# Shadow Estimation for Ultrasound Images Using Auto-Encoding Structures and Synthetic Shadows
## 4 Results
### Shadow Detection  
We evaluated the proposed method as a shadow detection method. In situations with labels, we investigated the performance on different numbers of labeled data. The numbers of labeled training data were set to 0, 42 (from 5 videos), 90 (from 10 videos), 177 (from 20 videos), and 259 (from all 30 videos). Since the proposed method estimates intensities of shadows as \(\hat{s}\), a threshold to convert \(\hat{s}\) to binary was searched using the validation dataset. The threshold is selected from \(\{0.001,0.002,\ldots,0.999\}\). For the random walk method [20] which estimates confidence maps, we also searched and applied a threshold in the same way as the proposed method. The selected thresholds are shown in Appendix C. The detection performance was evaluated by the DICE score [35] which is also known as F1 measure. Table 1 shows the results in the DICE score. Figures 2 and 3 shows examples of shadow detection of the methods that do not use labels and the methods that use labels, respectively (for additional results, see Figures A2 and A3). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \multicolumn{5}{c}{**Number of Labeled Images**} \\ \hline
**Method** & **0** & **42 (5 Videos)** & **90 (10 Videos)** & **177 (20 Videos)** & **259 (30 Videos)** \\ \hline Geometric method [19] & \begin{tabular}{c} 0.193 \\ (\(\pm\)0.210) \\ \end{tabular} & - & - & - & - \\ Random walk [20] & \begin{tabular}{c} 0.450 \\ (\(\pm\)0.142) \\ \end{tabular} & - & - & - & - \\ U-Net [30] & - & 0.610 & 0.655 & 0.681 & 0.698 \\  & \begin{tabular}{c} (\(\pm\)0.184) \\ \end{tabular} & \begin{tabular}{c} (\(\pm\)0.170) \\ \end{tabular} & \begin{tabular}{c} (\(\pm\)0.136) \\ \end{tabular} & \begin{tabular}{c} (\(\pm\)0.137) \\ \end{tabular} \\ Ours & \begin{tabular}{c} 0.578 \\ (\(\pm\)0.164) \\ \end{tabular} & \begin{tabular}{c} 0.666 \\ (\(\pm\)0.142) \\ \end{tabular} & \begin{tabular}{c} 0.686 \\ (\(\pm\)0.148) \\ \end{tabular} & \
\begin{tabular}{c} 0.707 \\ (\(\pm\)0.113) \\ \end{tabular} &
\begin{tabular}{c} 0.720 \\ (\(\pm\)0.151) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of shadow detection evaluated in the DICE score. The scores are calculated for each testing image, and means over them are shown. The numbers in parentheses are the standard deviations. Figure 2: Examples of shadow detection results for the methods that do not use labels. The lower side of each example shows detection results, and the upper side shows them overlayed to the input image. For overlayed images, blue corresponds to low intensities and red corresponds to high intensities. Figure 3: Examples of shadow detection results for the methods that use labels. The lower side of each example shows detection results, and the upper side shows them overlayed to the input image. For overlayed images, blue corresponds to low intensities and red corresponds to high intensities. In the unlabeled situation, we can see that the proposed method outperformed the other two methods from Table 1. The standard deviation was large for the geometric method. The score of the geometric method is low but Figure 2 shows that performed well in some examples. The random walk method scored better than that of the geometric method and detected shadows that the geometric method could not. However, the outputs of the random walk method tended to simply reflect the distance from the probe. The proposed method estimated the shapes of the shadows well although the estimation results tend to be blurred. Figure 2 also indicates that the proposed method successfully estimated the intensities of the shadows. In terms of the methods that use labeled data, that is, U-Net and the proposed method in semi-supervised situations, the proposed method performed slightly better than U-Net as Table 1 shows. We could see no clear trends for the standard deviations. The differences in the DICE score were larger when the numbers of labeled data were smaller. Figure 3 shows that the two methods detected shadows in almost the same performance.