Quantitative Evaluation in Synthetic Color Images

Canny [3] 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 two kinds of 256×256 synthetic color images which are shown in Figs. 4.5(a)(b) 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 [9], Canny edge detector [3], RCMG detector [11], and MVD edge detector [6].

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Fig. 4.5 (a) One kind of original image. (b) One kind of original image.

Fig. 4.6 show the edge detection results of 256×256 synthetic images which is Fig. 4.5(a) for comparison. For the Fig. 4.6(b), using the parameter 0.94, adjust the Medina et al. thresolding method for the compass operator with NMS. We can see that the result in Figs. 4.6(b) detect much noise in the regions near the corners. For MVD detector, we use the parameter k 2, l 4, and thresholding by Medina et al.

method with thinning process as shown in Fig 4.6(c). 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.

4.6(d), the continuity of the edges performs worse than the others, especially in the corners. Fig. 4.8(e) shows the result detected by RCMG with the parameter s1 in the 3 3 window. Fig. 4.6(f) shows the result with our method, and it detects less noise and produce continuous lines for edge detection. More results are shown in Figs.

4.74.9. In Fig. 4.7(b) and Fig. 4.9(b), some ideal edges are missed by the compass operator thresholding by Medina et al. method.

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Fig. 4.6 Edge detection results of the 256×256 synthetic image Sample 1 detected by different color edge detectors. (a) Original image. (b) The compass operator with NMS and thresholding by Medina et al. method. (c) MVD with thinning process and thresholding by Medina et al. method. (d) Color Canny result. (e) RCMG with thinning process and thresholding by Medina et al. method. (f) Our automatic color edge detector.

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Fig. 4.7 Edge detection results of the 256×256 synthetic image Sample 2 detected by different color edge detectors. (a) Original image. (b) The compass operator with NMS and thresholding by Medina et al. method. (c) MVD with thinning process and thresholding by Medina et al. method. (d) Color Canny result. (e) RCMG with thinning process and thresholding by Medina et al. method. (f) Our automatic color edge detector.

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Fig. 4.8 Edge detection results of the 256×256 synthetic image Sample 3 detected by different color edge detectors. (a) Original image. (b) The compass operator with NMS and thresholding by Medina et al. method. (c) MVD with thinning process and thresholding by Medina et al. method. (d) Color Canny result. (e) RCMG with thinning process and thresholding by Medina et al. method. (f) Our automatic color edge detector.

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Fig. 4.9 Edge detection results of the 256×256 synthetic image Sample 4 detected by different color edge detectors. (a) Original image. (b) The compass operator with NMS and thresholding by Medina et al. method. (c) MVD with thinning process and thresholding by Medina et al. method. (d) Color Canny result. (e) RCMG with thinning process and thresholding by Medina et al. method. (f) Our automatic color edge detector.

(A) Quantitative Performance Comparison

Tables 4.2, 4.3 and 4.4 show the average performances of the thirteen 256×256, eleven 256×256 synthetic images, and the total images for the compared detector. The order of the column 1 are the compass operator with NMS and Medina et al. method, 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 4.2

The average evaluation results of the thirteen 256×256 synthetic color images detected by the following detectors

Method FOM (%) TPR (%) TNR (%) NACC (%) Compass with NMS and

Medina et al. method 98.14⁴ 92.99 99.87 96.43₄ MVD with thinning and

Medina et al. method 99.70² 98.54 99.91 99.22₃ Color Canny with manual

thresholding 86.56⁵ 68.48 98.29 83.36₅ RCMG with thinning and

Medina et al. method 99.79¹ 98.98 99.94 99.46₂ Our method 99.25₃ 99.91 99.95 99.93₁

TABLE 4.3

The average evaluation results of the eleven 256×256 synthetic color images detected by the following detectors

Method FOM (%) TPR (%) TNR (%) NACC (%) Compass with NMS and

Medina et al. method 96.33⁴ 99.64 99.62 99.63₂ MVD with thinning and

Medina et al. method 99.61² 97.65 99.93 98.79₄ Color Canny with manual

thresholding 88.82⁵ 96.29 99.10 97.70₅ RCMG with thinning and

Medina et al. method 99.65¹ 97.92 99.91 98.92₃ Our method 98.363 99.73 99.82 99.78₁

TABLE 4.4

The average evaluation results of the total synthetic color images detected by the following detectors

Method FOM (%) TPR (%) TNR (%) NACC (%) Compass with NMS and

Medina et al. method 97.24⁴ 96.31 99.74 98.03₄ MVD with thinning and

Medina et al. method 99.66² 98.10 99.92 99.01₃ Color Canny with manual

thresholding 87.69⁵ 82.39 98.70 90.53₅ RCMG with thinning and

Medina et al. method 99.72¹ 98.45 99.93 99.19₂ Our method 98.81₃ 99.82 99.89 99.85₁

A noisy edge map may be good performance in the FOM evaluation because of 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 strictly forbids the deviation between ideal and detected edge (non-edge) points.

Therefore, 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.