Chapter 4 Experimental Results
4.3 Comparison with Other Color Edge Detector
4.3.1 Quantitative Evaluation in Synthetic Color Images
sensitive result within three thresholding methods in comparison, but it also detect more noise. The Yitzhaky and Peli method performs most rigorously and miss some edges that really exist in the image. In comparison, our thresholding method not only detects more true edges than the Yitzhaky and Peli method but also be less noisy than the Medina et al. method.
4.3 Comparison with Other Color Edge Detector
4.3.1 Quantitative Evaluation in Synthetic Color Images
Canny [1] presented the very popular aspects that good edge detection must not miss the true edge nor detect non-edge points as the edge points and produce thin and continuous lines. For these criteria, we also use the eleven 128×128 and eleven 256×256 synthetic color images for quantitative evaluation of the color edge detectors.
The performances of our automatic color edge detection techniques are compared to those by the compass operator of Ruzon and Tomasi [7], Canny edge detector [1], RCMG detector [9], and MVD edge detector [4].
Fig. 4.12 show the edge detection results of 128×128 synthetic images for comparison. For the Fig. 4.12(b), using the parameterσ =0.94, the figure is obtained by subjectively adjust the hysteresis thresholds for the compass operator with nonmaximal suppression (NMS). In contrast with Fig. 4.12(b), Fig. 4.12(c) shows the result that we adopted the Medina et al. thresolding method for the compass operator with NMS. We can see that both the result in Figs. 4.12(b) and (c) detect much noise in the regions near the corners. Setting the parameters to k =2 and l =4, the problem in Fig. 4.12(d), which is obtained by MVD detector, is that it has thicker
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(b) (c)
(d) (e)
(f) (g)
(h)
Fig. 4.12. Edge detection results of the 128×128 synthetic image Sample 1 detected by different color edge detectors. (a) Original image. (b) Compass result, (c) The compass operator with NMS and thresholding by Medina et al. method. (d) MVD result. (e) MVD with thinning process and thresholding by Medina et al. method. (f) Color Canny result. (g) RCMG with thinning process and thresholding by Medina et al. method. (h) Our automatic color edge detector.
responses for every edge point. Therefore, the thinning process is applied to MVD detector, and we also use the Medina et al. method for the edge detection and shown as Fig. 4.12(e). To apply Canny detector to color images, a method named Color Canny individually use Canny detector to detect edges for three dimensions in the color space, and determine the edge result by the majority vote fusion rule. In the edge result detected by Color Canny detector, which is shown in Fig. 4.12(f), the continuity of the edges perform worse than the others, especially in the corners. Fig.
4.12(g) shows the result detected by RCMG with the parameter s =1 in the 3×3 window . Fig. 4.12(h) shows the result with our method, and it detects less noise and produce continuous lines for edge detection. More results are shown in Figs.
4.13−4.15. In Fig. 4.13(c), some ideal edges are missed by the compass operator thresholding by Medina et al. method.
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(b) (c)
(d) (e)
(f) (g)
(h)
Fig. 4.13. Edge detection results of the 128×128 synthetic image Sample 2 detected by different color edge detectors. (a) Original image. (b) Compass result, (c) The compass operator with NMS and thresholding by Medina et al. method. (d) MVD result. (e) MVD with thinning process and thresholding by Medina et al. method. (f) Color Canny result. (g) RCMG with thinning process and thresholding by Medina et al. method. (h) Our automatic color edge detector.
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(b) (c)
(d) (e)
(f) (g)
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Fig. 4.14. Edge detection results of the 256×256 synthetic image Sample 3 detected by different color edge detectors. (a) Original image. (b) Compass result, (c) The compass operator with NMS and thresholding by Medina et al. method. (d) MVD result. (e) MVD with thinning process and thresholding by Medina et al. method. (f) Color Canny result. (g) RCMG with thinning process and thresholding by Medina et al. method. (h) Our automatic color edge detector.
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(b) (c)
(d) (e)
(f) (g)
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Fig. 4.15. Edge detection results of the 256×256 synthetic image Sample 4 detected by different color edge detectors. (a) Original image. (b) Compass result, (c) The compass operator with NMS and thresholding by Medina et al. method. (d) MVD result. (e) MVD with thinning process and thresholding by Medina et al. method. (f) Color Canny result. (g) RCMG with thinning process and thresholding by Medina et al. method. (h) Our automatic color edge detector.
Tables 4.4, 4.5 and 4.6 show the average performances of the eleven 128×128, 256×256 synthetic images and the total images for the compared detector. The order
of the column 1 are the compass operator with NMS, the compass operator with NMS and Medina et al. method, MVD detector, MVD detector with thinning process and Medina et al. method, Color Canny detector, RCMG detector with thinning process and Medina et al. method, and our automatic color edge detector. The column 2 to column 5 represents the quantitative evaluations of FOM, TPR, TNR, and NACC in percentage, respectively. For the criteria, a detector, which can detect less erroneous, thin, and continuous edges, will get high values of the FOM and NACC.
