4.3.1 Seed Point Extraction
To investigate the most efficient technique to perform the task of seed point extraction four meth-ods were compared: Sliding Band Filter (SBF), Distance Transform (DT), Ultimate Erosion for Convex Sets (UECS), and Fast Radial Symmetry (FRS).
Figure 18 demonstrates the result of seed point extraction applied to synthetic data of 50% maxi-mum overlap. Among all the methods, it can be seen that FRS outperforms other methods, while DT and UECS goes through under-segmentation, and SBF suffers from over-segmentation.
The overall quantitative results for each of the competing seed extraction methods applied to the synthetic and the real datasets are presented in Tables 1 and 2 respectively. In particular, TPR, PPV, and the pixel-wise Average Distance (AD) of the detected seed points to ground truth centroids were used as performance measures. The segmentation results obtained from the synthetic datasets (see Table 1) show that both FRS and SBF methods generally achieve better performance scores compared to DT and UECS. While, in terms of TPR and PPV scores both FRS and SBF methods are comparable; in terms of AD, FRS outperforms SBF.
(a) (b)
(c) (d) (e)
Figure 18. An example of synthetic image of 50% maximum overlap marked by the ground truth seed points and the seed points obtained from the competing methods. The encoding are as follows : (a) Ground truth seed points; (b) Fast Radial Symmetry (FRS); (c) Slide Band Filter (SBF); (d) Distance Transform (DT); (e) Ultimate Erosion for Convex Sets (UECS).
Table 1.The performance of the four seed point extraction methods with synthetic datasets.
Method Overlap Rate [%] TPR [%] PPV[%] AD[pixel]
FRS 40 98 99 1.90
SBF 40 99 99 2.93
DT 40 81 99 2.12
UECS 40 55 95 4.41
FRS 50 96 99.2 2.10
SBF 50 96 99 3.05
DT 50 73 99 2.43
UECS 50 55 94 4.58
FRS 60 93 99 2.44
SBF 60 94 99 3.31
DT 60 71 98 2.77
UECS 60 51 95 4.81
The results in Table 2 reflect the advantage of FRS applied to real dataset, over all other methods.
While the listed TPR and PPV values in the table indicate its higher accuracy, the lower AD reveals its performance in terms of seed point quality. Note that the FRS performs better than SBF in the case of the real dataset; it is more robust when the object shapes are less convex.
Table 2.The performance of the four seed point extraction methods with real dataset.
Method TPR [%] PPV [%] AD [pixel]
FRS 88 93 4.83
SBF 75 89 7.77
DT 45 98 5.1
UECS 42 97 6.26
4.3.2 Contour Evidence Extraction
In order to evaluate the strength and the performance of the edge-to-marker association method described in Section 3.3.1 for extracting contour evidence, it was coupled and applied with the ground truth and FRS seed points. The objective here was two-fold: to validate the edge-to-marker association for extracting contour evidence and to evaluate its performance when applied with estimated seed points.
Table 3 presents the corresponding results for synthetic and real dataset. Each row entry in the tables corresponds to the dataset and the columns represent the percentage of the correctly identified contour evidence with a distinct divergence weight factor λ, which is calculated by comparing the ground truth contour points with the estimated ones.
The second column of the table shows the percentage of contour evidence successfully extracted by edge-to-marker association along with object centroids as seed points. On average, around 93% and 82% of contour samples were retrieved in the case of the synthetic and real dataset respectively, confirming the validity of the edge-to-marker model for extraction of contour evi-dences.
The third and fourth columns represent the edge-to-marker results of the FRS estimated seed points and evaluate the effect of divergence condition on the performance of contour evidence estimation. It can be seen that more accurate results were achieved when no diverging condition was considered. Meanwhile, the percentage of extracted contour evidence was slightly lower as the result of inherent error in the number and the location of the estimated seed points. Overall, the detected seed points can be reliably applied to the contour inference.
Table 3.The performance of the edge-to-marker association with ground truth and the FRS seed points is quantified by the percentage of correctly identified edge points.
Dataset / Overlap Rate
Correct Matched [%]
GT FRS FRS
(λ= 0) (λ= 0) (λ= 0.03)
Synthetic - 40 93.05 90.61 83.27
Synthetic - 50 93.31 89.83 82.81
Synthetic - 60 92.81 86.98 80.28
Real 81.96 75.08 65.86
Table 4 demonstrates the results of the CBCS algorithm being applied to the contour evidence estimation. It should be noted that the indicated values are the percent of correct matches for dominant contour points and can not be compared to the edge-to-marker association results.
4.3.3 Contour Estimation
Following similar procedures employed in Section 4.3.2, contour estimation, ellipse fitting, was performed by means of the ground truth (GT) and the segmented contour evidence (SCE). It
Table 4.The performance of CBCS for contour evidence extraction applied to synthetic and real datasets.
The evaluation results are quantified by the percentage of correctly identified dominant points.
Method Dataset / Overlap Rate [%] Correct Matched [%]
CBCS Synthetic - 40 94.74
CBCS Synthetic - 50 92.97
CBCS Synthetic - 60 90.66
CBCS Real 88.86
should be recalled that segmented contour evidence was obtained by edge-to-marker association with FRS seed points and the numerically stable direct ellipse fitting [62] were chosen for the experiments. The corresponding performance statistics are shown in Table 5. In the case of the synthetic dataset , approximately all the contours of elliptical objects were retrieved correctly, as the shape of the objects under segmentation were prefect ellipses. The results from the segmented contours shows a decrease in the performance.
Table 5. The performance of contour estimation with the ground truth and the segmented contour evi-dence.
Dataset and Overlapping [%] TPR [%] PPV [%] JSC [%]
GT SCE GT SCE GT SCE
Synthetic - 40 100 92 100 95 99 88
Synthetic - 50 99 88 99 92 98 81
Synthetic - 60 98 81 98 86 97 71
Real 94 76 99 89 94 70