# A Prostate MRI Segmentation Tool Based on Active Contour Models Using a Gradient Vector Flow
## 4 Discussion of the Segmentation Method Results
In computer vision and image processing applications, the largest segmentation errors quantified using the Hausdorff Distance can be a good measure of the usefulness of the segmentation for the  
Figure 12: Segmentation results and ground truth for all the algorithms implemented. intended task. Intuitively, \(HD\) is the longest distance one has to travel from a point in one of the two sets to its closest point in the other set. In image segmentation, this metric is computed between boundaries of the estimated and the ground-truth segmentation, which consist of curves in 2D. We computed the Hausdorff distance between the generated segmentation and the ground truth. The methods with the lowest distance are considered to have yielded the best segmentation results. Another popular metric for image segmentation tasks is based on the Dice coefficient, which is essentially a measure of overlapping between two samples and it is equivalent to the F1 score. This measure ranges from 0 to 1, where a Dice coefficient of 1 denotes perfect and complete overlap. This metric is calculated as:  
\[Dice(A,B)=\frac{2\left|A\cap B\right|}{\left|A\cup B\right|} \tag{24}\]  
In Table 1, we summarize the results obtained from the performance analysis for the three segmentation methods, using the two above-mentioned metrics. This procedure has been done for each of the prostate's gland zones, which corresponds to the examples of the annotations depicted on Figure 12. The ground truth is used as a reference image to calculate all the measurements. First, according to the initialization image, a comparison of the results between _Simplified ACS_, _Basic ACS_ and _GVF ACS_ is performed. It can easily be inferred from the table that the _Basic ACS_ yields more accurate segmentation results in all the prostate zones than the _Simplified ACS_. Moreover, it can be seen that the _GVF ACS_ implementation improves the results in all the cases. The geometry of the \(CZ\) zone is considered the most difficult part of the prostate MR image because it is difficult sometimes to demarcate the edges of this area, given that it is surrounded by the other zones; for this reason, it is important to do a good initialization. The results for the \(PZ\) are good in all the cases, especially when GVF is used. Moreover, the results on the \(TZ\) area are good for all the algorithms considered in this study. Finally, the results for the tumor area indicate that the best segmentation is obtained using _GVF ACS_ methods. Finally, in order to assess the performance of the various studied segmentation methods, a time analysis has been performed. As in Table 1, the analysis has been divided by zones and by algorithm. Then, the execution time of the segmentation algorithm has been assessed for each zone, using the same initialization as in Figure 11. For this test, a computer with a microprocessor i7-8650U @ 1.90 GHz, 16 gb of RAM and running Linux 4.15.0-64 has been used. The execution times are depicted in Table 2. All the measurements has been done in milliseconds. Both _Simplified ACS_ and _Basic ACS_ run at maximum 200 iterations, and the _GVF ACS_ runs at maximum 80 iterations. Both Tables 1 and 2 confirm what it has been said about the _Simplified ACS_ algorithm. It is the least accurate, but it runs faster than the other ones. On the other hand, even though the _GVF ACS_ runs less iterations than the _Basic ACS_, their running time are similar. This is due to the _GVF ACS_ algorithm computes the same code, plus the additional ones in order to get the Gradient Vector Flow contribution. Nonetheless, for this work, this execution time could have been reduced if the equations related to the shape prior and the smoothness would have been removed. Only the weights have been set to zero for those priors.