**3. Results**

#### *3.1. Parameter Sensitivity Analysis*

The sensitivity analysis to determine optimum values of three morphological operations used to delineate markers indicated that overall accuracy was maximized for all models, with and without shadow removed, when the MKS was three (Figure 7b, Table 3). Overall accuracy decreased for all models when opening iteration was increased beyond one, except for the two ExGR models, in which case an opening iteration of two maximized the overall accuracy (Figure 7a, Table 3). Higher overall accuracy was achieved for ExGR\_s, ExGR\_ns, COM\_s, and GRB\_s when a dilation iteration of one

was used (Figure 7c, Table 3). For the remaining models, a dilation iteration of three increased the overall accuracy. Optimum values for the DTC were inconclusive (Figure 7d). The results indicate that, depending on the index image used for watershed segmentation, DTC can be selected accordingly to maximize accuracy (Figure 7d, Table 3). Across all models, overall accuracy ranged from 11.5 ± 0.01% for CIVE\_s to 93.4 ± 0.5% for GRB\_ns, the user's and producer's accuracies varied from 0% to 99.4 ± 0.01%.

**Figure 7.** Sensitivity analysis results for optimum values of (**a**) number of iterations for opening, (**b**) morphological kernel size, (**c**) number of iterations for dilation, and (**d**) distance transform coefficient for several vegetation indices (Table 2). ns = no shadow, s = with shadow. Error bars indicate 95% confidence intervals of the mean computed from the standard error.

**Table 3.** Optimum parameter values for marker detection using vegetation indices. For description purpose, subscript "\_ns" was added to the names of index images when shadows were removed after segmentation and "\_s" was added when shadows were not removed, for example, shadow removed ExG index image were named ExG\_ns and those with shadow present were named ExG\_s. Index names as in Table 1.



**Table 3.** *Cont.*

#### *3.2. Tree-Cover Area Estimation and Tree Detection Analysis*

Further analysis only considered models that had an overall accuracy of tree detection greater than 90% and that fell inside the confidence interval of the reference area estimate. The reference area was estimated from the reference dataset consisting of 2401 random point samples. The number of tree and no-tree samples was 650 and 1751, respectively, thus, on the basis of the sampling design to provide a 2% precision with a 95% confidence level, the percent tree cover was 27.1 ± 2%. Six models with shadow (COM\_s, ExG\_s, ExGR\_s, GRB\_s, TGI\_s, and VDVI\_s) and seven models after shadow removal (COM\_ns, ExG\_ns, ExGR\_ns, GRB\_ns, R-G\_ns, TGI\_ns, and VDVI\_ns) met both criteria (Table 4). Confusion matrix derived adjusted accuracy estimates for the selected shadow and shadow removed models are shown in Table 4. The overall accuracy for those 13 models ranged from 90.5 ± 0.6% to 93.4 ± 0.5% for VDVI\_s and GRB\_ns, respectively. User's accuracy was highest for GRB\_ns (90.1 ± 1.2%) and lowest for VDVI\_s (82.6 ± 1.5%), and producer's accuracy was highest for ExG\_s (87.4 ± 1.2%) and lowest for VDVI\_ns (81.1 ± 1.3%).

**Table 4.** Metrics derived from confusion matrix of segmented images by shadow removed and with shadow vegetation index models. Accuracies in percent ± standard errors. Index names as in Table 1.


We found that GRB\_ns model had highest overall accuracy of 93.4 ± 0.5%, closely followed by ExG\_s (93.1 ± 0.5%). The GRB\_ns also had the highest user's accuracy of 90.1 ± 1.2% followed by ExG\_ns (89.9 ± 1.2%). Higher user's accuracy of trees implies that trees were detected with lower commission error. Although the user's accuracy of ExG\_s was 87.9 ± 1.3%, this model had the highest

producer's accuracy of 87.4 ± 1.2%. Higher producer's accuracy indicates better performance of the models in detection of actual trees with the lowest omission error. The VDVI models, VDVI\_s and VDVI\_ns, had the lowest user's and producer's accuracy respectively (Table 4). The commission error in the GRB model decreased after shadow removal but the omission error increased slightly. When GRB\_ns was used, it attained the lowest commission error among all the index images (user's accuracy = 90.1 ± 1.2%), but had a higher omission error (producer's accuracy = 85.2 ± 1.3%) compared to ExG\_s, TGI\_ns, COM\_s, and GRB\_s. In contrast, ExG\_s and TGI\_ns had the lowest omission error (producer's accuracy = 87.4 ± 1.2% and 87.2 ± 1.2%, respectively). This indicated that the watershed segmentation using these two indices were able to detect trees with higher accuracy than other indices, but TGI\_ns had higher commission error (user's accuracy = 85.9 ± 1.4%) than ExG\_s (user's accuracy = 87.9 ± 1.3%).

