  One of the primary challenges in brain tumor segmentation arises from the
uncertainty of voxels close to tumor boundaries. However, the conventional
process of generating ground truth segmentation masks fails to treat such
uncertainties properly. Those "hard labels" with 0s and 1s conceptually
influenced the majority of prior studies on brain image segmentation. As a
result, tumor segmentation is often solved through voxel classification. In
this work, we instead view this problem as a voxel-level regression, where the
ground truth represents a certainty mapping from any pixel to the border of the
tumor. We propose a novel ground truth label transformation, which is based on
a signed geodesic transform, to capture the uncertainty in brain tumors'
vicinity. We combine this idea with a Focal-like regression L1-loss that
enables effective regression learning in high-dimensional output space by
appropriately weighting voxels according to their difficulty. We thoroughly
conduct an experimental evaluation to validate the components of our proposed
method, compare it to a diverse array of state-of-the-art segmentation models,
and show that it is architecture-agnostic. The code of our method is made
publicly available (\url{https://github.com/Oulu-IMEDS/SiNGR/}).
