# Shadow Estimation for Ultrasound Images Using Auto-Encoding Structures and Synthetic Shadows
## 5 Discussion  
Among the shadow detecting methods which do not use labels, the proposed method detected shadows the most correctly. The other two methods could suffer from the difference of domains; the domains for which the methods were built and the domain of fetal heart diagnosis that we used in this paper. Besides, the standard deviation of the DICE score for the geometric method was large. This means that its detection performance varies among the testing images. This is probably because the method heavily depends on the domain for which it is designed. In that sense, our method has an advantage because it is data-driven. Although the proposed method also uses domain-specific knowledge, it only requires rough possible shapes of shadows that are determined mainly by the type of the probe. In the situations that the labels are available, the proposed method achieved comparable detection performance to U-Net which is a popular segmentation method for medical images. When only 42 labeled images were used for training, our method was better than U-Net. The auto-encoding structure possibly helped detection by extracting features by the unlabeled data. The maximum number of labeled data, 259 from 30 videos, was relatively small in the context of DNNs, but both the proposed method and U-Net performed well. In terms of detecting shadows, the dataset was clean and in a narrow domain, and it might be easy to detect shadows. From the perspective of data collection, we revealed that a couple of hundred of labeled data is enough for one domain. The amount is reasonable when it comes to accumulating data of different multiple domains.  
One of the advantages of the proposed method is that it can estimate the intensities of shadows. Although we cannot obtain the ground truth of the intensities, our method estimated images of shadows which intensities are highly correlated to the brightness of the shadowed areas of the input images, at least. The correlation coefficients were higher than the other methods we used in the experiments. From the intensities of shadows, we can assess the quality of US images using them. If we detect shadows in a binary segmentation manner, the sizes of shadowed areas can be used for quality inspection. Our method can provide additional information, the intensities of shadows, and we can check US images based on it; an US image with large but light shadows should be allowed in some situations, for example.  
Although removing shadows is not the main target of our work, notably, our method removed shadows of input US images without training on losses that directly lead the decoder to output clean image as \(\hat{c}\). This result could come from the model structure that split the input into the estimated shadow and the estimated clean input and then compose them into the reconstruction. Besides, the estimated clean images were clear, thanks to the U-Net like structure that has skip-connections between the encoder and the decoder [37]. In a clinical sense, we cannot totally trust the estimated shadow-free images because the shadowed areas are completed statistically. It means that the images of popular and healthy cases are likely to appear even if the target of diagnosis has anomalies. However, generating shadow-free images can work as a pre-processing for image recognition techniques.