We found that on an average overall accuracy and user's accuracy increased by 0.5% (standard deviation (SD) = 0.7%) and 2.9% (SD = 4%), respectively, when shadows were removed (Table 5). However, average producer's accuracy and the proportion of the area covered by trees decreased by 1.4% (SD = 3.2%) and 1.1% (SD = 2.1), respectively (Table 5). Although on an average accuracy increased or decreased only slightly, it must be noted that the overall accuracy and user's accuracy increased for six out of seven indices when shadows were removed, whereas producer's accuracy increased for only one index model (Table 5). The highest increase in user's accuracy of ~10% was observed when shadows were removed from the R-G derived segmented image followed by VDVI (~4%), although user's accuracy declined by 3% when TGI was used. The highest decrease in producer's accuracy after shadow removal was observed for the R-G index (6.7%), although producer's accuracy increased after shadow removal when TGI was used (4%). The estimated proportional area decreased in six index images when shadows were removed. The highest decrease in the proportion of tree-cover area was ~5% when the R-G index image was used (Table 5).


**Table 5.** Difference in proportional area, user's accuracy, producer's accuracy, and overall accuracy between shadow removed and with shadow vegetation index models. SD = Standard Deviation.

#### *3.3. Object-Based Overlap Analysis*

Two models (one with shadow (ExG\_s) and the other without shadow (GRB\_ns) that had the highest point-based overall accuracy were selected for overlap accuracy assessment. Using an object-based approach, 50 randomly sampled polygons for each of the two maps covered polygon size distributions including the 5th up to the 97th percentile for ExG\_s, and from the smallest polygon up to the 99th percentiles for GRB\_ns. The highest overlap accuracy between predicted and reference data was achieved by ExG\_s (~95%) when compared to GRB\_ns (88%) (Table 6). Although the GRB\_ns model had the highest overall accuracy (93.4%) based on the point-based accuracy assessment, the ExG\_s model performed better in delineation of actual crowns by as much as 7%. The omission area was very low when ExG\_s model was used (~5%) compared to GRB\_ns model (~12%), but the

commission error was much higher with ExG\_s model (21.4%). This is in line with the point-based accuracy assessment, where the GRB\_ns model had higher user's accuracy and lower producer's accuracy compared to ExG\_s.

**Table 6.** Percent (%) overlap, omission, and commission areas of predicted trees with reference trees by vegetation index models.


The mean patch sizes of tree clumps predicted by GRB\_ns and ExG\_s di ffered substantially. Patches predicted by GRB\_ns were much larger than those predicted by ExG\_s because ExG\_s separated clumped trees better than GRB\_ns. The mean size of patches delineated by GRB\_ns was about 3.86 m<sup>2</sup> compared to roughly 1.16 m<sup>2</sup> by ExG\_s. The data sugges<sup>t</sup> that commission errors from GRB\_ns- and ExG\_s-predicted patches were similar, though GRB\_ns had a higher mean commission error (0.58 m2) compared to ExG\_s (~0.25 m2) (Figure 8). However, there was a significant di fference in omission error between the two, in which GRB\_ns had a higher mean omission error of 0.67 m<sup>2</sup> compared to 0.06 m<sup>2</sup> of ExG\_s model (Figure 8). The total cover estimated by GRB\_ns model was 0.49 hectare compared to ExG\_s model which was estimated as 0.53 hectare.

**Figure 8.** Comparison of omission and commission errors of patches predicted by GRB\_ns and EXG\_s models. Error bars are the 95% confidence intervals of the mean computed from the standard error.

Comparing the number of reference tree crowns that were fully within each of the predicted tree patches from the two models (GRB\_ns and ExG\_s), we found that ExG\_s detected more trees as individuals compared to GRB\_ns. The largest tree patch predicted by GRB\_ns had eleven reference trees compared to only three in ExG\_s. (Table 7). Individual predicted trees that coincided with one tree from the reference data were more common for ExG\_s, whereas more tree clumps were delineated by GRB\_ns (Table 7).

**Table 7.** Count of predicted tree crowns in patches versus number of reference tree crowns. 0 = tree not detected, 1 = individual isolated tree detected, >1 = number of tree crowns present in detected tree patch.

