# Dilated Filters for Edge-Detection Algorithms
## 5 Conclusions and Future Work  
In this paper, we extend our work (see the previous papers [11; 12]) regarding dilation of a classical convolution edge-detection filters. In Section 3, we present the theoretical background where we present the algorithms that took part in the simulation from Section 4. The experimental results confirm our hypothesis that the dilation of filters have a positive impact for edge detection. From the summary made in Table 1, we can state that the dilated filter yields, generally speaking, better results. This hypothesis was proven using two different metrics, \(PCM\) and \(SFoM\), on two different datasets. The evaluation that we performed helped us demonstrate the initial hypothesis that the dilation of the kernels leads to edge-detection improvements. Dilating first-order derivative kernels yields results similar to the classical 3 \(\times\) 3 kernel in the worst case, and sometimes significant improvements in the best case, as we can see in Figure 7d or Figure 8d. When experimenting with different kernels, we observed that the respective trends in terms of the results is maintained, see Figure 14.  
Dilating the second-order discrete approximation filter did yield considerable improvements to the edge map, as we see in Figure 9c when using the Marr-Hildreth algorithm or in Figure 9d for the Shen-Castan algorithm. When we experimented with different Laplace kernels, we observed the same behavior except with a reduced number of cases such as \(V3\) in the case of Laplace operator; see Figure 15a. When evaluating with the \(SFoM\) metric, we observed improvements overall when using the 5 \(\times\) 5 dilated kernels as we can see Figure 10a-d.  
Statistically and visually, we could observe that by dilating the filters we find more edge pixels than by the classical operators. By dilation, we obtained a better precision and \(F1\)-score, which can be observed in the results we presented. By the simple structure of the dilated filters, they are also a good choice when the runtime matters. The other classical filter extensions from [33; 35; 36; 37; 40] require a larger number of operations in order to return the resulting edge pixels, whereas the custom dilated filters always have the same number of operations for any extension. It seems that the gaps imply a speed up. We can point out that, for the ED algorithm, see Figure 14d, we have obtained the best results when using the \(7\times 7\) kernel with the Prewitt kernel. In Section 4.2, we explored the effect of noise on the dilated filter and concluded that it has a similar effect as in classical filters. We may, in our future work, continue this analysis of the dilated-threshold-noise effect by using different metrics, such as the minimum score proposed by [59]. In our research, we focused on dilating 3 \(\times\) 3 filters, but in our future work, we will concern ourselves in dilating bigger kernels as a starting point. This can be analyzed from the definition of the dilation. Another aspect worth exploring in the future would be to run experiments in automated threshold versions of the algorithms. Our current experiments focused on the classical version of edge-detection algorithms, but looking into the combined effects of dilating and automated threshold could enhance the resulted edge map. In our approach, for comparison purposes, the focus was to fine-tune the classical edge-detection algorithms in order to obtain the optimal threshold and sigma values. We are certain that if we would have fine-tuned the algorithms for the dilated kernel, the results would have been better. In general we can state that using the dilated kernels yields benefits regarding the edge map, as a result of the edge-detection of the classical algorithm and the run-time needed. We obtained similar or better results when taking into consideration a bigger neighborhood. **Author Contributions:** Conceptualization, C.O., V.B., C.B. and R.V. ; Methodology, C.O., V.B. and C.B. ; Software, C.O. ; Validation, C.O., V.B. and C.B. ; Formal analysis, V.B. and R.V.