The domain shift, or acquisition shift in medical imaging, is responsible for potentially harmful differences between development and deployment conditions of medical image analysis techniques. There is a growing need in the community for advanced methods that could mitigate this issue better than conventional approaches. In this paper, we consider configurations in which we can expose a learning-based pixel level adaptor to a large variability of unlabeled images during its training, i.e. sufficient to span the acquisition shift expected during the training or testing of a downstream task model. We leverage the ability of convolutional architectures to efficiently learn domain-agnostic features and train a many-to-one unsupervised mapping between a source collection of heterogeneous images from multiple unknown domains subjected to the acquisition shift and a homogeneous subset of this source set of lower cardinality, potentially constituted of a single image. To this end, we propose a new cycle-free image-to-image architecture based on a combination of three loss functions : a contrastive PatchNCE loss, an adversarial loss and an edge preserving loss allowing for rich domain adaptation to the target image even under strong domain imbalance and low data regimes. Experiments support the interest of the proposed contrastive image adaptation approach for the regularization of downstream deep supervised segmentation and cross-modality synthesis models.