# Efficient Filtering for Edge Extraction under Perspective Effect
## 5 Experiments
Hence, the optimal scale and the expected orientation could be computed for the optimal response at each location. In this paper, we use road images to validate the performance of the proposed algorithm. In this paper, we use a dataset provided by a previous study to compare the proposed edge detector with other algorithms [40]. This dataset consists of 116 high-quality color road images, which are captured in different scenarios. For each image, the lane marking areas are manually labeled as the ground truth. Some examples of the dataset and the corresponding human labeled ground truth are shown in Figure 11. We employ the whole dataset for evaluation. In the evaluation, if an edge point labeled by an algorithm is near the edge of the ground truth (the block distance between them is less than two pixels), we consider it to be marked correctly. In this experiment, both the ROC (receiver operating characteristic) curve [41] and DSC (dice similarity coefficient) curve [42] were used to evaluate these algorithms. ROC reflects the true-positive rate (hit rate) against the false-positive rate (false alarm rate) while shifting the threshold from zero to one. The area under the ROC curve (AUC) is called the ROC score and it reflects the performance of the algorithm. In this experiment, the false-positive rate and the true-positive rate were computed by matching the edge map given by an algorithm to the one of the ground truth at each threshold value. The DSC curve is another evaluation method, which records the DSC values against the thresholds. The maximum DSC values are a measure of the performance of an algorithm at the optimal threshold setting. The DSC value is defined as \(DSC=\frac{2*TP}{TP+TP+T}\), where TP is the true positive, FP is the false-positive, and T is the true point in the ground truth. We compared our approach oDoB, tuning both the orientation and scale to the Canny edge detector. There are two versions of our method: one is only tuning the orientation (oDoB); the other is tuning both the orientation and scale (osDoB). We slide the threshold for each model from 0 to 1 and recorded these threshold edge maps. We then computed the ROC and DSC curves for each model. Some examples of the comparison are shown in Figure 12. We show here six road images with different scenarios. In each grid, the top row shows the input image, the expected orientation map, and the expected scale map (from left to right). These maps can be computed using the estimated imaging parameters and the estimated vanishing points. In the lower part of the the figure, there are three columns showing the results of Canny, oDoB (only tuning the orientation) and oNoDo (tuning both the orientation and scale). Each column contains two maps: the gradient magnitude map (top) and the edge map (bottom). Figure 11: Some examples from the dataset and the corresponding labeled ground truths [40]. Figure 12: Some comparison results on road images. See text for more details. As shown in Figure 12, the proposed model can handle both curving lane markings (as shown in Figure 12e) and straight one. From these examples, we observe that the orientation tuning is of great importance for edge detection. As shown in Figure 12a,c, most of these heavy shadows in the road surface were removed. This is very helpful as, without it, the wrong edge points, such as those caused by the shadows on the road surface, referred to as the corresponding edge detection results by Canny, will yield spurious peaks in the Hough space. It has been believed that, for Canny edge detector, this type of problem can be handled by combining an orientation map. These false edge points can be removed by examining the orientation gradient at the expected orientation. In the following, we will show that this is not true. As shown in Figure 13, there are two cases in which orientation tuning will play an important role. In the first case, orientation tuning removes noisy edges with unexpected orientations.