# Dilated Filters for Edge-Detection Algorithms
## 4 Experimental Results
### Effect of Dilation
#### 4.1.1 Operators Based on First-Order Discrete Kernels  
In Figure 7a, we present the results for the first-order derivative orthogonal gradient operator. As we can observe, we have searched for the best \(F1\) results in a range of the threshold between 30 and 160 with a step of 10 and sigma value between 0.25 and 3.0 with a step of 0.25. As expected, a higher threshold will produce less edge points, as we can see in Figure A8, but with a fair confidence that resulted in a high \(R\) because of the lack of points. For the images, we use the following notations: Gaussian sigma is \(S\) and threshold is \(TG\). From the results presented in Figure 7a, we can observe that we obtain equal \(F1\) scores for the \(3\times 3\) classical, \(5\times 5\) extended and \(7\times 7\) dilated kernel versions. On the other hand, we clearly see that expanding the kernel to \(7\times 7\) performs worse than dilation; the best results with \(7\times 7\) extensions were 0.374. In Figure 7b, we follow the \(F1\) results for the first-order derivative compass gradient operators using some similar ranges of the threshold, between 30 and 160, and sigma value between 0.25 and 3.5. In the figure, we use the the same notations: Gaussian sigma is \(S\) and threshold is \(TG\). In Figure 7b, we can notice that the \(3\times 3\) classical kernel obtains equal results similar to the \(5\times 5\) dilated or \(7\times 7\) dilated version. A notable difference in this case is the lack of extended kernels as they were not present in the literature. The Frei-Chen operator is a special case of the compass gradient operators and is presented Section 3.4. We fine-tune the parameters of the algorithm for a range of the threshold between 30 and 160 and sigma value of the Gaussian filter blur between 0.25 and 3.2. The results are presented in Figure 7c, where we use the same notations: Gaussian sigma is \(S\) and threshold is \(TG\). In this case with the Frei-Chen operator, the \(7\times 7\) dilated kernel version yields the best \(F1\) results followed by the dilated \(5\times 5\) kernel. Similar to the compass gradient operators, an extension of this operator was not found in the literature for comparison. One of the most popular first-order-derivative-based edge-detector operator is Canny, presented in Section 3.8. For parameter tuning, we varied the following configurations: Gaussian sigma value from 0.2 to 3.0 with a step of 0.25, low threshold from 70 to 150 with a step of 10 and high threshold from 90 to 200 with a step of 10. We performed the parameter tuning phase for the original kernel, extended and dilated to find the best suited ones. For the images, we use the following notations: Gaussian sigma is \(S\), low threshold is \(TL\) and high threshold is \(TH\). Figure 7: Best results on \(BSDS500\) for classic, extended and dilated using different parameters for: (**a**) first-order derivative orthogonal gradient operators; (**b**) first-order derivative compass gradient operators; (**c**) Frei–Chen edge operator; (**d**) Canny operator; (**e**) ED edge operator. For the ED algorithm, described in Section 3.10, we searched for the best combination of Gaussian smoothing kernel size, gradient threshold, anchor threshold and scan interval interval. We varied the parameters as follows: Gaussian kernel (\(GK\)) between 3 to 9 with a step of 2; gradient threshold (\(TG\)) between 10 and 150 with a step of 10; anchor threshold (\(TA\)) between 10 and 60 with a step of 10; scan interval (\(SI\)) in range of 1, 3, 5. As we can see in Figure 7d,e, the best results we obtain were when using the \(7\times 7\) dilated filter. Another conclusion we draw is that using extended kernels will produce a significant degradation of the edge map results, supported by the lower score. An aspect worth mentioning for these two algorithms, Canny and ED, is the fact that for the ED algorithm, when using extended kernels, good results are obtained; it is also similar for the dilated \(7\times 7\) case.