## 3 Experimental Results
### Traffic Sign Candidate Detection and Classification Results  
To evaluate the performance of the proposed traffic sign candidate detection and classification method, we conducted extensive experiments on the same 20 sections of the road. Figure 7 presents extracted road regions in both color images and their associated LiDAR data for four selected regions, which were cropped from the sections of the road for better illustration purpose. In each row, we demonstrate the color image of one of four cropped sections of the road and its corresponding road extraction results alongside with its associated geo-referenced LiDAR data and its corresponding road extraction results. It should be mentioned that these four sections contained various objects including the road, buildings, parking lots, vegetation, traffic signs, billboards, and bridges to illustrate the effectiveness of traffic sign detection results. Figure 7 clearly shows that road regions extracted from color images were correctly mapped to the corresponding road regions in the LiDAR data by employing the image to global coordinate projection. Since it is much easier to extract road regions in a color image using complementary features, we utilized road extraction results in color image to quickly find road regions in LiDAR data. Utilizing a histogram to obtain height statistics, we could quickly remove high elevated objects above the road to find traffic sign candidates in the LiDAR data. Figure 8 demonstrates traffic sign candidates that were extracted from road regions presented in Figure 7, where each row shows extracted traffic sign candidates for each section of the road. These candidates were fed into the sparse classifier optimization model to be classified to a traffic sign class or a non-traffic sign class by empirically setting the parameter \(p\) to be 0.6 as shown in Figure 2. We labeled the classification result of each traffic sign candidate at the bottom left of each airborne color image with \"TS\" indicating a traffic sign and \"NTS\" indicating a non-traffic sign. To quantitatively evaluate the proposed traffic sign detection method, we provided its true positives, false negatives, and true negatives on all the 20 sections of the dataset containing 17 traffic signs in total. The proposed method extracted 24 traffic sign candidates by removing high elevated objects above the road in the LiDAR data. The deep-features-based sparse classifier correctly classified 14 out of 24 candidates as traffic signs (true positives), incorrectly classified three out of 24 candidates as non-traffic signs (false negatives), and correctly classified seven out of 24 candidates as non-traffic signs (true negatives). In other words, the proposed method was able to successfully extract 14 out of 17 traffic signs and achieved the detection accuracy of 82.35%. We further provided four evaluation measures including recall (detection rate), precision, \(F_{1}\)-measure, and quality in Table 1. These measures were computed as follows:  
\[Recall=\frac{\text{True Positives}}{\text{True Positives}+\text{False Positives}} \tag{11}\]  
\[Precision=\frac{\text{True Positives}}{\text{True Positives}+\text{False Negatives}} \tag{12}\]  
\[F_{1}\text{-}measure=2\times\frac{\text{Precision}\times\text{Recall}}{ \text{Precision}+\text{Recall}} \tag{13}\]  
\[quality=\frac{\text{True Positives}}{\text{True Positives}+\text{False Positives}+\text{False Negatives}} \tag{14}\]  
It shows that the proposed method achieved an average precision of 82.35%, a recall of 100%, a \(F_{1}\)-measure of 90.32%, and a quality of 82.35%. This performance is attributed to the use of the optimization with equality constraints to more accurately classify a pixel as road or non-road, the use of deep features to more accurately representing the visual data of candidates, and the use of the sparse classifier optimization model to more accurately classify each candidate as traffic sign or non-traffic sign.