# Efficient Filtering for Edge Extraction under Perspective Effect
## 1 Introduction
There have been several studies on the process of computing the edge response at an arbitrary orientation and scale, such as steerable filter [19] and deformable filter [20], but the original purpose of these studies is to obtain the responses from multiple orientations and multiple scales with only a few basic filters. For high accuracy of edge response, they still need to spend a large amount of time using a large number of basic filters. In this paper, we propose a novel efficient filtering approach called _orientation and scale tuned_ difference of boxes (osDoB) for edge extraction. By implementing the difference of boxes (DoB) filter [7] on an integration map, we can reduce the computation needed for local filtering to only five add/subtract operations. This allows us to tune the box size, which is related to the scale of the edge, to any value easily. By rotating the original image to multiple orientations to generate the integration map, we can tune the relative pose of the image and filter to a specific orientation. By adjusting the aspect ratio of the DoB filter, we can gain a response with sharp directional profile. The osDoB filters can thus be easily tuned by scale and orientation, and also efficiently realized. Recently, deep learning (DL) has achieved great success in computer vision tasks, including edge detection [21; 22]. Most DL-based methods directly regress the edge map after training on a dataset. Compared to these DL methods, our method has three main advantages. First, our method is hand-crafted while DL methods are data-driven. Thus, our method does not require large-scale and expensive pixel-level annotations, which are  
Figure 1: Illustration of the orientation and scale tuning at each location of the input image. (**a**) Kernels of different scale and orientation for best detection of the lane markings. (**b**) Scale and orientation assignment according to the prior knowledge. essential for DL methods. Second, our method of working by linear filtering is very efficient and hardware-friendly. Nevertheless, DL methods have a large number of parameters and occupy huge computation resources, which is a big challenge for deployment on low-cost on-chip devices. Considering that edge detection is usually only used as a prerequisite for other advanced tasks, this challenge is even more severe. Third, due to the high degree of non-linearity, DL methods are difficult to interpret. In contrast, with our method it is easy to analyze and interpret the results. The performance of our method is verified on both synthetic and real data. The real data is from the traffic scene and we choose lane marking as the target for edge extraction. Edge extraction for lane markings is a typical application in driver assistant systems (DAS). Furthermore, it is possible for us to compute the localized target size and localized target orientation ahead of edge extraction. Experimental results show that performance can be improved by assigning appropriate orientation and scale parameters for edge extraction. We also demonstrate that the early stage orientation tuning strategy used in our method cannot be replaced by a refined Canny detector combined with an orientation map at a later stage. The main contributions of this work are threefold:  
* We deduce the relationship between the best scale parameter of certain filters and the localized target size. * A novel approach, called osDoB, is proposed for edge extraction. The proposed method can extract edges efficiently with preset scale and orientation. * We demonstrate that osDoB can improve the performance of edge extraction for lane marking by tuning the local filter ahead of time. The paper is organized as shown in Figure 2: in Section 2, we discuss the problem of optimal scale and orientation assignment for the local edge detector.