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We propose a client-server system which allows for the analysis of multi-centric medical images while preserving patient identity. In our approach, the client protects the patient identity by applying a pseudo-random non-linear deformation to the input image. This results into a proxy image which is sent to the server for processing. The server then returns back the deformed processed image which the client reverts to a canonical form. Our system has three components: 1) a flow-field generator which produces a pseudo-random deformation function, 2) a Siamese discriminator that learns the patient identity from the processed image, 3) a medical image processing network that analyzes the content of the proxy images. The system is trained end-to-end in an adversarial manner. By fooling the discriminator, the flow-field generator learns to produce a bi-directional non-linear deformation which allows to remove and recover the identity of the subject from both the input image and output result. After end-to-end training, the flow-field generator is deployed on the client side and the segmentation network is deployed on the server side. The proposed method is validated on the task of MRI brain segmentation using images from two different datasets. Results show that the segmentation accuracy of our method is similar to a system trained on non-encoded images, while considerably reducing the ability to recover subject identity.