120.00 
  
E 
8 
   
  
  
  
  
  
Cumulative percentage of 
number of pixels 
Graded limits of per pixel RMSE 
Figure 2. Variation of cumulative percentage of 
number of pixels with per-pixel RMSE 
Further, observation on the data reveals that about 90% of 
pixels vectors lie below the RMSE of 0.06 which may be 
considered as quite satisfactory. 
5.3 Class independent error in membership value 
In an attempt to illustrate the behavior of the outputs with 
respect to the individual fuzzy membership values 
irrespective of their class assignment, range of algebraic error 
and mean absolute errors for the tested discrete membership 
values are computed and presented in Table 2. 
All the mean error values are seen to be lower than 0.031 
which amounts to only about 15 m? corresponding to one 
pixel coverage of LISS III scene (= 525 m?). The important 
observation on the range of algebraic error is the occurrence 
of the positive and negative error almost uniformly 
distributed within the range of -0.139 to +0.113, which 
signifies the desirable random nature of the output. Another 
desirable outcome is that the variation of mean absolute error 
for all the membership values is very small and within the 
range between 0.021 and 0.046 (below 5%). 
Table2. Class independent error for a set of typical discrete 
membership values 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Membership Range of Mean absolute 
value algebraic error error 
0 -0.082 to 0.102 0.030 
0.05 -0.081 to 0.084 0.028 
0.10 -0.080 to 0.083 0.026 
0.15 -0.078 to 0.079 0.025 
0.20 -0.075 to 0.070 0.024 
0.25 -0.071 to 0.065 0.024 
0.30 -0.067 to 0.061 0.023 
0.35 -0.064 to 0.055 0.022 
0.40 -0.060 to 0.051 0.021 
0.45 -0.068 to 0.058 0.023 
0.50 -0.079 to 0.064 0.025 
0.55 -0.090 to 0.069 0.028 
0.60 -0.100 to 0.074 0.029 
0.65 -0.111 to 0.029 0.029 
0.70 -0.120 to 0.082 0.029 
0.75 -0.128 to 0.086 0.033 
0.80 -0.134 to 0.090 0.034 
0.85 -0.138 to 0.095 0.037 
0.90 -0.139 to 0.101 0.039 
0.95 -0.137 to 0.107 0.042 
1.00 -0.132 to 0.113 0.046 
  
  
  
     
  
IAPRS & SIS, Vol.34, Part 7, “Resource and Environmental Monitoring", Hyderabad, India,2002 
5.4 Class specific error analysis 
For assessing the contribution of different classes to the overall 
error scenario of the outputs, class specific error analysis are 
carried out in terms of correlation between the predicted and 
known fuzzy membership values. 
  
Classi: Marshy water 
R°=0.9719 
ee re EE EEE 
0 599400 0200 0.400 0600 0.800 1.000 1200 
  
Predicted membership 
Known membership values 
  
  
  
(A) 
  
Class2: Aquatic vegetation 
R* « 0.9938 
1.500 - 
1.000 | 
   
    
0.500 - 
0.000 4 mi 
0509000 0200 0.400 0600 0.800 
1.000 1.200 
em E —— 
— 
Predicted membership 
values 
Known membership values 
  
  
  
(B) 
  
Class3: Residential area 
R? - 0.9928 
     
—— 
0.506 000 0.200 0.400 0.600 0.800 1.000 1.200 
Predicted membership 
values 
© 
C 
S 
Known membership values 
  
  
  
(C) 
Figure 3. Correlation between predicted and knewn 
membership values for the three classes