# Autonomous Prostate Segmentation in 2D B-Mode Ultrasound Images
## 6 Results
To calculate the volume of the prostate for the algorithm \(Vol_{A}\) and clinician contours \(Vol_{C}\), the area of each slice was multiplied by the 5 mm TRUS image slice stepping distance and summed for all of the slices in the image set, such that  
\[Vol_{A}=\sum_{i=0}^{nSlice}\frac{\mathrm{5 mm}*Area_{A}(i)}{1000} \tag{58}\]  
\[Vol_{C}=\sum_{i=0}^{nSlice}\frac{\mathrm{5 mm}*Area_{C}(i)}{1000}\]  
with the factor of 1000 used to scale the output volumes to mL. The calculated prostate volumes, for each of the nine prostates incorporated in the experimental results, are shown in Figure 14. For the results presented in Table 2, the volume difference in mL and % were calculated by  
\[\mathrm{VolumeDifference(mL)}=Vol_{C}-Vol_{A} \tag{59}\]  
Figure 11:0  
where a positive value for the prostate contour volume difference indicates that the algorithm segmented prostate contour was larger than the clinician-segmented contour, and a negative difference indicates that the algorithmic segmented contour was smaller. As an additional metric to evaluate the performance of the prostate contouring algorithm, the Jaccard index was also analyzed. The Jaccard index gives a measure between 0 and 1 that indicates how well the algorithmic output of the prostate contour matches with the clinician-segmented contour, with a value of 1 indicating a perfect match. The Jaccard index is given by  
Figure 11:1  
where \(R(\theta,i|\boldsymbol{\beta}_{A})\) is the output contour of our proposed prostate segmentation algorithm, for a particular TRUS image set, and \(R(\theta,i|\boldsymbol{\beta}_{C})\) is the clinician-segmented contour for the same image set. Figure 15 shows the average Jaccard index score values with respect to the \(z\)-axis depth of the TRUS image, where the first image slice at a depth of 0 mm corresponds to the base of the prostate, the midgland of the prostate is located at 15 mm, and the apex of the prostate is at a depth of 30 mm, as indicated in Figure 11:2  
Figure 11:3 The volume of prostate measured from the algorithm segmented contours compared with clinician-segmented contours for the same prostate image sets. Figure 11:4 Bounding box, indicated in red, and shaded-blue polygon contour area used for prostate contour height, width, and volume measurements. Figure 11:5 Average width and height of the algorithmic and clinician segmented prostate contours, measured in the \({}^{U}x\) and \({}^{U}y\) axes, respectively. Tables 2 and 3 show the resulting values of the metrics, comparing the output contours from our proposed prostate segmentation algorithm (the input parameters used for the superpixel algorithm for the results given in Table 2 were \(\lambda_{\mu}=100\), \(\lambda_{L2}=125\), \(\lambda_{KS}=0.2\), \(s_{grid}=256\) px, \(r_{darea}=512\) px, \(r_{min}=256\) px, \(c_{min}=192\) px, \(c_{max}=4\), and the parameters for the graph-cut segmentation were \(\lambda_{DP}=3.1\), \(\lambda_{DL}=1.8\), \(\mu_{l}=40\), \(\lambda_{S}=1.5\)) for nine patient TRUS image sets, where each image set consisted  
The average mean absolute difference (average MAD) for all of the trials was 2.52 (\(\pm\)1.66) mm and the average maximum absolute difference (average MaxD) was 7.19 (\(\pm\)1.22) mm. For context, using values reported by [9], we will discuss these results with respect to three semi-autonomous 3D prostate TRUS segmentation algorithms within the literature [14; 26; 27] that are the most comparable to our proposed method. The active contour model algorithm proposed by [14] reported an MAD of 7.01 \(\pm\) 1.04 mm and an MaxD of 1.09 \(\pm\) 0.49 mm. The active-shape-model-based contouring algorithm of [26] provided an MAD of 7.27 \(\pm\) 2.32 mm and an MaxD of 1.26 \(\pm\) 0.41 mm. The hybrid active contour/active shape model system developed in [27] had an MaxD of 4.06 \(\pm\) 1.25. While the mean absolute difference of our algorithm is slightly larger than comparable results presented in the literature, the maximum absolute difference is in line with those reported in the literature.