The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
2.3 Optimal parameters selection based on JM-distance
3. RESULTS AND DISCUSSION
The performance of a parameter value of texture features can be
evaluated through its effectiveness in classification. The
probability of classification error is used to decide the selection
of optimal parameters. The smaller the probability of
classification error is, the better the parameter value. However,
the classification error method need a lot of computation time
especially more candidate values for a certain parameter. For
the statistical separability of classes is inversely proportional to
the probability of error, people turn to use statistical separabilty
of class as texture parameter selection criterion. For example,
the divergence criterion, the transformed divergence criterion,
the Bhattacharyya distance and the Jeffreys-Matusita (JM)
distance are most widely used criteria (Swain and Davis, 1978).
An IKONOS panchromatic imagery that has a spatial resolution
of 1 meter was used for the experiment. The image covers the
test area of Wangjing District that locates in the north-east
fringe of Beijing city of China with a mixture of thee types of
residential areas and complex background cover types including
grassland, woodland, river, pond, main road, bare ground and
bare farmland (Figure 1). Representative training sites for the
residential class (including three types of residential areas) and
background ((including water bodies, grass land, wood land,
road, bare farmland, barren ground, etc.) were selected through
accurate analysis with the reference to multi-spectral images
covering the same area by using a polygon-based approach.
The JM-distance is an appropriate technique of measuring the
average separability between different classes. lit behaves much
more like probability of correct classification (Swain et al.1971).
For two densities p\(x) and p^fx) » the JM-distance J is given
by
2
J =i\_ylp\( x )~ylP2( x )~\ dx (3)
JC
Which can also be written in the form
J=2(l-e 8x2 )
(4)
In which B\ 2 (Bhattacharya distance) is given by
X1+X2
1-1
ÿXi+12]
VI11II12I
(5)
Where //; is the mean vector for class i and £ i is the
corresponding class covariance matrix. Since 0<e 8x2 <\ ,
J ranges from 0 to 2 with 2 corresponding to the largest
separation.
In this paper, to evaluate and optimize of parameters for
computing textural features to discriminate residential areas
from their background class, the JM-distance is used. The
procedure can be achieved through four steps:
(1) For those textures which have more than one parameter,
multiple texture images were produced by changing each
parameter of texture features with fixed all other parameters;
(2) Selecting appropriate samples of residential class and
background class from each texture image computed from
candidate values, separately. A set of JM-distances will be
obtained according to formula (4) and (5);
(3) Making a statistics of JM-distances changes;
(4) The optimum parameter value is then determined by those
with the largest JM-distance values.
Figure 1. The test image (IKONOS panchromatic band at 1
meter resolution 2719x2449 pixels)
3.1 Optimal parameter value of window size
In this paper, different window sizes (5x5 to 29x29) were tested
for deriving every texture feature. The 29x29 was selected as
the upper limit of window size because the obvious ‘window
problem’ was observed for those with greater window sizes.
The JM-distance between residential class and its background
classes was calculated on each texture measurement with
different window sizes. Figure 2 shows the statistical results, on
which it is clear that except MEAN (17x17), SD (9x9) and ED,
the optimal window size for all texture bands is 25x25 pixels,
supported by the largest JM-distance between residential class
and background. For MEAN and SD, although the JM-distances
were peaked with different window size, the actual differences
to those with the 25x25 window were quite minimal. This also
applied to ED, which is peaked with the 29x29 window with
only minimal difference from the 25x25 window. Therefore,
the 25x25 window size is selected as the optimal window size
for deriving texture features for the residential class.
J optimal — max( J/ )
Where i is the number of candidate values.
(6)