# Estimation of the Prostate Volume from Abdominal Ultrasound Images by Image-Patch Voting
## 4 Experiments and Results
### Data Set and Manual Annotations on AUS and MR Images  
Our data set consisted of 305 AUS patient samples with transverse and sagittal images. Of these samples, 75 also had corresponding MR images from transverse and sagittal planes. Manual annotations of these AUS and MR images were done during medical treatments by several experts. The AUS annotations were used to train and test our system, and MR annotations were used as the gold standard. Of these 305 AUS and 75 MR images, 251 AUS and 73 MR images were annotated by two different experts (exp1 and exp2) at two different marking sessions (mark1 and  
Figure 8: For a given transverse image, (**a**) shows the voting arcs (without thickness); (**b**) shows the detected points (reds are expert marked locations, while greens are the detected locations of the diameter end points); and (**c**) shows the voting maps for \(e_{1},e_{2},e_{3}\), and \(e_{4}\) endpoints. Figure 9: Creation of the voting maps for a given location \(T^{j}(x,y)\) on a transverse image \(T^{j}\). mark2) within our experiments. These annotations were used to obtain intra-expert and inter-expert volume-estimation differences and to compare expert estimations with our system's estimations. We defined functions \(D_{W}(M(T^{j}))\), \(D_{H}(M(T^{j}))\), and \(D_{L}(M(S^{j}))\) as the diameters of the width, the height, and the length of the ellipsoid, respectively. \(M\) represents the measurement by the experts or the computer. \(T^{j}\) represents transverse and \(S^{j}\) represents sagittal images for the patient \(j\). We calculated the Mean Absolute Value Difference (MAVD) between two different measurements \(M_{1}\) and \(M_{2}\) as  
\[MAVD(M_{1},M_{2})=\frac{1}{N}\sum_{j=1}^{N}\Big{|}V_{1}^{j}-V_{2}^{j}\Big{|}, \tag{2}\]  
where  
\[V_{k=1,2}^{j}=V(D_{W}(M_{k}(T^{j})),D_{H}(M_{k}(T^{j})),D_{L}(M_{k}(S^{j})))\]  
and \(V\) is defined in Equation (1). \(N=251\) when both of the measurements are from AUS images, and \(N=73\) when at least one of the measurements is from a MR image. The top eight rows of Table 1 show intra-expert and inter-expert MAVD values of manual prostate-volume-estimations from AUS and MR images. The respective standard deviation values are shown in Table 2. The column and the row headings of the top part are defined as \(IT_{e}^{k}\) and represent the modality or the image type \((IT=AUS,MR)\), the expert ID \((e=exp1,exp2)\), and the annotation session ID \((k=mark1,mark2)\). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \(MEAN\) & \(AUS_{exp1}^{mark1}\) & \(AUS_{exp1}^{mark2}\) & \(AUS_{exp2}^{mark1}\) & \(AUS_{exp2}^{mark2}\) & \(MR_{exp1}^{mark1}\) & \(MR_{exp1}^{mark2}\) & \(MR_{exp2}^{mark1}\) & \(MR_{exp2}^{mark2}\) \\ \hline \(AUS_{exp1}^{mark1}\) & & 3.67 & 5.38 & 8.35 & 6.97 & 6.29 & 5.32 & 5.33 \\ \(AUS_{exp1}^{mark2}\) & 3.67 & & 5.03 & 7.70 & 8.05 & 7.21 & 5.88 & 5.75 \\ \(AUS_{exp2}^{mark1}\) & 5.38 & 5.03 & & 7.56 & 10.51 & 9.68 & 7.49 & 6.73 \\ \(AUS_{exp2}^{mark2}\) & 8.35 & 7.70 & 7.56 & & 10.68 & 9.71 & 6.92 & 6.50 \\ \(MR_{exp1}^{mark1}\) & 6.97 & 8.05 & 10.51 & 10.68 & & 2.63 & 6.01 & 5.92 \\ \(MR_{exp1}^{mark2}\) & 6.29 & 7.21 & 9.68 & 9.71 & 2.63 & & 4.83 & 5.16 \\ \(MR_{exp2}^{mark1}\) & 5.32 & 5.88 & 7.49 & 6.92 & 6.01 & 4.83 & & 2.60 \\ \(MR_{exp2}^{mark2}\) & 5.33 & 5.75 & 6.73 & 6.50 & 5.92 & 5.16 & 2.60 & \\ \hline \(AUS_{QN}\) & 5.70 & 5.05 & 5.46 & 8.12 & 9.15 & 7.88 & 6.51 & 5.25 \\ \(AUS_{BL}\) & 7.46 & 7.12 & 5.98 & 8.90 & 11.17 & 10.07 & 7.36 & 7.09 \\ \hline \end{tabular}
\end{table} 
Table 2: The corresponding SDAVD values of Table 1.