## 4 Results  
In order to control the accuracy of the presented fuzzy classification method a check project is defined for each dataset, so that the same rules are used but with crisp thresholds. In other words, instead of using fuzzy member ship functions for classification, crisp threshold are used. For example, the fuzzy rule used for vegetation detection is:  
If **NIR ratio** is _high_ and **NDVI** is _high_ then segment is _Vegetation_. In the check project, the threshold values are calculated as the middle point of the fuzzy area. As explained earlier in Section 3.2.2, \(T_{1}\) and \(T_{2}\) specify the fuzzy area for vegetation. In the check project, the crisp threshold is considered to be the middle point between \(T_{1}\) and \(T_{2}\), which is \(\frac{T_{1}+T_{2}}{2}\). Thus, those segments which have NIR Ratio more than 0.275 and NDVI more than 0.15 are assigned to the vegetation class. The same procedure is done for other classes as well. Figure 10 shows some parts of the original images, images classified using crisp thresholds (check project) and the images classified using the presented fuzzy rule-based system for both datasets. As can be seen, the images classified using the presented fuzzy rule-based system (Figure 10b,e,h,k) are more successful in terms of defining image objects compared to the check projects (Figure 10c,f,i,l). Figure 10: **(a)**,(**d**) original image of GeoEye; **(b)**,(**e**) GeoEye image classified using crisp borders; **(c)**,(**f**) GeoEye image classified using fuzzy functions. **(g)**,(**j**) original image of QB; **(h)**,(**k**) QB image classified using crisp borders; **(i)**,(**l**) QB image classified using fuzzy functions. In this figure red, green, magenta, blue, and yellow colors stand for shadow, vegetation, building, road, and bare land classes, respectively. In order to evaluate the quality of the results of the presented method, a random part (400 pixels \(\times\) 500 pixels) of each image is classified manually using human expertise. Then, using the manual classification result as control information, the confusion matrix is generated for both the presented method as well as the check project. Tables 1 and 2 show the related confusion matrices. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **Building** & **Road** & **Shadow** & **Vegetation** & **Bare Land** & **Sum** & **User’s Accuracy** \\ \hline Building & 47,839 & 4,732 & 59 & 17 & 637 & 53,284 & 0.90 \\ Road & 1,770 & 31,851 & 11 & 0 & 3,781 & 37,413 & 0.85 \\ Shadow & 35 & 424 & 2,981 & 171 & 74 & 3,685 & 0.81 \\ Vegetation & 31 & 12 & 147 & 34,510 & 392 & 35,092 & 0.98 \\ Bare Land & 18,339 & 849 & 400 & 1,378 & 47,322 & 68,288 & 0.69 \\ Sum & 68,014 & 37,868 & 3,598 & 38,314 & 52,206 & 200,000 & \\ Producer’s Accuracy & 0.70 & 0.84 & 0.83 & 0.90 & 0.91 & & \\ \hline \end{tabular}
\end{table} 
Table 1: Confusion Matrix for the presented method results (Geo-Eye Data). \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **Building** & **Road** & **Shadow** & **Vegetation** & **Bare Land** & **Sum** & **User’s Accuracy** \\ \hline Building & 35,648 & 3,780 & 107 & 0 & 5,863 & 45,398 & 0.79 \\ Road & 789 & 21,598 & 579 & 108 & 3,583 & 26,657 & 0.81 \\ Shadow & 15 & 1,879 & 2,150 & 587 & 579 & 5,210 & 0.41 \\ Vegetation & 38 & 17 & 24 & 28,780 & 785 & 29,644 & 0.97 \\ Bare Land & 31,524 & 10,594 & 738 & 1,480 & 48,753 & 93,089 & 0.52 \\ Sum & 68,014 & 37,868 & 3,598 & 38,314 & 52,206 & 200,000 & \\ Producer’s Accuracy & 0.52 & 0.57 & 0.60 & 0.75 & 0.93 & & \\ \hline \end{tabular}
\end{table} 
Table 2: Confusion Matrix for the check project (Geo-Eye Data).