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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.

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