# Efficient Filtering for Edge Extraction under Perspective Effect
## 5 Experiments  
We first used a synthesized image to show the performance of the proposed method in detecting objects with different scales and orientations. Then, we performed experiments on real-world images under the perspective effect. Many edge detectors have been developed in the last few decades, such as those of Sobel, Prewitt, Roberts, etc. Though the Canny detector [37] was proposed in the early days of computer vision, it is still a state-of-the-art edge detector with high efficiency. Edge detectors with better performance than Cannyusually require longer computation time [38; 39]. Thus, in this experiment, we qualitatively compared our method with the Canny detector, and compared our method with the Canny, Sobel, Prewitt and Roberts detectors quantitatively. Figure 10 shows the synthesized image employed for comparison. The objects we used were rectangles from different orientations and scales. In this image, there are nine objects in a 3 \(\times\) 3 array. In each row, objects have the same scale. In each column, objects have the same orientation. Here, we chose the direction of the longer side of rectangle as the localized target orientation for osDoB. Therefore, osDoB was supposed to only extract the edge along the orientation of object and have little response on other orientations, especially in the direction of the shorter side of the rectangle. Thus, Canny is supposed to extract all the edges of the objects. Images near the top of Figure 10 show the noisy initial image, the gradient map produced by the proposed method (osDoB, tuning both the scale and orientation), and the edge map produced by osDoB. Near the bottom of the figure, there are three edge maps produced by the Canny edge detector with different scales for the Gaussian blurring kernels. We can see that osDoB only extracts edges corresponding to the preset orientation, but has the ability to detect all of the objects well with quite acceptable localization accuracy. However, for the Canny detector, it is difficult to detect all the objects simultaneously, even using different scales. We observe that, if the Gaussian kernel scale is small, false edges caused by noise will pop out; if the scale is large, the small objects will disappear and the shapes of large objects will be deformed. Another reason why the shape of the large objects was destroyed is as follows. In the Canny detector, a symmetric kernel is used (Gaussian kernel). The aspect ratio of this kernel is 1. As discussed above, such an aspect ratio corresponds to a very low angular accuracy, so it must affect the localization accuracy. However, in the proposed method, the aspect ratio can be selected arbitrarily. In this experiment, we use a 3:1 aspect ratio, and thus yield a quite good angular accuracy. It is worth noting that osDoB may totally fail if we have no knowledge of the localized target orientation. Thankfully, in a real scene, which we will discuss below, we can obtain both the localized target size and localized target orientation from prior knowledge about the scene and perspective effect in imaging process. The perspective effect is always present in the imaging process in both human and mechanical vision. In computation, it is very hard to assign the special orientation and scale for each location in the image. The expected orientation and scale can be determined using the following two factors: first, the extrinsic and intrinsic parameters of the imaging equipment; second, the prior of the targets/objects to be detected. As mentioned in the  
Figure 10: Performance of the proposed method and Canny detector on a noisy synthesized image. proceeding section, there is one case, road detection, in which we can determine the orientation map and scale map ahead of time under certain constraints. The intrinsic and extrinsic parameters of the imaging equipment are known beforehand, and other parameters regarding the road shape and the relative relationship between the road and vehicle can either be obtained by tracking or set to constants.