## 3 Experimental Results
### Road Extraction Results  
To evaluate the performance of the proposed road extraction method, we conducted extensive experiments on 20 sections of the road. Each section section(i) (\(i=1,\cdots,20\)) contained different kinds of objects such as road, buildings, vegetation, parking lots, etc. Figure 3 demonstrates _section(1)_ of a geo-referenced color image of the dataset that contains objects such as road, vehicles, building, and vegetation commonly seen on a highway. We generated six feature matrices from over-segmented regions [27] of the input image on six sets of complementary layers [11], which represented the input image from different perspectives. The six sets of layers included color layers of CIE-LAB and \(YC_{b}C_{r}\) color spaces, gradient layers of Gaussian and Laplacian of Gaussian, soft segmentation layers [28] of first three principal components, a texture layer [29], a combined color and soft segmentation layer, and a combined color, gradient, soft segmentation, and texture layer. We then extracted local spectral histogram (LSH) for image  
Figure 3: A sample section of a geo-referenced color image of the dataset. six layers. A feature vector by averaging features of all pixels within a region represented characteristic features of the region. The feature vectors for each over-segmented region were combined to construct the corresponding feature matrix. For the last step of road and non-road extraction, we extracted the aforementioned local features for \(n_{sf}\) pixels in road regions and construct the road dictionary. Similarly, we built the non-road dictionary by extracting the local features for \(n_{sf}\) pixels in non-road regions. For all experiments, we set \(\gamma\) in (3) as 10 to control the smoothness of the result. We qualitatively demonstrated road extraction results on four sections of the road (i.e., _section(1), section(2), section(3)_, and _section(4)_) in Figure 4 and another four sections of the road (i.e., _section(5), section(6), section(7)_, and _section(8)_) in Figure 5. The _section(1)_ and _section(2)_ in Figure 4 demonstrate the conditions with low traffic flows while _section(7)_ and _section(8)_ in Figure 5 demonstrated the conditions with high traffic flows. The _section(6)_ and _section(8)_ in Figure 5 had road bypass with vegetation in between. The _section(1)_, _section(3)_, and _section(4)_ in Figure 4 had buildings along the road and _section(2)_ had the highest vegetation along the road among all the demonstrated sections. The road extraction results for all sections shown in Figures 4 and 5 clearly demonstrated the robustness of the proposed method in extracting road regions under multiple conditions including different traffic flows, different road-side buildings, various road shapes, and various road-side objects (i.e., vegetation, building, and parking lot). Figure 4: Road extraction results for four sections of the road, _section(1), section(2), section(3)_, and _section(4)_. To demonstrate the effectiveness of the last learning step of the road extraction method, we further compared road extraction results with the results without involving learning on 20 sections of airborne color images. Figure 6 compares road extraction results before employing the last learning step and after employing the last learning step for four selected sections, namely, _section(1), section(3), section(5)_, and _section(7)_. The results before learning (BL) clearly showed that buildings, parking lots, and vegetation regions were part of road extraction results since they were similar to the road. The results after learning (AL) showed that with the help of the learning step, the proposed road extraction method effectively identified the road region and removed buildings, parking lots, and vegetation regions that were similar to the road region. These comparison results showed the effectiveness of using the optimization with equality constraints to remove objects that were similar to the road from the extraction results (i.e., to better classify a pixel as road or non-road).