Projected pooling loss for red nucleus segmentation with soft topology constraints

Deep learning is the standard for medical image segmentation. However, it may encounter difficulties when the training set is small. Also, it may generate anatomically aberrant segmentations. Anatomical knowledge can be potentially useful as a constraint in deep learning segmentation methods. We propose a loss function based on projected pooling to introduce soft topological constraints. Our main application is the segmentation of the red nucleus from quantitative susceptibility mapping (QSM) which is of interest in parkinsonian syndromes.

This new loss function introduces soft constraints on the topology by magnifying small parts of the structure to segment to avoid that they are discarded in the segmentation process. To that purpose, we use projection of the structure onto the three planes and then use a series of MaxPooling operations with increasing kernel sizes. These operations are performed both for the ground truth and the prediction and the difference is computed to obtain the loss function. As a result, it can reduce topological errors as well as defects in the structure boundary. The approach is easy to implement and computationally efficient.

When applied to the segmentation of the red nucleus from QSM data, the approach led to a very high accuracy (Dice 89.9%) and no topological errors. Moreover, the proposed loss function improved the Dice accuracy over the baseline when the training set was small. We also studied three tasks from the medical segmentation decathlon challenge (MSD) (heart, spleen, and hippocampus). For the MSD tasks, the Dice accuracies were similar for both approaches but the topological errors were reduced.

We propose an effective method to automatically segment the red nucleus which is based on a new loss for introducing topology constraints in deep learning segmentation.