## 3 Computational Methods
### U-Net Extensions  
Quite a few studies have substantiated that detecting ovaries is a much more difficult problem than detecting follicles in ultrasound images/volumes [5]. This is reflected in the much greater inter-rater variability of ovary annotations in respect to the variability of follicle annotations in the USOVA3D database [7]. Through experimentation, we found that training an independent U-Net network either to predict solely ovaries, or jointly, to predict ovaries and follicles, resulted in poorly detected ovaries and in a lower precision metric if follicles were detected as well. On the other hand, training the U-Net for follicle detection only improved results (i.e., recognition rate and accuracy).  
It is known from the anatomy that the follicles are always located inside the ovary. In this work, we aim to exploit this relationship and the follicle segmentation results to improve the ovary segmentation. We developed a two-stage architecture for follicle and ovary detection. Follicles are detected in the first stage, and the prior knowledge of the ovary-follicles relationship is utilised in the second stage. The idea is similar to the 3D DWT baseline function [7], except that this baseline function did not perform well when detecting ovaries.  
We have implemented two different extensions of the U-Net architecture to exploit the ovary-follicles relationship. Both CNNs consist of one base U-Net network trained to detect follicles. The extension is then applied to this network to predict ovary segments.  
The first extension, EXT 1, shown in Figure 4, brings in a full additional U-Net network. The implementation is trivial and straightforward. An output of the first network, i.e., a segmentation map for follicles, is concatenated with the input volume and passed to the second U-Net network. By providing the segmentation maps of follicles we submit seeding information about potential ovary location to the second network. Such information focuses the second U-Net on the important parts of the input volume.  
The second extension, EXT 2, not only utilises the segmentation of follicles, but also exploits the extracted features used to predict such segmentation. The EXT 2 extension is depicted in Figure 5. The predictive features at each level of the base U-Net are passed to the same level of the second network aimed for detecting the ovaries. These features have already gone through the encoders of the base U-Net. However, these features have been optimised for the follicle detection. In order to adapt them for ovary detection, we introduced additional convolution blocks at the lowest layer, and additional decoders on the higher levels of the second CNN.  
Additional outputs are added to both extensions, as shown in grey in Figures 4 and 5 when training with Deep Supervision.  
Figure 4: Example of the first proposed U-Net extension, EXT 1—two consecutive U-Nets: The segmentation map of the first stage is concatenated with the input and passed as the input to the second stage. The first stage detects follicles, while the second stage identifies the ovary. Deep Supervision outputs are shown in a grey box.