# Shadow Estimation for Ultrasound Images Using Auto-Encoding Structures and Synthetic Shadows
## 6 Conclusions  
We proposed an auto-encoding structure-based DNN that estimates acoustic shadows in US images. The method estimates not only the location of shadows but also their intensities. We also introduced the loss functions for training the model on both unlabeled data and labeled data. For unlabeled data, synthetic shadows are generated using the knowledge that the probes decide the shapes of shadows, and used as pseudo labels. If binary pixel-level labels that tell us areas with shadows are given, they are effectively utilized by converting them to labels with estimated intensities. By experiments on US images for fetal heart diagnosis, we showed that our method detected shadows better than the conventional methods in the situation without labels and did better to the DNN-based segmentation method U-Net in the situations with labels available. In terms of estimating the intensities of shadows, the proposed method performed the best. Moreover,we suggested the capability of our method in removing shadows as supplemental outputs, not just estimating them.  
Although our method employs the auto-encoding structure that extracts features from input images, the difference in detection performance between fully-supervised U-Net and semi-supervised our method was small. One possible reason for this result is that the detection was easy; the images in the dataset were relatively clear and belonged to the narrow domain. Applying to datasets that are in different domains or have more variations of images has remained as one of the future work.  
The proposed method can work with any US image recognition methods as a pre-processing. We can reject low-quality data based on the estimated shadow images. The use in such quality assessing ways is one of the possible future directions.  
Conceptualization, S.Y., T.A., R.M., and A.S. ([PERSON]); methodology, S.Y., A.S. ([PERSON]); software, S.Y.; validation, S.Y.; formal analysis, S.Y., T.A., and R.M.; investigation, S.Y., T.A., and R.M.; resources, T.A., R.M., R.K., and A.S. ([PERSON]); data curation, S.Y., T.A., and R.M.; writing--original draft preparation, S.Y., T.A., and R.M.; writing--review and editing, A.S. ([PERSON]), R.K., K.S., A.D., H.M., K.A., S.K., A.S. ([PERSON]), R.H., and M.K.; visualization, S.Y.; supervision, R.H. and M.K.; project administration, S.Y., T.A., and R.M. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the subsidy for Advanced Integrated Intelligence Platform (MEXT), and the commissioned projects income for RIKEN AIP-FUIITSU Collaboration Center.  
The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Institutional Review Board of RIKEN, Fujitsu Ltd., Showa University, and the National Cancer Center (approval ID: Wako1 29-4).  
This research protocol was approved by the medical ethics committees of the four collaborating research facilities, and data collection was conducted in an opt-out manner.  
Data Availability Statement: Data sharing is not applicable owing to the patient privacy rights.  
The authors wish to acknowledge [PERSON] and [PERSON] for great supports, the medical doctors in the Showa University Hospitals for data collection.  
R.H. has received the joint research grant from Fujitsu Ltd. The other authors declare no conflict of interest.