# SNR Analysis for Quantitative Comparison of Line Detection Methods
## 2 Related Work  
Pixels in an image were classified into edges, ridges, valleys, and other geometric features based on the analysis of the coefficients resulting from fitting a Legendre polynomial of 2 degrees or less with local intensity in [22]. However, this approach has a nontrivial problem with line detection because it requires multiple steps to detect line pixels and a set of well-tuned thresholds. In another study, ridges and valleys were detected by finding zero crossings of the first-order directional derivatives in [1]. The method was based on 10 coefficients resulting from fitting a bivariate cubic polynomial to local intensities. One of the limitations of this method is that it may produce nontrivial ringing artifacts, and the approach requires a large window size for the 10 coefficients of the bivariate cubic polynomial to be calculated. A Zernike moment-based edge and line detection method was proposed in [23], which was a parameter-based edge and line detection method. Differential geometry was used to detect the line pixels in [2,3]. One of the limitations with this approach is that it requires a high processing time to calculate the first-, second-, and third-order derivatives. A line detection approach based on second-order derivatives was proposed in [19,24]. In a similar study, this SD-based approach was used to detect line pixels in aerial images and synthetic aperture radar (SAR) images [25,26]. However, as it will be shown in the following sections, the SD-based line detection methods have limitations under relatively large line widths. A multi-scale-based line detection approach was proposed in [24]. This approach may, however, face limitations when line features are located close to other non-homogeneous features. These limitations are attributed to the blending of neighboring features at a larger scale.  
A simple line detection method using relational operations was proposed in [4]. Although its computational cost is low, one of the limitations of this approach is that selecting an appropriate window size depends on the width of a line to be detected.  
However, multi-scale anisotropic Gaussian kernels were used for line detection in [27]. This approach has a problem of high computational cost. Moreover, a multi-step-based line detection approach was proposed in [28], and its computation is cost-intensive because of the convolution of a set of filters and a sequence of steps. Recently, a convolutional neural network-based approach was proposed to detect the boundaries among walls, floors, and ceilings in [29]. However, this approach requires a well-trained network to implement boundary detection and detects only predefined types of boundary pixels such as wall-wall, wall-ceiling, and wall-floor.  
Furthermore, a creaseness measure was used to detect line pixels in [21]. One of the limitations of this approach is that a simple sum of gradient differences may lose the direction information in detecting line pixels. The SGAD-based line detection approach resolved this limitation using the addition of absolute values of gradient angle differences [6].