# Dilated Filters for Edge-Detection Algorithms
## 4 Experimental Results
### Noise Effect on Dilation  
Edge detection algorithms have a different sensitivity regarding the noise level of the input image. In this section, we analyze the effect that the addition noise had upon the resulting edge map, when using a dilated filter. To do so, we used an image from the synthetic dataset [12] and applied it to different levels of noise (Gaussian noise) at various peak signal-to-noise ratio (PSNR) values (from 16 dB to 10 dB), see Figure 11. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Operator** & & & & **PCM [69]** & & & **SFOM [58]** \\ \hline  & **Kernel** & \(P\) & \(R\) & \(F1\) & **Parameters** & **Kernel** & **SFOM** & **Parameters** \\ \hline First Order Orthogonal & 7 \(\times\) 7(D) & 0.571 & 0.679 & 0.621 & \(\text{TG}=50,5=2.75\) & 7 \(\times\) 7(D) & 0.754 & \(\text{TG}=30,5=2.25\) \\ First Order Compass & 5 \(\times\) 5(D) & 0.565 & 0.687 & 0.620 & \(\text{TG}=50,5=2.25\) & 7 \(\times\) 7(D) & 0.753 & \(\text{TG}=30,5=2.25\) \\ [PERSON] & 5 \(\times\) 5(D) & 0.554 & 0.673 & 0.608 & \(\text{TG}=60,5=2.25\) & 7 \(\times\) 7(D) & 0.481 & \(\text{TG}=30,5=0.25\) \\ Laplace & 7 \(\times\) 7(D) & 0.309 & 0.794 & 0.445 & \(\text{TG}=95\) & 5 \(\times\) 5(D) & 0.478 & \(\text{TG}=15\) \\ LoG & 7 \(\times\) 7(D) & 0.490 & 0.659 & 0.562 & \(\text{TG}=30,5=18\) & 7 \(\times\) 7(D) & 0.491 & \(\text{TG}=5,5=1.0\) \\ Marr-Hildreth & 7 \(\times\) 7(D) & 0.450 & 0.744 & 0.561 & \(\text{TG}=62,5=2.0\) & 5 \(\times\) 5(D) & 0.411 & \(\text{TG}=62,5=1.6\) \\ Canny & 7 \(\times\) 7(D) & 0.478 & 0.813 & 0.602 & \(\text{TG}=15,\text{TL}=90,\text{TL}=130\) & 7 \(\times\) 7(D) & 0.679 & \(\text{S}=2.25,\text{TL}=70,\text{TL}=100\) \\ Shen-Castan & 7 \(\times\) 7(D) & 0.483 & 0.711 & 0.576 & \(\text{TG}=4,\text{SF}=90,\text{WL}=11,\text{TL}=0\) & 5 \(\times\) 5(D) & 0.442 & \(\text{TG}=4,\text{SF}=90,\text{WL}=11,\text{TL}=0.5\) \\ ED & 7 \(\times\) 7(D) & 0.556 & 0.704 & 0.621 & \(\text{TG}=50,\text{TL}=5,\text{S}=1,\text{GK}=7\) & 3 \(\times\) 3 & 0.673 & \(\text{TG}=50,\text{TL}=5,\text{S}=1,\text{GK}=7\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overall best results for each edge operator analyzed. In order to have a complete evaluation of the dilated filter impact, we conducted similar experiments for noise sensibility analysis, as was presented in [58; 59; 75]. To maintain consistency in our evaluation, we used the two algorithms presented in Section 3. For each image with different noise levels, we varied the algorithm parameter as we described in Section 4.1; however, we evaluated them using the \(SFoM\) measure. We chose the first-order derivative orthogonal gradient algorithm as we consider it to be the most sensitive to noise from the first-order derivative group. Similar to the second-order derivative group, we chose the Laplace operator. In order to have a more objective analysis we have eliminated the smoothing step from the first-order gradient, see Algorithm 2. Further, for a complete evaluation of the dilated filter impact we conduct similar methodology for noise sensibility analysis, as was presented in [58; 59]. In Figure 12, we highlighted the visual results obtained for first-order gradient algorithm. In the first row are the filtered images without any noise, for 3, 5, 7, dilated 5 and dilated 7 filters. For each new row the noise increases from 16 dB to 10 dB. We can observe that dilation is not that sensible for noise, and requires statistical analysis. Interpreting the statistical results that we obtained in Figure 13, one can observe that the noise has the same effect upon the classical or dilated versions of the filters. We can observe as the noise level is growing the median and maximum value of the \(SFoM\)  
Figure 11: Image used to evaluate at different levels of noise (PSNR). Figure 12: Visual results at different levels of noise (PSNR) for one image. Rows represent: original; 16 dB; 14 dB; 12 dB; 10 dB. decreases. For the first-order derivative orthogonal gradient operator, the noise does not have a huge impact over our dilated proposed approach.