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Fig 13: Comparison of the execution times of two algorithms having similar parameters using Lenna image International Journal of Computer Applications (0975 — 8887) Volume 103 — No.4, October 2014

Figure 13 Comparison of the execution times of two algorithms having similar parameters using Lenna image International Journal of Computer Applications (0975 — 8887) Volume 103 — No.4, October 2014

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This step is one of the key parts of this algorithm which reduces the execution time. Assuming existence of edge environs the central pixel, if the value of central pixel is higher (brighter) than the average value of its neighboring pixels, the central pixel cannot be an edge, because there are pixel(s) in the neighborhood of this pixel, which are boundary of intensity; so there is no necessity to carry out calculations on the central pixel. The proposed algorithm limits calculations to the pixels which are darker or equal to average of their neighboring pixels that leads to reduce the processing effort. Pixels which match the equation 1 are selected for the next steps. Fig 1: Determining gradient value and angle class. Angle class of: a) zero and 180, b) 45 and 225, c) 90 and 270, d) 135 and 315 degrees
This step is one of the key parts of this algorithm which reduces the execution time. Assuming existence of edge environs the central pixel, if the value of central pixel is higher (brighter) than the average value of its neighboring pixels, the central pixel cannot be an edge, because there are pixel(s) in the neighborhood of this pixel, which are boundary of intensity; so there is no necessity to carry out calculations on the central pixel. The proposed algorithm limits calculations to the pixels which are darker or equal to average of their neighboring pixels that leads to reduce the processing effort. Pixels which match the equation 1 are selected for the next steps. Fig 1: Determining gradient value and angle class. Angle class of: a) zero and 180, b) 45 and 225, c) 90 and 270, d) 135 and 315 degrees
Fig 4: Post reduction of noise. a) The pattern which is removed, b) The pattern which is not removed Now, edges are obtained with one pixel width and it is likely that there are pixels in image which are not along the edges. This is related to selecting threshold. When a threshold is lower than its proper value, although more edges are obtained, noisy points increase. In fact, this step is designed for making flexibility to select threshold and also completing the smoothing step of this algorithm.
Fig 4: Post reduction of noise. a) The pattern which is removed, b) The pattern which is not removed Now, edges are obtained with one pixel width and it is likely that there are pixels in image which are not along the edges. This is related to selecting threshold. When a threshold is lower than its proper value, although more edges are obtained, noisy points increase. In fact, this step is designed for making flexibility to select threshold and also completing the smoothing step of this algorithm.
Accuracy is ratio of total number of correct detection to total number of correct and incorrect detection. Accuracy diagram (Figure 7) shows higher values in all the thresholds for the proposed algorithm. Fig 7: Accuracy diagram for comparison to Canny’s algorithm and LOG algorithm having similar parameters
Accuracy is ratio of total number of correct detection to total number of correct and incorrect detection. Accuracy diagram (Figure 7) shows higher values in all the thresholds for the proposed algorithm. Fig 7: Accuracy diagram for comparison to Canny’s algorithm and LOG algorithm having similar parameters
Fig 6: Precision-Recall diagram for comparison to Canny’s algorithm and LOG algorithm having similar parameters
Fig 6: Precision-Recall diagram for comparison to Canny’s algorithm and LOG algorithm having similar parameters
Fig 8: ROC diagram for comparison to Canny’s algorithm and LOG algorithm having similar parameters International Journal of Computer Applications (0975 — 8887) Volume 103 — No.4, October 2014
Fig 8: ROC diagram for comparison to Canny’s algorithm and LOG algorithm having similar parameters International Journal of Computer Applications (0975 — 8887) Volume 103 — No.4, October 2014
Fig 10: Rosin-Venkatesh diagram for comparison to Canny’s algorithm and LOG algorithm having similar parameters Fig 9: F-Measure diagram for comparison to Canny’s algorithm and LOG algorithm having similar parameters
Fig 10: Rosin-Venkatesh diagram for comparison to Canny’s algorithm and LOG algorithm having similar parameters Fig 9: F-Measure diagram for comparison to Canny’s algorithm and LOG algorithm having similar parameters
Fig 12: Evaluated area of the outputs with similar parameters compared to the white area in the main image. Results of: a) The proposed algorithm with average filter, b) The proposed algorithm with Gaussian filter, c) Canny’s algorithm For evaluation of locality of edges, a separate evaluating program was implemented in C# and one of the famous images in edge detection field was used. Figure 11 illustrates this image that contains types of straight, diagonal and curve lines. So this is appropriate for evaluation of locality.
Fig 12: Evaluated area of the outputs with similar parameters compared to the white area in the main image. Results of: a) The proposed algorithm with average filter, b) The proposed algorithm with Gaussian filter, c) Canny’s algorithm For evaluation of locality of edges, a separate evaluating program was implemented in C# and one of the famous images in edge detection field was used. Figure 11 illustrates this image that contains types of straight, diagonal and curve lines. So this is appropriate for evaluation of locality.
Fig 11: Applied image for evaluation of locality
Fig 11: Applied image for evaluation of locality
Therefore we can conclude that in this algorithm, there are fewer displacements of edges compared to Canny’s algorithm.
Therefore we can conclude that in this algorithm, there are fewer displacements of edges compared to Canny’s algorithm.
As Table 2 shows, because Canny’s algorithm checks threshold at the end of the algorithm, changing thresholds does not change the execution time. The subject that affects the speed of Canny’s algorithm is to trace pixels between two thresholds in order to find a path to the edges.
As Table 2 shows, because Canny’s algorithm checks threshold at the end of the algorithm, changing thresholds does not change the execution time. The subject that affects the speed of Canny’s algorithm is to trace pixels between two thresholds in order to find a path to the edges.
Fig 14: Visual comparison of the output results of two algorithms having similar parameters. a) Result of the proposed algorithm, b) Result of Canny’s algorithm ig 15: Visual comparison of the output results of two algorithms having similar parameters. b) Result of the proposed algorithm, c) Result of Canny’s algorithm
Fig 14: Visual comparison of the output results of two algorithms having similar parameters. a) Result of the proposed algorithm, b) Result of Canny’s algorithm ig 15: Visual comparison of the output results of two algorithms having similar parameters. b) Result of the proposed algorithm, c) Result of Canny’s algorithm
Fig 16: Visual comparison of the output results of two algorithms having similar parameters. b) Result of the proposed algorithm, c) Result of Canny’s algorithm International Journal of Computer Applications (0975 — 8887) Volume 103 — No.4, October 2014
Fig 16: Visual comparison of the output results of two algorithms having similar parameters. b) Result of the proposed algorithm, c) Result of Canny’s algorithm International Journal of Computer Applications (0975 — 8887) Volume 103 — No.4, October 2014
Fig 17: Visual comparison of the output results of two algorithms having similar paramete b) Result of the proposed algorithm, c) Result of Canny’s algorithm
Fig 17: Visual comparison of the output results of two algorithms having similar paramete b) Result of the proposed algorithm, c) Result of Canny’s algorithm
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