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Modern Geomatics Technologies and Applications

Fig. 7. Comparing the accuracy of clustering techniques
against the Grid methods using 80%-Overlap images

As seen in above figures, in general the methods Average Linkage, SOM, and FCM have the best accuracy. For example, as seen
in Figure 8, Average Linkage, SOM, and FCM have an RMSE equal to 35.09, 44.01, and 49.57cm, respectively. In the mean
time, the Single Linkage and Complete Linkage methods have the worst results in the same dataset, with 102.38 and 72.34
respectively. In other words, the use of the clustering algorithm has not helped much to the accuracy of the adjustment. However,
the methods Average Linage, SOM, FCM always perform better or equal to that of the Grid pattern. This means that the control
point locations suggested by these techniques are equivalent to or better than those that are empirically defined. It was also
observed that sometimes the clustering techniques select points in exact locations defined in Grid technique. Figure 9 shows an
example of such produced by the SOM technique. In such cases, the accuracy achieved using the clustering technique is exactly
the same as that of the counterpart Grid method.

3.2 Investigating the distribution of produced ground control points (cluster centres)

Another important parameter that is usually considered in choosing the control points is how well they are distributed across
the area. It is usually said that the control points must be distributed evenly in plan and height. Therefore, in this section, the
distribution of the points determined by all of the clustering algorithms is examined. In this regard, the variance to mean ratio
(vmr) [23] is used. This criterion represents the variance of the number of control points in different parts of the region to their
average number in the whole region. To calculate it, the area is divided into 8 parts (Fig. 10) and the number of control points in
each section is, then, determined. Accordingly, a vector X = [x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8] is formed, in which x_i is
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the number of control points in the region i. In this case, VMR = S / m is used as the criterion for the distribution of control
points by each of the clustering method. The smaller the VMR value, the better the points are distributed. Figure 11 shows the
VMR for the clustering techniques used in this paper. As can be seen, the value of the VMR of K-Medoids, K-Means, FCM,
GA, PSO, Complete linkage, Average Linkage, Gclust, SOM and Mean Shift methods is less than 1, whereas this value for
Optic, Dbscan, Single Linkage is larger than 1. In the meantime, the K-Means method has the lowest variance while the Single
Linkage method with a variance to maximum mean had the worst distribution of points. Figure 12 shows an example of clustering
of the initial points of the Ardabil area with a larger vmr criterion and smaller than 1.

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