coefficients of the linear equation derived from tle
relative atmospheric correction. In order to detect the ar&
of change, the distance d of A(t2)/A(t1) from the value of
was introduced and the threshold of d was automatically
determined by using the 2-dimensional frequency
distribution of distance values in different spectral bands.
As a result, it was shown that the values of A(t2)/A() af
almost normally distributed around the value 1 in eve
spectral band. It was also found that the areas of land cov
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996
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