## 3 Experimental Results and Evaluations
### Evaluation of the Sensitivity of the Thresholds  
The proposed approach uses several thresholds in the segmentation process such as (1) searching radius; (2) buffer threshold; (3) co-planarity test threshold; (4) proximity threshold; (5) minimum size of detectable peak; and (6) accumulator cell resolution (please refer to the justifications of these thresholds in Table 3). First of all, _proximity threshold_ is defined as the value which is approximately equal to the average point spacing of the laser data. The average point spacing of the laser data is, usually, provided by a data vendor or can be simply calculated. The other threshold, _minimum size of detectable peak_, is defined as the value which is based on prior knowledge about building planar patch size within the area of interest. This threshold can be changed according to the minimal planar patch size that the user wants to derive for his or her purpose of work. Hence, at this stage, the authors can mention that the two thresholds, _proximity threshold_ and _minimum size of detectable peak_ are not significant values and can be determined easily. The other three thresholds, which are _buffer threshold_, _co-planarity test threshold_, and _accumulator cell resolution_ are all defined as the same value which is two times the accuracy of the laser data in the depth direction (refer to the justification in Table 3). Hence, knowing the accuracy of the laser data is significantly important to determine these three thresholds. Similar to the average point spacing of the laser data, the accuracy of the laser data is usually known or provided by a data vendor. For example, as addressed in Section 3.3, the values from the Vaihingen, Toronto, and Seoul datasets, respectively, were given as 0.15 m, 0.15 m, and 0.10 m. On the other hand, the remaining threshold, _searching radius_, is defined as the value which is for including sufficient number of points to define reliable attributes. Even though the values of the four thresholds (_i.e._, buffer threshold, co-planarity test threshold, accumulator cell resolution, and searching radius) can be determined properly and easily as above-mentioned, the additional analyses are carried out in this section to evaluate the sensitivity of the thresholds while changing the values of the accuracy of the laser data and searching radius. Figure 22: Segmentation results according to changing the threshold, searching radius, from 0.5 m to 5.0 m (the accuracy of the laser data is 0.15 m for all cases). Searching radius: (**a**) 0.5 m; (**b**) 1.0 m; (**c**) 2.0 m; (**d**) 3.0 m; (**e**) 4.0 m; (**f**) 5.0 m.  
For this analysis, building #3 in Toronto data (see Figure 14) is utilized. The first analysis is about the threshold, searching radius while changing the values from 0.5 m to 5 m. When radius is 0.5 m, the segmentation process missed several patches located at the four corners and the left roof side of the building as can be seen in Figure 22a. Moreover, the segmented patches do have less number of points compared to the other cases (_i.e.,_ the cases of Radius of 1.0 m to 5.0 m). This comes from the small searching radius which causes unreliable attribute computation due to the insufficient number of points for neighborhood definition. On the other hand, the good segmentation results are acquired and they are almost similar to each other when the radius is increased (_i.e.,_ 1.0 m to 3.0 m, also see Figure 22b-d). However, in case of too large searching radius (more than 4.0 m), the results were losing two small patches at the left roof side of the building (Figure 22e-f). Also, large searching radius increases the computational load since the number of points in the neighborhood is too large. In summary, searching radius can be determined to include sufficient number of points to define reliable attributes. Moreover, the thresholds from 1.0 m to 3.0 m derived good segmentation results; which means that the range of the proper searching radius threshold is wide enough in the proposed approach.