# Vision-Aided Localization and Mapping in Forested Environments Using Stereo Images
## 4 Analysis and Discussion
### Mapping  
In order to generate a stem map, we performed global alignment using all the coordinates from the GPS track and the VO path shown in Figure 5a,b. Figure 12 shows the result after clustering the observed tree stem position. The black dots in the figure denote the cluster centers, and the ellipses around each center show the covariance matrix of the clusters at four standard deviations. There was a total of 6205 tree stem observations and 140 clusters, i.e., individual tree stems. Figure 13 shows the optimized cluster centers, i.e., tree stem positions, and the covariance structure of the observations at four standard deviations. Local refinement converged after nine iterations. Note that the ellipses representing the covariances of the clusters are smaller after local refinement. This is a result of simultaneously optimizing the position track and the cluster centers.  
To test the accuracy of the stem map generated from the local refinement step, we collected a ground truth stem map of the 12 acre forest, from which we acquired the video and GPS track. We obtained global coordinates for each individual tree in the stand using a TruePulse 360B laser range finder and a 13-bit BEI industrial rotary encoder mounted on a tripod. We installed a reflector target near the center of the stand, at which a GPS coordinate was acquired using a mapping grade receiver. We mapped subsections of the stand by first aligning the laser and encoder to north, using the appropriate declination for the area, then recorded the distance and angle to the target to globally localize the plot center. We recorded the distance and angle to each individual tree within view from the plot center. We repeated this process moving clockwise around the reflector target mapping small subsections of the stand until the entire stand was mapped.  
Figure 14 shows the ground truth stem map (green triangles), the predicted tree stem position from the camera (red circles), and the optimized position track (yellow line) superimposed on an aerial photograph of the stand. We manually associated each observed tree stem position from the camera with its corresponding ground truth tree stem. Among the 140 predicted tree stem positions, we classified 2 observations as false positives, i.e., predicted tree stems that correspond to a tree in the aerial photograph that were not recorded during the collection of the ground truth stem map, and 7 tree stems as duplicate observations, i.e., observed tree stems that belong to the same ground truth stem. For all predicted and ground truth stem correspondences (\(n=140\)), we calculated a RMSE of 2.16 m. This is a 46% improvement over the best-case expected accuracy of a consumer-grade GPS device under forest canopy (4 m).  
Figure 11: Converged globally aligned path with intermittent GPS reception.  
Figure 14: Ground truth tree stem positions and estimated tree stems positions superimposed on an aerial photograph of the 12 ac forest stand. Green triangles denote ground truth stem positions, red circles show the estimated stem position from the camera, the yellow line denotes the optimized position track, and the blue lines show association between observed and estimated tree positions.  
Figure 12: Tree stem position averages (black dots), tree stem position covariances (black ellipses), and pose track (red line) before local refinement  
Figure 13: Tree stem position averages (black dots), tree stem position covariances (black ellipses), and pose track (red line) after local refinement.