TABLE 4.4
The average evaluation results of the eleven 128×128 synthetic color images detected by the following detectors
Method FOM (%) TPR (%) TNR (%) NACC (%) Compass with NMS with
manual thresholding 99.484 96.87 99.87 98.374 Compass with NMS and
Medina et al. method 98.845 96.80 99.93 98.374
MVD with manual
thresholding 93.866 63.18 100.00 81.597
MVD with thinning and
Medina et al. method 99.681 98.10 99.91 99.012 Color Canny with manual
thresholding 83.797 70.65 97.47 84.066
RCMG with thinning and
Medina et al. method 99.493 98.11 99.87 98.993
Our method 99.542 99.98 99.96 99.971
TABLE 4.5
The average evaluation results of the eleven 256×256 synthetic color images detected by the following detectors
The average evaluation results of the total synthetic color images detected by the following detectors
A noisy edge map may be high performance in the FOM evaluation due to the FOM only considers the accuracy of edge points and uses a scaling constant α for the penalty between smeared and offset edges. In other hand, the NACC calculates not only the accuracy of edge points but also the accuracy of non-edge points and rigorously forbids the deviation between ideal and detected edge (non-edge) points.
Thus, although both MVD and RCMG with thinning and Medina et al. method are better than our method for the FOM evaluation, TPR and TNR shows the fact that they produce more smeared edge points and misses more ideal edge points than our method. Indeed, the NACC evaluation supply more reliable results by using the TPR and TNR, and our method is the best one in the NACC evaluation.
4.3.2 Comparison in Nature Color Images
In this section, we will compare our method in nature color images with other detectors mentioned above. Unlike the synthetic images, we can not use the FOM evaluation or ROC analysis to provide the absolute quality measures when GT images in real world images are both difficultly and subjectively chosen, but we can provide the information for relatively robustness and reliability.
Figs. 4.16 and 4.17 show the edge detection results of the Peppers and Lena image. We also use the parameter σ =0.94 for the compass operator, k =2 and
thigh , are chosen subjectively for the compass operator with NMS, and the very noisy edge result for thresholding by Medina et al. method is shown as Fig. 4.16(c).
Both MVD result, where thresholding by hysteresis threshold tlow =15 and
=30
thigh shown as Fig. 4.16(d) and thresholding by Medina et al. method with
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(b) (c)
(d) (e)
(f) (g)
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Fig. 4.16. Edge detection results of the Peppers image detected by different color edge detectors. (a) Original image. (b) Compass result, (c) The compass operator with NMS and thresholding by Medina et al. method. (d) MVD result. (e) MVD with thinning process and thresholding by Medina et al. method. (f) Color Canny result. (g) RCMG with thinning process and thresholding by Medina et al. method. (h) Our automatic color edge detector.
thinning process shown as Fig 4.16(e), detect more true edges but less noise although they provide the very thick responses. Figs. 4.16(f)−(h) show the result of Color Canny, RCMG and our method. Color Canny and our method not only provide
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Fig. 4.17. Edge detection results of the Lena image detected by different color edge detectors. (a) Original image. (b) Compass result, (c) The compass operator with NMS and thresholding by Medina et al. method. (d) MVD result. (e) MVD with thinning process and thresholding by Medina et al. method. (f) Color Canny result. (g) RCMG with thinning process and thresholding by Medina et al. method. (h) Our automatic color edge detector.
Thinner and less noisy edges but also catch the boundaries such as the three marked black ellipse regions that are difficult to distinguish.
Another experiment for compared results is shown as Fig. 4.17. We are
interesting in comparing the marked rectangle regions. Figs. 4.17(c) and (e) detect more edge in these regions, but they also provide too much noise. In the left rectangle region, the compass operator shown as Fig. 4.17(b) produces stronger response for edge detection, but in the regions of the middle and right rectangles, the results of Figs. 4.17(f) and (h) detected by color Canny and our method are better than the compass operator.
Chapter 5 Conclusion
In this thesis, we have proposed to apply vector order statistics and fuzzy gradient to our automatic color edge detection. By using the fuzzy derivative estimation, the fuzzy rules are fired to consider the gradient direction of every processing pixel. Additionally, the shape of the membership function is adapted to the local variation around the processing pixel. Therefore, the proposed detector improve the drawbacks of the original VMD detector due to the gradient directions are exactly estimated, and our thresholding method choose an reasonable parameter set from all possible values and find the best hysteresis threshold set within it.
Experimental results have shown that our automatic color edge detection techniques produce excellent edge detection accuracy in the synthetic and nature images. In this way, the performances of higher level image processing tasks such as segmentation and object recognition can be improved because of the improvement of edge detection result.
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