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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
This method classifies each group of pixels as a unit.
This will tend to minimize misclassification for isolated
pixels with outlier spectral characteristics.
3-2. Region-based maximum likelihood classification
with pdf
The method suggested in this study can be summarized
as a comparison of the pdf of an unknown group with
pdfs of each of the training data sets. If two samples
originate from the same population, the pdfs of the two
groups should be similar to each other. Significantly,
the distribution of radiance values that causes
misclassification in pixel-based approaches (Swain and
Davis, 1978), is critical information for the method
developed in this study.
To simplify the explanation, suppose two normally
distributed populations have means 4; and u,, and
standard deviation o, and o5 , respectively.
Figure 3 represents three different cases that could
occur. If two populations are very similar, then the
two pdfs almost completely overlap (Figure 3a). If it
is possible to estimate the area of the overlapped
region, it should be close to 1, because the sum of all
possible probabilities is equal to 1. However, if two
populations are very different from each other, there
should only be a very small overlap area for the two
pdfs (Figure 3c). Thus it can be seen that the size of
the overlapped area is proportionate to the similarity of
the two pdfs. If the two pdfs are identical to each
other, the overlapping area is equal to 1, if completely
different, then 0, and the values between are an index of
similarity (Figure 3b). The area of overlap can be
found by integrating the relevant overlap portions of the
two pdfs:
Class 15} Class i Class
a)
Class : Class |
c)
Figure 3. Likelihood measured with pdf. The areas
with diagonal lines indicate the degree of similarity
between two classes. (a) Two almost completely
overlapping class. | (b) Two partially overlapping
classes. (c) Two almost completely separated classes.
0j 7 ra esta Lm Ë pax, 6)
m m
Where: 0} likelihood index between X| and X,
m-2for X| z.Y.
m-Tlfor Xi X»
When the likelihood index is extended to a multivariate
pdf, with p variables and multiple samples, the
equation is modified as follows:
t M oo 1 1
Ojj = po [7 sees PC. git m
2x Il
7 sts 7d T :
Émile (Ay NE tin dp
(5)
Where Oj; : likelihood index between X; and X;
i : patch id under investigation
j : training data set id under investigation
m= gj for X; 2X;
J
m= for KA;
The decision rule in this study is extracted from the
relationship between the likelihood and similarity as
follows:
Os = Ojj (6)
Thus a patch is assigned to class c if the maximum of
the likelihood index values is found for the pdf
comparison of the patch and training data set C.
With this method, a very stable similarity index is
obtained because the variance and covariance
information, as well as the class mean, are all directly
used. One disadvantage of this method is that it
requires much computing time.
4. APPLICATION OF THE PIXEL AND REGION-
BASED CLASSIFICATION METHODS
The ADAR data is used to compare the new approach
with traditional methods. The system captures images
1,000 by 1,500 pixels in size, each pixel approximately
1 x 1 meter. The ADAR system acquires four bands
of data with four separate digital cameras sensitive to
blue, green, red, and infrared wavelengths covering the
range from 400 to 1,000 nm.
The data were acquired at 19:42:18 GMT (2:42 pm
local time) on March 24 1997 (early spring, prior to
tree leaf-out) from an altitude of 2,522 meters. Leaf-
off data provides clearer observation of ground
features, but less spectral discrimination of forest cover.
The analysis procedure in this study comprises three
stages. It is assumed that patches have previously
been identified by image segmentation using the region
growing process incorporating thresholding and region
growing. In the first stage, statistics for the patches
are computed. The statistics used were the same as
those used in the region growing stage, including the
mean vectors and variance-covariance matrices.
For the second stage, representative patches were
selected to build a training data set for seven classes:
Building, Road, Forest, Lawn, Shadowed Vegetation,
Water, and Shadow. The patches selected as training