## 4 Experiments and Discussions  
The numerical experiments were carried out using Matlab on an AMD Rysen 5 2500U, 2 GHz. The software is a version of the image edge detection using Ant Colony Optimization version 1.2.0.0. from MATLAB Central File Exchange [27]. The MATLAB implementation [28] of the Canny edge detection algorithm is based on [15].The software makes use of two thresholds in order to detect strong and weak edges; the weak edges are provided in the solution only if they are connected to the strongest ones: \"a high threshold for low edge sensitivity and a low threshold for high edge sensitivity\", as is specified in the software documentation [28]. In order to convert a gray-scale input image to a binary image, thresholding is used. _Data set._ A dataset of medical images, free of copyright, was used for these experiments: _Brain CT_ (could be provided by request from the authors), _Hand X-ray_[29], (reduced resolution from \(225\times 225\) to \(128\times 128\)) and _Head CT_[30]. Several details are included in the Github page (Representation of results available at [[https://github.com/cristina-ticala/Sensitive_ACO](https://github.com/cristina-ticala/Sensitive_ACO)]([https://github.com/cristina-ticala/Sensitive_ACO](https://github.com/cristina-ticala/Sensitive_ACO)); accessed on October 2021). _Filtering._ In order to filter the medical images, the De-Noise convolutional neural network (DnCNN) was used in the present study, as well as in our previous related work [18]. The Image Processing Toolbox and Deep Learning Toolbox from Matlab [31] were used. _Parameters._ Most of the parametric numbers are from [22]. In our previous work [18], we tested several parameters; in the present study, we used the best of them. _Image-related parameters:_ The image dimension influences and gives ACO and SACO a number of artificial ants \(K=\lfloor\sqrt{M1\times M2}\rfloor\), where \(\lfloor\) and \(\rfloor\) are the left and right rounded values to the nearest integers less than or equal to \(x\); e.g., for a \(128\times 128\) image resolution, the number of ants is considered 128. Iterations related parametersIn [18] just 30,000 iterations for \(L=100\) steps were considered; here, we tested a smaller (1200 iterations for \(L=4\) steps) and a higher number of steps \(L=1000\) (300,000 iterations). An ant makes 300 moves at each step; e.g., for 128 ants (e.g. image resolution: \(128\times 128\)), 38,400 moves are made during each step. Therefore, for \(L=4\), it is a total of 153,600 moves, 3,840,000 moves for \(L=100\) and a total of 38,400,000 ants' moves for \(L=1000\) steps. Connectivity-related parametersThe connectivity neighborhood parameter \(\Sigma=8\) is based on the ants' movement range (Equation (6)). Pheromone trail parametersthe value of each matrix component \(\tau_{init}=0.0001\); the weighting factors of pheromone information \(\alpha=1\) and of heuristic information \(\beta=0.1\) (Equation (6)); the evaporation rate, \(\rho\), is 0.1 (Equation (9)) and the value of the pheromone decay coefficient \(\psi\) is 0.001 (Equation (12)). Other parametersThe adjusting factor \(\lambda\) of the functions (Equations (3)-(5)) is 10. The tolerance parameter (\(\epsilon=0.1\)) is used in the decision process. The stopping criterion is given by the maximal number of steps (\(L\)) set by the user. ComparisonBeside the Canny algorithm, the Roberts, the Sobel and Prewitt edge algorithms were also used for comparison; the last two methods compute the horizontal and the vertical gradient of an image by using two orthogonal filter kernels, and after filtering, they compute the gradient magnitude and apply a threshold in order to find the regions of the image corresponding to the edges. Furthermore, the Roberts algorithm detects image edges at angles of 45 degrees and/ or 135 degrees from horizontal [32].