# Why do the authors of this paper down-sample by $ds_1 / 2$ (in the context of coarse-to-fine segmentation)?

This question is a follow-up of this post and based on this paper. In section 2.2, the authors write:

In the first level, the 3D FCN is trained on images of the lowest resolution in order to capture the largest amount of context, downsampled with a factor of $$d s_{1}=2 S$$ and optimized using the Dice loss $$\mathcal{L}_{1} .$$ This can be thought of as a form of deep supervision. In the next level, we use the predicted segmentation maps as a second input channel to the 3D FCN while learning from the images at a higher resolution, downsampled by a factor of $$d s_{2}=d s_{1} / 2$$, and optimized using Dice loss $$\mathcal{L}_{2} .$$

What does it mean by downsampling again by ds2? Shouldn't they upsample prediction by 2 or to the original size of a high-resolution patch?

We usually down-sample by an integer factor, right? Then why fraction $$ds_1 / 2$$?

In my understanding the framework is:

down-sample > train > prediction mask > up-sample > concatenate with high-res

Please explain with image size if possible.