# _M\({}^{2}\)_Gf: Multi-Scale and Multi-Directional Gabor Filters for Image Edge Detection
## 4 Experiments
### Experiments on the BSDS and NYUD Dataset  
The BSDS and NYUD dataset are widely used for the performance comparison of edge detection methods. Many works have been evaluated on it recently. On the BSDS datasets, the proposed method achieves the maximum area in the PR curves of the compared approaches, which are depicted in Figure 9(a). The results of six  
Figure 9: The magnitudes of pixel values of the “Puppy” image in _RGB_ and CIE \(L^{*}a^{*}b^{*}\) models. (**a**) The “Puppy” image in CIE \(L^{*}a^{*}b^{*}\)_space. (**b**) The “Puppy” image in _RGB_ space. edge detection algorithms on the NYUD dataset are depicted in Figure 10b. Although the algorithm proposed in this paper is not as good as some methods ([42; 43]) based on deep learning in performance, these methods need an extra training process and more parameter operations. In addition, the algorithm designed is higher than most algorithms in the index of F-measure and AP. It is because the designed approach uses the \(L^{*}a^{*}b^{*}\) color space, Gabor filters and some local detail processing, which can accurately obtain the information of edges. In addition, the application of multi-scale and multi-direction technology makes it have better anti-noise performance. At the same time, the indexes of \(F_{ODS}\), \(F_{OIS}\), and \(R50\) are illustrated in Tables 1 and 2, and the designed approach achieves better performance. In this experiment, four original color images are depicted in the first column of Figure 11. The ground truths of the corresponding images are presented in the second column of Figure 11. The detection results of the Color Canny method [37], the CMG method [26], the Laplacian method [30], the I-Sobel method [31], the AGDD method [20], the ColorED method [35] and the proposed method are depicted in the 3 th, 4 th, 5 th, 6 th, 7 th, 8 th and 9 th columns of Figure 11, respectively. Intuitively, the designed method can accurately extract and detect edge information. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & \(\mathbf{F}_{ODS}\) & \(\mathbf{F}_{OIS}\) & **AP** & **R50** \\ \hline Color Canny [37] & 0.563 & 0.576 & 0.570 & 0.578 \\ Laplacian [30] & 0.598 & 0.615 & 0.583 & 0.725 \\ I-Sobel [31] & 0.581 & 0.587 & 0.586 & 0.693 \\ CMG [26] & 0.611 & 0.636 & 0.607 & 0.751 \\ ColorED [35] & 0.617 & 0.629 & 0.618 & 0.771 \\ AGDD [20] & 0.634 & 0.651 & 0.632 & 0.797 \\ Proposed & 0.672 & 0.695 & 0.652 & 0.828 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation indicators obtained on the BSDS dataset. Figure 10: The results on the BSDS [48] and NYUD [49] datasets. (**a**) Detection performance based on the BSDS dataset. (**b**) Detection performance based on the NYUD dataset. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & \(\mathbf{F}_{ODS}\) & \(\mathbf{F}_{OIS}\) & **AP** & **R50** \\ \hline CMG [26] & 0.651 & 0.661 & 0.637 & 0.773 \\ ColorED [35] & 0.673 & 0.667 & 0.653 & 0.794 \\ AGDD [20] & 0.677 & 0.716 & 0.629 & 0.804 \\ HED [42] & 0.741 & 0.757 & 0.749 & 0.900 \\ RCF [43] & 0.765 & 0.780 & 0.760 & 0.888 \\ Proposed & 0.685 & 0.708 & 0.689 & 0.843 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evaluation indicators obtained on the NYUD dataset. In addition, when noise of \(\varepsilon_{w}=15\) is added to the above four images, the performance of the different approaches is as depicted in Figure 12. The noisy color images are depicted in the first column of Figure 12. The ground truth maps of the noisy images are depicted in the second column of Figure 12. The detection results of the Color Canny method [37], the CMG method [26], the Laplacian method [30], the I-Sobel method [31], the AGDD method [20], the ColorED method [35] and the proposed method are shown in the 3 th, 4 th, 5 th, 6 th, 7 th, 8 th and 9 th columns of Figure 12, respectively. The FOMs of the different edge detection methods are described in Table 3. The comparison illustrates that the designed approach has better noise robustness. However, it is complicated and time-consuming to use multi-direction