1140 Muhammad Burhan Khan et al.
Table 2. Mean Values of the Segmentation Assessment Metrics (the Best Result are Shown in Bold).
Algorithm Edge
Texture
Watershed Kittler
Accuracy FNR 0.9970
0.9887 0.9967 0.9965
FPR
0.8266 0.6812 0.8868 0.946
0.0006 0.0094 0.0008 0.0007
FNR, false negative ratio; FPR, false positive rate; RI, Rand index.
Table 3. Standard Deviation of the Segmentation Assessment Metrics (the Best Results are Shown in Bold).
Algorithm Edge
Texture
Watershed Kittler
Accuracy FNR 0.0025
0.0334 0.0021 0.0029
FPR
0.2196 0.2602 0.1204 0.1348
0.0015 0.034
0.0014 0.002
FNR, false negative ratio; FPR, false positive rate; RI, Rand index.
Table 1, the algorithms still worked fine for the other images. For example, split-and-merge methods resulted in FNR of 0.5575 for images which could not be segmented by Kittler and watershed-based algorithms. However, the edge-based algorithmgave a better FNR of 0.265, and k-means performed even better by giving an FNR of 0.2198. The performance of the watershed-based segmentation
across the successful segmentations as shown in Table 3. We conclude that if watershed-based algorithm is successful, its accuracy will not deviate significantly from 0.9967. Despite the failure for some images as reflected in
was found to be very sensitive to the preprocessing step of average filtering. In case of failure of the preprocessing, the watershed algorithm results in failed segmentation. When it fails, it detects false objects (flocs and filaments) in addition to the failure to detect the actual object. It failed for 8% of the images used for the assessment as shown in Table 1. For the rest of images, it succeeded with a mean FNR smaller than Kittler’s thresholding-based algorithm, and greater than texture and edge-based algorithms. Although the edge-based algorithm performed the best with respect to accuracy, FPR, and Rand index, the texture-based algorithm performed better in the sense of FNR. Smaller FNR shows increased TP and so, overall better segmentation of the filaments. The decrease in accuracy is caused by increased FP and FPR, which implies over-segmentation of filaments. Contrary to the texture-based algorithm, the other three algorithms resulted in under-segmentation implied by decreased FPR, and increased FNR and accuracy. Therefore, the decision of the best algorithm depends on the choice of extent to which over- or under-segmentation is permitted. We have also compared the textured-based algorithm
(with the best mean result as shown in Table 2 with reference to FNR) with the other three algorithms using a t-test. The resultant p-values are tabulated in Table 4. We have
Table 6. Performance Metrics for the Image and its Segmentation Shown in Figure 12.
Algorithm Edge
Texture
Watershed Kittler
Accuracy FNR 0.9974
1
0.9977 0.9972 0.9974
0.8763 1 1
FPR
3.92 ×10−5 5.97 ×10−6 1.90 ×10−4 0
FNR, false negative ratio; FPR, false positive rate; RI, Rand index.
shown that there is a statistically significant difference between FNR results of the four selected algorithms. Very small one-tailed p-values for the watershed and Kittler algorithms prove the superiority of texture-based algorithm over them. In order to explain the trade-off of under- and over-
segmentation, the best FNR and FPR results were particu- larly observed. Resultant segmentations of the best FPR and FNR are shown in Figures 11 and 12 with the corresponding values of performance metrics in Tables 5 and 6. The best FNR and FPR were achieved by the texture-based algorithm, though the performance metrics for the algorithm have shown appreciable variations compared with other algorithms as shown in Table 3. For the best FNR image, over-segmentation by the texture-based algorithm and under-segmentation by other algorithms can be clearly observed as shown in Figure 11. The texture-based algorithm detected all the filaments with observably small over- segmentation. However, the other algorithms even fail to detect all the filaments, making under-segmentation obser- vably significant. The trend can also be observed in Table 5 by a large FPR for the texture-based algorithm. However, in terms of accuracy, the edge-based segmentation remained the best due to small FP. We can conclude that FP affect the accuracy more significantly than FN. In case of the best FPR image, all the algorithms did under-segmentation as shown
RI
0.9948 0.9955 0.9945 0.9949
RI
0.0051 0.0568 0.0042 0.0058
RI
0.9939 0.9794 0.9933 0.993
Table 4. t-Test for Statistical Difference With Texture-Based Algorithm.
Segmentation algorithm Edge Watershed 0.00286 3.9×10−6
One-tailed p-value Kittler 2.3×10−8
Table 5. Performance Metrics for the Image and its Segmentation Shown in Figure 11.
Algorithm Edge
Texture
Watershed Kittler
Accuracy FNR 0.9963
0.9946 0.9951 0.9946
FPR
0.2650 0.1417 0.8027 1
0.0022 0.0046 0.0006
0.00003 FNR, false negative ratio; FPR, false positive rate; RI, Rand index. RI
0.9927 0.9894 0.9903 0.9892
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