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)