  We introduce a deep learning image segmentation framework that is extremely
robust to missing imaging modalities. Instead of attempting to impute or
synthesize missing data, the proposed approach learns, for each modality, an
embedding of the input image into a single latent vector space for which
arithmetic operations (such as taking the mean) are well defined. Points in
that space, which are averaged over modalities available at inference time, can
then be further processed to yield the desired segmentation. As such, any
combinatorial subset of available modalities can be provided as input, without
having to learn a combinatorial number of imputation models. Evaluated on two
neurological MRI datasets (brain tumors and MS lesions), the approach yields
state-of-the-art segmentation results when provided with all modalities;
moreover, its performance degrades remarkably gracefully when modalities are
removed, significantly more so than alternative mean-filling or other synthesis
approaches.
