  Fully convolutional deep neural networks carry out excellent potential for
fast and accurate image segmentation. One of the main challenges in training
these networks is data imbalance, which is particularly problematic in medical
imaging applications such as lesion segmentation where the number of lesion
voxels is often much lower than the number of non-lesion voxels. Training with
unbalanced data can lead to predictions that are severely biased towards high
precision but low recall (sensitivity), which is undesired especially in
medical applications where false negatives are much less tolerable than false
positives. Several methods have been proposed to deal with this problem
including balanced sampling, two step training, sample re-weighting, and
similarity loss functions. In this paper, we propose a generalized loss
function based on the Tversky index to address the issue of data imbalance and
achieve much better trade-off between precision and recall in training 3D fully
convolutional deep neural networks. Experimental results in multiple sclerosis
lesion segmentation on magnetic resonance images show improved F2 score, Dice
coefficient, and the area under the precision-recall curve in test data. Based
on these results we suggest Tversky loss function as a generalized framework to
effectively train deep neural networks.
