Cross-modality image synthesis is an active research topic with multiple medical clinically relevant applications. Recently, methods allowing training with paired but misaligned data have started to emerge. However, no robust and well-performing methods applicable to a wide range of real world data sets exist. In this work, we propose a generic solution to the problem of cross-modality image synthesis with paired but non-aligned data by introducing new deformation equivariance encouraging loss functions. The method consists of joint training of an image synthesis network together with separate registration networks and allows adversarial training conditioned on the input even with misaligned data. The work lowers the bar for new clinical applications by allowing effortless training of cross-modality image synthesis networks for more difficult data sets.

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