  Annotating lots of 3D medical images for training segmentation models is
time-consuming. The goal of weakly supervised semantic segmentation is to train
segmentation models without using any ground truth segmentation masks. Our work
addresses the case where only image-level categorical labels, indicating the
presence or absence of a particular region of interest (such as tumours or
lesions), are available. Most existing methods rely on class activation mapping
(CAM). We propose a novel approach, ToNNO, which is based on the Tomographic
reconstruction of a Neural Network's Output. Our technique extracts stacks of
slices with different angles from the input 3D volume, feeds these slices to a
2D encoder, and applies the inverse Radon transform in order to reconstruct a
3D heatmap of the encoder's predictions. This generic method allows to perform
dense prediction tasks on 3D volumes using any 2D image encoder. We apply it to
weakly supervised medical image segmentation by training the 2D encoder to
output high values for slices containing the regions of interest. We test it on
four large scale medical image datasets and outperform 2D CAM methods. We then
extend ToNNO by combining tomographic reconstruction with CAM methods,
proposing Averaged CAM and Tomographic CAM, which obtain even better results.
